UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

NMRON studies of insulating magnetic materials Le Gros, Mark 1990

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1990_A1 L44.pdf [ 6.99MB ]
Metadata
JSON: 831-1.0084990.json
JSON-LD: 831-1.0084990-ld.json
RDF/XML (Pretty): 831-1.0084990-rdf.xml
RDF/JSON: 831-1.0084990-rdf.json
Turtle: 831-1.0084990-turtle.txt
N-Triples: 831-1.0084990-rdf-ntriples.txt
Original Record: 831-1.0084990-source.json
Full Text
831-1.0084990-fulltext.txt
Citation
831-1.0084990.ris

Full Text

NMRON STUDIES OF INSULATING MAGNETIC MATERIALS By Mark Le Gros B.Sc.Massey University 1981 M.SC. University of British Columbia 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMANTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA AUGUST 1990 © Mark Le Gros In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) A b s t r a c t S e l e c t i v e e x c i t a t i o n p u l s e d NMRON, CW-NMRON and Thermal NMR methods have been used t o s t u d y t h e low t e m p e r a t u r e S 4Mn n u c l e a r s p i n - l a t t i c e r e l a x a t i o n mechanisms i n m a g n e t i c i n s u l a t o r s . The s e l e c t i v e s i n g l e and d o u b l e quantum e x c i t a t i o n sequences have been used f o r t h e f i r s t t i m e i n NMRON t o o b t a i n s i n g l e and do u b l e quantum r o t a t i o n p a t t e r n s , F r e e I n d u c t i o n Decays, Hahn s p i n echoes and p u l s e d T measurements. Two i n s u l a t i n g magnets have been s t u d i e d ; M n C l 2 . 4 H 2 0 and Mn(COOCH ) .4H0. I n t h e 5 4Mn-MnCl .4H 0 system t h e t e m p e r a t u r e v 3' 2 2 2 2 J • c dependence o f t h e 5 4Mn s p i n - l a t t i c e r e l a x a t i o n t i m e a t z e r o f i e l d was measured between 35 mK and 90 mK and i t was found t h a t t h e dominant r e l a x a t i o n p r o c e s s between 65 mK and 90 mK i s an e l e c t r o n i c magnon Raman p r o c e s s and below 65 mK a d i r e c t r e l a x a t i o n p r o c e s s dominates. S i n g l e and d o u b l e quantum F r e e I n d u c t i o n Decays and Hahn s p i n echoes have been used t o d e t e r m i n e t h e magnitude and n a t u r e o f t h e s p i n - s p i n r e l a x a t i o n mechanism f o r 5 4Mn o r i e n t e d i n MnCl 2. 4 H 20 a t z e r o a p p l i e d f i e l d . NMRON was o b s e r v e d f o r t h e f i r s t t i m e i n t h e pa r a m a g n e t i c phase o f MnCl 2.4H 20. The reso n a n c e l i n e s a r e inhomogeneously broadened and 300 kHz wide. A v a l u e o f < 5 4AS>/h=-513.6(3) MHz has been d e t e r m i n e d f o r t h e pa r a m a g n e t i c phase h y p e r f i n e c o u p l i n g c o n s t a n t , and t h i s v a l u e has been used t o d e t e r m i n e t h e z e r o p o i n t s p i n d e v i a t i o n o f t h e a n t i f e r r o m a g n e t i c phase. The f i e l d and t e m p e r a t u r e dependence o f t h e 5 4Mn T was measured f o r v a l u e s o f f i e l d above t h e s p i n f l o p p a r a m a g n e t i c phase t r a n s i t i o n and a f i e l d dependent minimum was d i s c o v e r e d a t B =2.64 T. a F o r t h e 5 4Mn-Mn(COOCH 3) « 4H 20 system two S 4Mn r e s o n a n c e s have been o b s e r v e d and t h e v a l u e o f t h e hy p e r f i n e c o u p l i n g c o n s t a n t s f o r t h e two s i t e s were found t o be < 5 4AS>/h=-435 (1) MHz f o r t h e 5 4 M n l s i t e and < 5 4AS>/h=-478(l) MHz f o r t h e 5 4Mn2 s i t e . The h i g h f i e l d s p i n - l a t t i c e r e l a x a t i o n b e h a v i o r has a l s o been i n v e s t i g a t e d and a T minimum a t B =2.74 T analogo u s t o t h a t o b s e r v e d i n MnCl .4H O was d i s c o v e r e d . 2 2 A Hahn echo s t u d y o f t h e low f i e l d s i n g l e quantum s p i n - s p i n r e l a x a t i o n p r o c e s s e s has been p e r f o r m e d and anomalous b e h a v i o r o f t h e s p i n echo a m p l i t u d e r e v e a l e d . i i i Table of Contents Abstract i i L i s t of Tables v i L i s t of Figures v i i Acknowledgements x 1 Introduction 1.1 A B r i e f H i s t o r y o f NMRON 1 1.2 P u l s e d NMRON i n M a g n e t i c I n s u l a t o r s 3 2 The Theory of NMRON i n Ordered Magnetic Insulators 2.1 I n t r o d u c t i o n 8 2.2 S p i n P r o p e r t i e s o f t h e a 5 4 M n 2 + I m p u r i t y Moment 11 2.3 S p i n Dynamics and y-Ray D e t e c t e d NMR 18 2.4 S p i n L a t t i c e R e l a x a t i o n 26 2.5 The M a g n e t i c E x c i t a t i o n s o f a Ferromagnet 30 2.6 S p i n - L a t t i c e R e l a x a t i o n i n M a g n e t i c I n s u l a t o r s 41 3 Experimental Techniques 3.1 I n t r o d u c t i o n 48 3.2 The NMRON Ap p a r a t u s 51 3.3 Sample p r e p a r a t i o n 56 3.4 S e t t i n g Up A P u l s e d NMRON Experiment 58 3.5 P u l s e Sequences and M u l t i p l e Quantum NMRON 60 4 NMRON i n Manganese Chloride Tetrahydrate 4.1 The M a g n e t i c P r o p e r t i e s o f MnCl 2.4H 20. 76 4.2 Zero F i e l d s p i n - L a t t i c e r e l a x a t i o n 79 4.3 The Spectrum o f t h e Pa r a m a g n e t i c Phase 84 4.4 Zero P o i n t M o t i o n i n t h e A n t i f e r r o m a g n e t i c Phase 88 4.5 S p i n - L a t t i c e R e l a x a t i o n i n t h e P a r a m a g n e t i c Phase.... 90 i v 4.6 Thermal NMR in the Paramagnetic Phase 96 5 NMRON i n Manganese A c e t a t e T e t r a h y d r a t e 5.1 NMRON in Mn(COOCH3) 2.4H20 101 5.2 The Magnetic properties of Mn(COOCH3)2.4H20 102 5.3 The CW NMRON 54Mn Resonance spectrum 115 5.4 The Field Dependence of T 120 5.5 Thermal NMR in Mn(COOCH3) .4H20 124 5.6 54Mn Spin-Lattice Relaxation in Mn(COOCH3) .4H20 130 5.7 Spin Echoes in Mn(C00CH3) .4H20 141 6 Summary and Concluding Remarks 6.1 Summary and Concluding Remarks 14 6 Bibliography 151 Appendix A A.l Details of the NMRON probe and sample preparation... 154 v L i s t o f T a b l e s .1 Measurements o f t h e P a r a m a g n e t i c Phase H y p e r f i n e C o u p l i n g C o n s t a n t s v i L i s t o f F i g u r e s 2.1: The A x i a l NMRON Spectrum o f t h e A n t i f e r r o m a g n e t i c Phase o f MnCl .4H 0 16 2 2 2.2: The E q u a t o r i a l NMRON Spectrum o f t h e A n t i f e r r o m a g n e t i c Phase o f MnCl .4H0 17 2 2 2.3: S e l e c t i v e S i n g l e and Double Quantum P u l s e Sequences... 20 2.4: M a g n e t i c E x c i t a t i o n Spectrum F o r A Ferromagnet 40 3.1: B l o c k Diagrame o f t h e NMRON A p p a r a t u s 52 3.2: S i n g l e Quantum R o t a t i o n P a t t e r n 59 3.3: A x i a l Double Quantum R o t a t i o n P a t t e r n 64 3.4: E q u a t o r i a l Double Quantum R o t a t i o n P a t t e r n 65 3.5: S o f t Double Quantum F r e e I n d u c t i o n Decay 66 3.6: Decay o f t h e S i n g l e Quantum S p i n Echo A m p l i t u d e 68 3.7: Decay o f t h e Double Quantum S p i n Echo A m p l i t u d e 69 3.8: P u l s e d Resonance S e a r c h 74 3.9: P u l s e d S p i n L a t t i c e R e l a x a t i o n Time Measurement 75 4.1: The Phase Diagram ( a ) , and M a g n e t i c U n i t C e l l (b) o f MnCl .4H 0 77 2 2 4.2: The t e m p e r a t u r e Dependence o f T"1 i n t h e A n t i f e r r o m a g n e t i c Phase o f . 81 4.3: A CW NMRON Resonance L i n e i n t h e P a r a m a g n e t i c Phase o f MnCl .4H0 85 2 2 4.4: F i e l d Dependence o f t h e P a r a m a g n e t i c Phase Resonance F r e q u e n c i e s 86 4.5: The F i e l d Dependence o f T i n t h e P a r a m a g n e t i c Phase o f MnCl .4H0 a t 35 mK 92 4.6: The F i e l d Dependence o f T i n t h e P a r a m a g n e t i c Phase o f MnCl .4H O a t 55 mK 2 2 v i i 4.7: The Temperature Dependence o f T _ 1 i n t h e P a r a m a g n e t i c phase f o r B =3 T 94 4.8: The Temperature Dependence o f T"1 i n t h e P a r a m a g n e t i c phase f o r B =2.1 T 95 a 4.9: Thermal NMR L i n e i n t h e Pa r a m a g n e t i c Phase o f MnCl .4H 0 99 2 2 4.10: The Pa r a m a g n e t i c Phase Magnon Spectrum 100 5.1: The Low Temperature S p i n Arrangement i n Mn(COOCH ) .4H0 104 3' 2 2 5.2: The Low F i e l d Phase Diagram o f Mn(COOCH3) . 4H 20 105 5.3: The S 4Mn N u c l e a r Resonance S i t e s 107 5.4: The Low F i e l d e f f e c t i v e S p i n S t r u c t u r e o f Mn(COOCH ) .4H0. 108 x 3' 2 2 5.5: The Complete Manganese NMR Spectrum f o r Mn(COOCH3) . 4HzO a t B =0.4 T 109 a 5.6: The E x c i t a t i o n Spectrum f o r t h e Model Mn(COOCH3) . 4H 20 a t B =0. n T I l l 5.7: The E x c i t a t i o n Spectrum f o r t h e Model Mn(COOCH3) .4H20 System f i e l d s above 0.014 T 112 5.8: The F i e l d Dependence o f t h e 5 4Mn Resonance F r e q u e n c i e s 116 5.9: The 5 4Mn NMRON Resonance i n Mn(COOCH ) .4H O 1 3' 2 2 f o r B =0.2 T 117 a 5.10: The 5 4Mn2 NMRON Resonance i n Mn(COOCH ) .4HO 3 2 2 f o r B =0.5 T. 118 a 5.11: The F i e l d Dependence o f T± i n Mn(C00CH 3) 2.4H 20 f o r B =0 T t o 0.25 T 122 cl 5.12: F i e l d Dependence o f T f o r B=2.3 T t o 3 T 123 l a 5.13: 5 SMn Thermal NMR a t Zero A p p l i e d F i e l d 127 5.14: 5 5Mn Thermal NMR a t Zero A p p l i e d F i e l d 128 v i i i 5.15: 5 5Mn Thermal NMR a t B =2.64 T 129 5.16: H i g h Order N u c l e a r Magnon R e l a x a t i o n P r o c e s s e s 132 5.17: D i r e c t P r o c e s s N u c l e a r Magnon R e l a x a t i o n 138 5.18: The A m p l i t u d e o f t h e Hahn S p i n Echo a t B a=0.3 T 144 5.19: The A m p l i t u d e o f t h e Hahn S p i n Echo a t B_==0.4 T 145 A . l : The NMRON probe and sample mount 155 A.2: The NMRON probe mounted i n t h e IK h e a t s h i e l d 156 A.3: Sample growth p r o c e d u r e s 158 i x Acknowledgements I t i s my p l e a s u r e t o thank my s u p e r v i s o r P r o f . B. G. T u r r e l l f o r h i s g u i d a n c e , h e l p , encouragement and p a t i e n c e o v e r t h e y e a r s t h i s work was performed. I would a l s o l i k e t o t h a n k P r o f . A. K. K o t l i c k i f o r h i s h e l p and acknowledge h i s i m p o r t a n t c o n t r i b u t i o n t o t h e work. I would l i k e t o t h a n k A n n i e and B r i a n T u r r e l l f o r t h e h o s p i t a l i t y and g e n e r o s i t y t h e y extended t o me d u r i n g my t i m e as a g r a d u a t e s t u d e n t , and t h e F a c u l t y and S t a f f o f t h e UBC p h y s i c s department f o r making my s t a y a t UBC a p l e a s a n t and r e w a r d i n g e x p e r i e n c e . x Chapter 1 I n t r o d u c t i o n 1.1 A B r i e f H i s t o r y o f NMRON The f i r s t s u g g e s t i o n t o d e t e c t t h e r e s o n a n t a b s o r p t i o n o f photons by an o r d e r e d r a d i o a c t i v e n u c l e a r ensemble v i a changes i n t h e d i r e c t i o n a l d i s t r i b u t i o n o f t h e r a d i o a c t i v e decay 1 2 p r o d u c t s came from Bloembergen and Temmer i n 1953 ' . T h i s s u g g e s t i o n l e a d t o t h e development o f N u c l e a r M a g n e t i c Resonance o f O r i e n t e d N u c l e i (NMRON), an e x o t i c N u c l e a r M a g n e t i c Resonance (NMR) t e c h n i q u e w h i c h p r e s e n t l y combines a l m o s t t h e f u l l range o f modern p u l s e d NMR t e c h n o l o g y w i t h t h e v e r y h i g h s e n s i t i v i t y o f h i g h energy p a r t i c l e / r a d i a t i o n d e t e c t e d NMR. I n f a v o r a b l e c i r c u m s t a n c e s h i g h s i g n a l t o n o i s e NMR can be p e r f o r m e d on a n u c l e a r ensemble w i t h as few as 1 0 7 n u c l e i . The f i r s t e x p e r i m e n t a l d e m o n s t r a t i o n o f NMRON was per f o r m e d 3 by Mattheas and H o l l i d a y i n 1967 . They o b s e r v e d t h e r e s o n a n t d e s t r u c t i o n o f gamma r a y a n i s o t r o p y from o r i e n t e d 6 0Co n u c l e i d i f f u s e d i n t o a m a g n e t i c a l l y s a t u r a t e d f e r r o m a g n e t i c i r o n h o s t . The o r i e n t a t i o n i n t h e m a g n e t i c a l l y s a t u r a t e d h o s t r e s u l t e d from t h e h y p e r f i n e c o u p l i n g between t h e n u c l e u s and t h e ma g n e t i c e l e c t r o n s w i t h t h e d e s t r u c t i o n o f gamma r a y a n i s o t r o p y o c c u r r i n g when t h e f r e q u e n c y o f t h e a p p l i e d r f f i e l d was swept t h r o u g h t h e n u c l e a r h y p e r f i n e resonance l i n e s . P r i o r t o 1977 t h e common NMRON t e c h n i q u e s i n use were s a t u r a t i o n c o n t i n u o u s wave (CW) methods i n w h i c h t h e r e s o n a n t d e s t r u c t i o n o f a n i s o t r o p y i s caused by t h e a p p l i c a t i o n o f a 1 s t r o n g f r e q u e n c y modulated r a d i o f r e q u e n c y ( r f ) f i e l d . The CW NMRON t e c h n i q u e has t h e g r e a t v i r t u e o f e x p e r i m e n t a l s i m p l i c i t y , b u t i t i s n e c e s s a r i l y a s a t u r a t i o n method and t h e r e f o r e s u b j e c t t o r e s t r i c t i o n s on t h e range o f s p i n - l a t t i c e r e l a x a t i o n t i m e s amenable t o s t u d y and t h e maximum u s a b l e r f power. NMRON r e q u i r e s a v e r y low t e m p e r a t u r e environment and t h e r f power i s l i m i t e d by non-resonant h e a t i n g caused by r f l o s s e s i n t h e sample and eddy c u r r e n t h e a t i n g o f t h e sample c o l d f i n g e r . I t a l s o s u f f e r s from t h e u s u a l d i f f i c u l t i e s e n c o u n t e r e d w i t h t h e i n t e r p r e t a t i o n o f s a t u r a t i o n NMR l i n e shapes. The r e q u i r e m e n t o f h i g h s a t u r a t i o n i s d i r e c t l y r e l a t e d t o t h e u n u s u a l n a t u r e o f t h e NMRON o b s e r v a b l e , t h e gamma r a y a n i s o t r o p y p a t t e r n . T h i s o b s e r v a b l e p o s s e s s e s t h e i n h e r e n t s t a t i s t i c a l e r r o r f o u n d when me a s u r i n g r a d i o a c t i v e decay and i t s magnitude i s p r o p o r t i o n a l t o h i g h r a n k d i a g o n a l components o f t h e n u c l e a r s p i n d e n s i t y m a t r i x . These p r o p e r t i e s d i c t a t e t h a t t h e sample t e m p e r a t u r e s h o u l d be o f t h e same o r d e r as t h e n u c l e a r s p i n l e v e l energy s p l i t t i n g s and t h a t t h e r e s o n a n t p e r t u r b a t i o n o f t h e l e v e l p o p u l a t i o n s be l a r g e . 4 The p u l s e d NMRON methods o f f e r many advantages o v e r t h e CW approach such as i n c r e a s e d s i g n a l s i z e s , t h e o b s e r v a t i o n o f t h e f r e e i n d u c t i o n decay, ( F I D ) , measurement o f s p i n - l a t t i c e r e l a x a t i o n t i m e s T t down i n t h e m i l l i s e c o n d regime and t h e use o f s p i n echoes t o u n t a n g l e competing s p i n decoherence mechanisms. The p i o n e e r i n g p u l s e d NMRON work was t h e Duntroon 60 5 group's s t u d y o f t h e CoFe system . These e x p e r i m e n t s p r o d u c e d many i m p r e s s i v e r e s u l t s , b u t t h e measurements were hamper by g e n e r a l problems o f p u l s e d NMR i n m e t a l s , i . e . a2 b r o a d r e s o n a n c e l i n e , s k i n d e p t h e f f e c t s and a l i m i t e d range o f o b s e r v a b l e T v a l u e s . 1.2 P u l s e d NMRON i n M a g n e t i c I n s u l a t o r s The o b s e r v a t i o n by K o t l i c k i and T u r r e l l o f 5 4Mn NMRON i n t h e i n s u l a t i n g a n t i f e r r o m a g n e t Manganese C h l o r i d e T e t r a h y d r a t e ( M n C l 2 . 4 H 2 0 ) 6 , 7 , 8 paved t h e way f o r f u r t h e r development o f p u l s e d NMRON i n a much more r e w a r d i n g and p l i a n t c l a s s o f m a t e r i a l s . T h i s t h e s i s p r e s e n t s t h e r e s u l t s o f NMRON e x p e r i m e n t s on 5 4Mn o r i e n t e d i n two i n s u l a t i n g m a g n e t i c s a l t s , Manganese C h l o r i d e T e t r a h y d r a t e , (MnCl 2 >4H 20) , a f o u r s u b l a t t i c e a n t i f e r r o m a g n e t w i t h b i a x i a l s i n g l e i o n a n i s o t r o p y (see page 76) f o r a d i s c u s s i o n o f t h e p r o p e r t i e s o f MnCl 2.4H 20), and Manganese A c e t a t e T e t r a h y d r a t e , (Mn(COOCH 3) .4H 20), a complex 12 s u b l a t t i c e a n t i f e r r o m a g n e t (see page 101 f o r a d i s c u s s i o n o f t h e p r o p e r t i e s o f Mn(C00CH 3) .4H 20). The f i r s t f o u r s e c t i o n s o f Chapter 2 c o n t a i n a d i s c u s s i o n o f t h e t h e o r y o f p u l s e d NMRON a p p l i c a b l e t o a p o l a r i s e d 5 4Mn 2 + i o n . The t h e o r y p r e s e n t e d i s a s i m p l i f i e d v e r s i o n o f t h e g e n e r a l t h e o r y o f p u l s e d NMRON and t a i l o r e d t o systems w i t h an NMRON l e v e l s t r u c t u r e amenable t o s t u d y by s e l e c t i v e e x c i t a t i o n p u l s e d t e c h n i q u e s . The f i n a l two s e c t i o n s o f t h i s c h a p t e r d i s c u s s t h e t h e o r y o f NMR i n o r d e r e d magnetic i n s u l a t o r s w i t h emphasis on elements o f t h e t h e o r y r e l e v a n t t o t h e NMRON s p i n - l a t t i c e r e l a x a t i o n measurements p r e s e n t e d i n c h a p t e r s 4 and 5. Cha p t e r 3 b e g i n s w i t h a b r i e f d i s c u s s i o n o f t h e CW-NMRON, t h e r m a l NMR and p u l s e d NMRON methods i n s e c t i o n 3.1. S e c t i o n s 3.2 and 3.3 c o n t a i n d e t a i l s o f t h e a p p a r a t u s , sample p r e p a r a t i o n 3 and t h e d a t a a n a l y s i s . The f i n a l s e c t i o n s o f c h a p t e r 3 d e a l e x c l u s i v e l y w i t h p u l s e d NMRON methods and t h e s e s e c t i o n s c o n t a i n many new r e s u l t s d e m o n s t r a t i n g s e l e c t i v e e x c i t a t i o n m u l t i p l e quantum p u l s e d NMRON. I n s e c t i o n 3.4 t h e r e i s a d i s c u s s i o n o f s e t t i n g up p u l s e d NMRON e x p e r i m e n t s , t h e use o f Magnon C o o l i n g , e x p e r i m e n t a l examples o f d o u b l e quantum r o t a t i o n p a t t e r n s and FID, and a d e m o n s t r a t i o n o f t h e use o f s i n g l e and d o u b l e quantum echoes t o d e t e r m i n e s p i n - s p i n i n t e r a c t i o n s i n MnCl2.4H2<3. The f i n a l e x p e r i m e n t s d e s c r i b e d i n c h a p t e r 3 a r e p u l s e d T measurements and t h e use o f p u l s e d methods f o r f i n d i n g s h o r t T re s o n a n c e s . C h a p t e r 4 i s i n t h e main a s t u d y o f 5 4Mn s p i n - l a t t i c e r e l a x a t i o n phenomena i n MnCl .4H 0. S e c t i o n 4.1 d e s c r i b e s t h e c 2 2 b a s i c p r o p e r t i e s o f t h e a n t i f e r r o m a g n e t and c o n c e n t r a t e s on t h e f i e l d dependence o f t h e magn e t i c e x c i t a t i o n s p ectrum. S e c t i o n 4.2 p r e s e n t s t h e r e s u l t s o f a s t u d y o f t h e t e m p e r a t u r e dependence o f t h e z e r o a p p l i e d f i e l d , s p i n - l a t t i c e r e l a x a t i o n t i m e , o f 5 4Mn o r i e n t e d i n MnCl 2.4H 20. The f o c u s o f t h i s s t u d y i s t h e t e m p e r a t u r e dependence o f t h e l i m i t i n g low t e m p e r a t u r e r e l a x a t i o n p r o c e s s e s . NMRON was o b s e r v e d f o r t h e f i r s t t i m e i n t h e p a r a m a g n e t i c phase o f MnCl 2.4H 20 and s e c t i o n 4.4 i s a s t u d y o f t h e l i n e shape and f i e l d dependence o f t h e f r e q u e n c i e s o f t h e par a m a g n e t i c phase resonance l i n e s . An a n a l y s i s o f t h e f i e l d dependence o f t h e re s o n a n c e f r e q u e n c i e s has produced two i n t e r e s t i n g p h y s i c a l q u a n t i t i e s , t h e z e r o p o i n t m o t i o n o f t h e a n t i f e r r o m a g n e t i c phase ground s t a t e and t h e d i f f e r e n c e o f t h e f e r r o m a g n e t i c and a n t i f e r r o m a g n e t i c exchange f i e l d s f e l t by each Mn 2 + s p i n i n t h e magn e t i c u n i t c e l l (see page 76) . A comparison 4 o f t h e p a r a m a g n e t i c phase h y p e r f i n e f i e l d s f o r t h e manganese i o n s w i t h t h e h y p e r f i n e f i e l d s measured i n t h e g a n t i f e r r o m a g n e t i c phase by t h e O x f o r d Group has a l l o w e d a d e t e r m i n a t i o n o f t h e a n t i f e r r o m a g n e t i c phase z e r o p o i n t s p i n g d e v i a t i o n . The same a n a l y s i s and comparison w i t h p r e v i o u s work a l s o y e i l d s t h e d i f f e r e n c e o f t h e f e r r o m a g n e t i c and . 2 + a n t i f e r r o m a g n e t i c exchange f i e l d s f e l t by t h e Mn s p i n s . S e c t i o n 4.5 examines t h e t e m p e r a t u r e and f i e l d dependence o f t h e pa r a m a g n e t i c phase 5 4Mn s p i n - l a t t i c e r e l a x a t i o n t i m e . There i s a r e p o r t o f t h e d i s c o v e r y o f a p e c u l i a r , f i e l d dependent, r e l a x a t i o n t i m e minimum and a d i s c u s s i o n o f t h e n a t u r e o f t h e d o m i n a t i n g s p i n - l a t t i c e r e l a x a t i o n p r o c e s s e s as a f u n c t i o n o f a p p l i e d m a g n e t i c f i e l d . The f i n a l s e c t i o n o f t h i s c h a p t e r d i s c u s s e s t h e pa r a m a g n e t i c phase t h e r m a l NMR spectrum o f 5 5 M n 7 . Ch a p t e r 5 i s an NMRON s t u d y o f t h e 5 4Mn-Mn(COOCH 3) 2-4H 20 s y s t e m . % Mn(COOCH 3) 2.4H 20 p o s s e s s e s a complex c r y s t a l l o g r a p h i c and m a g n e t i c s t r u c t u r e and t h e f i r s t two s e c t i o n s o f t h i s c h a p t e r a r e de v o t e d t o t h e e x p l a n a t i o n o f t h e ma g n e t i c s t r u c t u r e and t h e development o f a s i m p l e model t o d e s c r i b e t h e low t e m p e r a t u r e m a g n e t i c e x c i t a t i o n s o f t h e system. S e c t i o n 5.3 d e s c r i b e s t h e complete CW-NMRON and t h e r m a l NMR re s o n a n c e spectrum, d i s c u s s e s t h e CW-NMRON l i n e s h a p e a t v a r i o u s f i e l d s and p r e s e n t s measured v a l u e s o f t h e h y p e r f i n e f i e l d s f o r t h e re s o n a n c e s i t e s . S e c t i o n 5.4, 5.5 and 5.6 a r e c o n c e r n e d w i t h t h e f i e l d dependent r e l a x a t i o n b e h a v i o r o f 5 4Mn. The s t u d y i l l u s t r a t e s t h e a p p l i c a t i o n o f a l l t h e above mentioned o r i e n t e d n u c l e i r e s o n a n c e t e c h n i q u e s , (CW-NMRON, p u l s e d NMRON and t h e r m a l NMR), t o t h e e l u c i d a t i o n o f complex s p i n - l a t t i c e r e l a x a t i o n 5 mechanisms. The ob s e r v e d s p i n - l a t t i c e r e l a x a t i o n b e h a v i o r was q u i t e u n e x p e c t e d and t h e r e s u l t s p r e s e n t e d i n t h e s e s e c t i o n s i l l u s t r a t e t h e e f f i c a c y o f NO-NMRON methods a p p l i e d t o a complex system e x h i b i t i n g b o t h v e r y s h o r t , <100ms, and v e r y l o n g , 1 0 6 s r e l a x a t i o n t i m e s . The f i n a l s e c t i o n o f t h i s c h a p t e r p r e s e n t s t h e r e s u l t s o f a s p i n - e c h o s t u d y i n t h e p a r a m a g n e t i c phase o f Mn(COOCH ) .4H 0. x 3' 2 2 There a r e two main themes i n t h e t h e s i s : one i s t h e development o f p u l s e d NMRON s e l e c t i v e e x c i t a t i o n methods; t h e o t h e r i s a s t u d y o f low t e m p e r a t u r e n u c l e a r s p i n - s p i n , and s p i n - l a t t i c e r e l a x a t i o n phenomena o f 5 4 M n 2 + i m p u r i t y i o n s i n mag n e t i c i n s u l a t o r s . The s e l e c t i v e e x c i t a t i o n methods d e v e l o p e d a r e q u i t e g e n e r a l and t h e y can be a p p l i e d t o any r a d i o a c t i v e - i m p u r i t y h o s t system; p r o v i d e d t h e NMRON spectrum c o n s i s t s o f a w e l l r e s o l v e d m u l t i p l e t o f reso n a n c e l i n e s . W e l l r e s o l v e d 5 4Mn n u c l e a r m a g n e t i c r e s o n a n c e s p e c t r a a r i s e i n a v a r i e t y o f 5 4Mn doped o r d e r e d and d i s o r d e r e d i n s u l a t i n g m a g n e t i c m a t e r i a l s and t h e methods s h o u l d have many a p p l i c a t i o n s i n such systems. The s t u d y o f low t e m p e r a t u r e r e l a x a t i o n p r o c e s s e s i n mag n e t i c i n s u l a t o r s p r o v i d e s i m p o r t a n t i n f o r m a t i o n r e l a t i n g t o t h e p r o b l e m o f c o o l i n g t h e s e m a t e r i a l s because t h e m a j o r i t y o f t h e low t e m p e r a t u r e h e a t c a p a c i t y r e s i d e s i n t h e S 4Mn n u c l e a r s p i n h y p e r f i n e r e s e r v o i r . S t u d i e s o f f i e l d dependent n u c l e a r s p i n - l a t t i c e r e l a x a t i o n a r e i m p o r t a n t f o r d i s c o v e r i n g ways t o c o o l t h e n u c l e a r ensemble t o low t e m p e r a t u r e s i n a s h o r t t i m e . The o b s e r v a t i o n o f v e r y s h o r t , low t e m p e r a t u r e , n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t i m e s i n magn e t i c i n s u l a t o r s s u g g e s t s 6 t h a t t h e s e m a t e r i a l s may be u s e f u l as h o s t m a t e r i a l s f o r NO s t u d i e s o f n u c l e a r s t r u c t u r e . I n p a r t i c u l a r t h e t e c h n i q u e o f On L i n e N u c l e a r O r i e n t a t i o n f o r t h e s t u d y o f s h o r t h a l f l i f e r a d i o a c t i v e n u c l e i c o u l d b e n e f i t from t h e d i s c o v e r y o f a h i g h h e a t c a p a c i t y , i n s u l a t i n g , NO h o s t m a t e r i a l i n w h i c h t h e s p i n l a t t i c e r e l a x a t i o n t i m e i s v e r y s h o r t , (see R e f . 2 ) . To c o n c l u d e t h e i n t r o d u c t o r y c h a p t e r i t i s a p p r o p r i a t e t o comment on t h e d i v e r s i t y o f t h e combined NO-NMRON t e c h n i q u e s . Not o n l y does NO-NMRON measure t h e p u l s e d and CW NMR o f a h i g h l y d i l u t e n u c l e i ensemble, t h e n u c l e a r s p i n t e m p e r a t u r e and t h e f i e l d dependent magnetic s t r u c t u r e o f t h e h o s t , b u t i t can a l s o measure r e s o n a n t power a b s o r p t i o n by t h e h o s t medium. I n t h e most p e r f e c t r e a l i z a t i o n o f t h e t h e r m o m e t r i c method one t a k e s t h e l o w e s t h e a t c a p a c i t y thermometer known, a s m a l l o r i e n t e d r a d i o a c t i v e n u c l e a r ensemble, and i n t e r m i n g l e s i t w i t h t h e m a t e r i a l o f t h e resonance medium. Thermometric NMR m o n i t o r s t h e power absorbed by an abundant n u c l e a r s p i n system t h r o u g h t h e s p i n t e m p e r a t u r e o f t h e n u c l e a r thermometer. The method c a p t u r e s t h e a p p e a l i n g b r u t i s h s i m p l i c i t y o f CW NMRON and a l l o w s t h e o b s e r v a t i o n o f resonance l i n e s w h i c h c o u l d be v e r y d i f f i c u l t t o ob s e r v e u s i n g c o n v e n t i o n a l methods. 7 Chapter 2 The Theory o f NMRON i n Ordered M a g n e t i c I n s u l a t o r s 2.1 I n t r o d u c t i o n A m a g n e t i c i m p u r i t y i o n i n a s o l i d i s s e n s i t i v e t o t h e s t a t i c and dynamic e l e c t r o m a g n e t i c p r o p e r t i e s o f t h e h o s t l a t t i c e . The e l e c t r o n i c moment c o u p l e s s t r o n g l y t o t h e l o c a l f i e l d s and t h e n u c l e u s o f t h e i o n f e e l s t h e e f f e c t s o f such f i e l d s t h r o u g h t h e h y p e r f i n e i n t e r a c t i o n . T h i s t h e s i s c o n c e r n s NMR e x p e r i m e n t s on t h e n u c l e u s o f a p o l a r i s e d 5 4 M n 2 + i m p u r i t y embedded i n an i n s u l a t i n g l a t t i c e . The e l e c t r o n i c moment i s formed from t h e v a l e n c e e l e c t r o n s o f a 5 4 M n 2 + i m p u r i t y i o n and t h e h o s t l a t t i c e i s t h a t o f a mag n e t i c i n s u l a t o r . The h y p e r f i n e i n t e r a c t i o n between t h e n u c l e u s and t h e e l e c t r o n i c moment i s t h e major c o u p l i n g mechanism d e t e r m i n i n g t h e n u c l e a r s p i n energy l e v e l s t r u c t u r e . T h i s l e v e l s t r u c t u r e does n o t depend on t h e e x a c t n a t u r e o f t h e f i e l d w h i c h o r d e r s t h e e l e c t r o n i c moment p r o v i d e d t h a t t h e f i e l d b r e a k s t i m e r e v e r s a l symmetry. The o r d e r i n g f i e l d c o u l d be an e x t e r n a l l y a p p l i e d m a g n e t i c f i e l d o r i t may a r i s e from a c o m b i n a t i o n o f exchange i n t e r a c t i o n s and t h e f o r c e s c o u p l i n g t h e moment t o t h e l a t t i c e . I n s e c t i o n 2.2 t h e p r o p e r t i e s o f t h e n u c l e a r s p i n energy 8 l e v e l s o f a 5 4Mn 2* i o n p o l a r i s e d by an a p p l i e d m a g n e t i c f i e l d a r e d e r i v e d . The systems o f i n t e r e s t a r e a n t i f e r r o m a g n e t i c i n s u l a t o r s and t h e e q u a t i o n s g o v e r n i n g t h e n u c l e a r l e v e l s t r u c t u r e a r e a l s o g i v e n f o r t h e case o f an i m p u r i t y moment p o l a r i z e d by a c o m b i n a t i o n o f exchange f i e l d s , a p p l i e d m a g n e t i c f i e l d and c r y s t a l l i n e a n i s o t r o p y f i e l d s . P u l s e d NMRON e x p e r i m e n t s i n v o l v e t h e m a n i p u l a t i o n o f t h e n u c l e a r s p i n o f t h e i m p u r i t y i o n by l a r g e r f p u l s e s r e s o n a n t w i t h t h e h y p e r f i n e l e v e l s p l i t t i n g s , and i n s e c t i o n 2.3 t h e t h e o r y o f s p i n dynamics and y - r a y d e t e c t e d NMR i s d e v e l o p e d f o r t h e 5 4 M n 2 + i m p u r i t y system. There i s a d i s c u s s i o n o f s e l e c t i v e s i n g l e quantum and do u b l e quantum e x c i t a t i o n sequences and t h e e q u a t i o n s r e l a t i n g t h e r - r a y d i s t r i b u t i o n p a t t e r n t o t h e n u c l e a r s p i n energy l e v e l p o p u l a t i o n s a r e g i v e n . The s t r o n g e s t i n t e r a c t i o n f e l t by t h e i m p u r i t y n u c l e u s i s t h e s t a t i c h y p e r f i n e f i e l d from t h e p o l a r i s e d e l e c t r o n i c moment and t h i s f i e l d d e t e r m i n e s t h e b a s i c n u c l e a r s p i n l e v e l s t r u c t u r e . I n a s t r o n g l y p o l a r i s e d 5 4Mn 2* i m p u r i t y w i t h 1=3 i t prod u c e s 6 h y p e r f i n e m u l t i p l e t s each o f w h i c h c o n s i s t s o f 7 n u c l e a r s p i n energy l e v e l s . F l u c t u a t i o n s i n t h e h y p e r f i n e f i e l d a r e caused by m o t i o n o f t h e s u r r o u n d i n g l a t t i c e and t h e e f f e c t s o f t h i s m o t i o n a r e m a n i f e s t e d i n t h e n u c l e a r s p i n r e l a x a t i o n phenomena. S e c t i o n 2.4 c o n t a i n s a b r i e f d i s c u s s i o n o f h y p e r f i n e m e d i a t e d n u c l e a r s p i n - l a t t i c e r e l a x a t i o n ; t h e d i s c u s s i o n i s t a i l o r e d t o " n o n - s p i n t e m p e r a t u r e " r e l a x a t i o n p r o c e s s e s as t h e r e q u i r e m e n t s f o r n o n - s p i n t e m p e r a t u r e r e l a x a t i o n a r e o f t e n s a t i s f i e d by i s o l a t e d 5 4 M n 2 + i m p u r i t i e s , (See C h a p t e r 12 o f r e f . 2 ) . 9 The systems o f i n t e r e s t a r e 5 5 M n 2 + m a g n e t i c i n s u l a t o r s i n w h i c h a v e r y s m a l l f r a c t i o n o f t h e mag n e t i c atoms have been r e p l a c e d by r a d i o a c t i v e 5 4 M n 2 + i m p u r i t y atoms. A t low t e m p e r a t u r e s t h e magnets o r d e r i n t o m u l t i - s u b l a t t i c e e l e c t r o n i c s p i n a r r a y s and a t l o w e r t e m p e r a t u r e s t h e n u c l e i o f t h e ma g n e t i c atoms a l s o become h i g h l y m a g n e t i z e d by t h e l o c a l h y p e r f i n e f i e l d s . The q u a l i t a t i v e and some o f t h e q u a n t i t a t i v e f e a t u r e s o f NMRON i n t h e systems o f i n t e r e s t can be d e s c r i b e d i n terms o f an a r r a y o f f e r r o m a g n e t i c a l l y c o u p l e d Mn 2 + i o n s , and i n s e c t i o n 2.5 t h e s p e c t r a l p r o p e r t i e s o f such a f e r r o m a g n e t i c a r r a y a r e d e r i v e d . The fer r o m a g n e t has two s u b l a t t i c e s , one c o n s i s t i n g o f e l e c t r o n i c s p i n s , and t h e o t h e r n u c l e a r s p i n s . I n t h e low t e m p e r a t u r e o r d e r e d phase t h e n u c l e a r moment p o i n t s i n t h e . • > . 2+ o p p o s i t e d i r e c t i o n t o t h e e l e c t r o n i c moment, b u t b o t h t h e Mn h y p e r f i n e i n t e r a c t i o n and t h e e l e c t r o n i c exchange i n t e r a c t i o n have a n e g a t i v e s i g n and so t h e two s u b l a t t i c e o r d e r e d s t r u c t u r e w i l l be c a l l e d a f e r r o m a g n e t . (The e l e c t r o n i c and n u c l e a r s p i n s a r e p a r a l l e l ) . I n s e c t i o n 2.6 5 5Mn 2* n u c l e a r s p i n - l a t t i c e r e l a x a t i o n mechanisms i n v o l v i n g t h e e x c i t a t i o n s o f m a g n e t i c a l l y o r d e r e d e l e c t r o n i c and n u c l e a r s u b l a t t i c e s a r e d i s c u s s e d . The s e c t i o n c o n c e n t r a t e s on t h e f l u c t u a t i o n s o f t h e mag n e t i c l a t t i c e , b u t t h e r e i s some d i s c u s s i o n o f r e l a x a t i o n mechanisms i n v o l v i n g t h e phonons o f t h e i n s u l a t i n g l a t t i c e because t h e phonon d e g r e e s o f freedom can p l a y a r o l e i n d i r e c t p r o c e s s r e l a x a t i o n . 10 2.2 S p i n P r o p e r t i e s o f t h e a 5 4Mn 2* I m p u r i t y Moment. The ground s t a t e c o n f i g u r a t i o n o f t h e f i v e 3d e l e c t r o n s i n an i s o l a t e d Mn 2 + i o n i s an o r b i t a l s i n g l e t s t a t e . Each e l e c t r o n o c c u p i e s a s e p a r a t e 3d o r b i t a l and a l l e l e c t r o n i c s p i n s a r e p a r a l l e l , t h u s t h e f r e e e l e c t r o n i c moment i s a ' s p i n - o n l y ' moment o f t o t a l s p i n S=5/2. I n a s o l i d t h e Mn2* i o n s a r e s u r r o u n d e d by a cage o f n e g a t i v e l y c h a r g e d l i g a n d s w h i c h produce a n o n - s p h e r i c a l l y s ymmetric p e r t u r b a t i o n o f t h e i o n i c v a l e n c e s h e l l . The s p h e r i c a l symmetry and s t r o n g Coulomb c o r r e l a t i o n energy o f t h e o r b i t a l s i n g l e t s t a t e h e l p t o s t a b i l i z e t h e f r e e i o n ground s t a t e a g a i n s t d e f o r m a t i o n by t h e s e c r y s t a l l i n e e l e c t r i c f i e l d s , and t h e v a l e n c e e l e c t r o n s o f Mn 2 + i n a s o l i d a r e u s u a l l y w e l l d e s c r i b e d as f o r m i n g a l o c a l i z e d s p i n 5/2 moment. Fo r Mn2* embedded i n an i n s u l a t i n g s o l i d , l e v e l s p l i t t i n g s i n d u c e d by t h e e l e c t r i c f i e l d a r e o f t e n much l e s s t h a n t h o s e due t o t h e f i e l d w h i c h p o l a r i s e s t h e e l e c t r o n i c moment. One o f t h e a p p e a l i n g f e a t u r e s o f t h e 5 4 M n 2 + i m p u r i t y system i s t h a t t h e weak c o u p l i n g between t h e e l e c t r o n i c s p i n and t h e c r y s t a l l i n e l a t t i c e p e r m i t s t h e easy p o l a r i z a t i o n o f t h e moment a l o n g t h e d i r e c t i o n o f an a p p l i e d m agnetic f i e l d . The 5 4Mn n u c l e a r s p i n has s p i n 3 and i t i n t e r a c t s m a i n l y w i t h t h e m a g n e t i c e l e c t r o n s o f t h e Mn2* i o n t h r o u g h t h e h y p e r f i n e i n t e r a c t i o n ; i t i s a l s o c o u p l e d t o t h e l o c a l e nvironment t h r o u g h b o t h magnetic d i p o l e and e l e c t r i c q u a d r u p o l e i n t e r a c t i o n s , b u t t h e s e c o u p l i n g s produce a v e r y s m a l l p e r t u r b a t i o n o f t h e h y p e r f i n e i n d u c e d l e v e l s t r u c t u r e . I t i s a 11 r a d i o a c t i v e n u c l e u s w h i c h decays f i r s t by e l e c t r o n c a p t u r e t o an e x c i t e d s t a t e o f 5 4 C r w h i c h t h e n d e - e x c i t e s t o i t s ground s t a t e w i t h t h e e m i s s i o n o f an 840 keV E2 r _ r a y (See C h a p t e r 16 o f r e f . 2) . The a n g u l a r d i s t r i b u t i o n o f t h e e m i t t e d gamma r a y s depends on t h e s p i n s t a t e o f t h e 5 4Mn n u c l e u s and t h i s y - r a y d i s t r i b u t i o n p a t t e r n i s t h e measured o b s e r v a b l e i n t h e NMRON ex p e r i m e n t s . The energy l e v e l s and e i g e n f u n c t i o n s f o r t h e n u c l e u s o f a mag n e t i c f i e l d o r d e r e d 5 4 M n 2 + i m p u r i t y i o n can be c a l c u l a t e d from t h e f o l l o w i n g H a m i l t o n i a n : 5 4 H = H + H ' (2.1a) H = -g/n B S + 5 4 A I o s - f i 5 4 r B I (2.1b) 0 b a z z z n a z H'= ( 5 4 A/2) ( I + S " + I"S + ) (2.1c) Here g i s t h e e l e c t r o n i c g - f a c t o r , 5 4 A i s t h e m a g n e t i c h y p e r f i n e c o u p l i n g c o n s t a n t , 5 4 y i s t h e 5 4Mn gy r o m a g n e t i c r a t i o and B i s n a t h e a p p l i e d f i e l d w h i c h i s d i r e c t e d a l o n g t h e z - a x i s . I f t h e l e v e l s p l i t t i n g s due t o t h e a p p l i e d f i e l d a r e l a r g e compared t o t h e h y p e r f i n e s p l i t t i n g s , t h e n t h e p r o p e r t i e s o f t h e n u c l e a r h y p e r f i n e m u l t i p l e t s can be c a l c u l a t e d by a low o r d e r p e r t u r b a t i o n e x p a n s i o n i n H'. The f i r s t o r d e r s t a t e s o f t h e l o w e s t energy h y p e r f i n e m u l t i p l e t a r e c h a r a c t e r i z e d by t h e quantum numbers -5/2 and I 2=±m. (S=-5/2 r e f e r s t o t h e s i t u a t i o n o f t h e e l e c t r o n i c moment p a r a l l e l t o t h e e x t e r n a l f i e l d ) . To second o r d e r i n H' t h e r e a r e seven l e v e l s and s i x u n e q u a l l y spaced Am=±l magnetic d i p o l e t r a n s i t i o n s from t h e 12 l e v e l S=-5/2, I =m t o t h e l e v e l S=-5/2, I =m+l. The energy ' z z d i f f e r e n c e s between a d j a c e n t l e v e l s i s t o second o r d e r i n H' E - E =-(5/2) 5 4A- h 5 4 r B + ^f/V*1 -5/2,m+l -5/2, m v ' 1 n a Q U B b a (2.2) The f i n a l t e r m o f e q u a t i o n 2.2 d e s c r i b e s t h e energy s p l i t t i n g s o f t h e t r a n s i t i o n s and i s c a l l e d t h e mag n e t i c pseudoquadrupole i n t e r a c t i o n . The u n - n o r m a l i s e d wave f u n c t i o n s o f t h e l o w e s t h y p e r f i n e m u l t i p l e t a r e t o f i r s t o r d e r i n H' 3 > = 1 3 >l -5/2 > + 0(3O) 1 / 2 1 2 >l -3/2 > 2 > = 1 2 >l -5/2 > + • 0 ( 5 0 ) 1 / 2 | 1 >l -3/2 > 1 > = | 1 >l -5/2 > + 0 ( 6 0 ) 1 / 2 1 0 >l -3/2 > 0 > = 1 0 >l -5/2 > + 0 ( 6 0 ) 1 / 2 1 - 1 > | -3/2 > -1 > = 1 - 1 >l -5/2 > + 0 ( 5 0 ) 1 / 2 |-2 >l -3/2 > -2 > = 1 " 2 >l -5/2 > + 0(3O) 1 / 2 1 " 3 >l -3/2 > -3 1 " 3 >l -5/2 > (2.3a) 0 = 1/2 A ^ " b B a (2.3b) The e f f e c t o f H' on t h e wave f u n c t i o n s a p p e a r s as an enhancement o f t h e t r a n s v e r s e n u c l e a r m a g n e t i c moment. T h i s i s e v i d e n t i n t h e m a t r i x element f o r an o s c i l l a t i n g t r a n s v e r s e m a g n e t i c f i e l d c o n n e c t i n g t h e s t a t e s |-2 > t o |-3 >: <-3| h B (y S x + 5 4 y I x ) cos(wt)|-2> • r f v e n 5 4 ' * ' I 13 = hB ( 1 0 1 / 2 5 4 y • 6(5) 1 / 2 r £) cos((Jt)=hu c o s ( u t ) (2.4) rf n e E The magnitude o f t h e t r a n s i t i o n moment depends on whi c h t r a n s i t i o n i s b e i n g e x c i t e d . F o r example t h e r a t i o o f t h e t r a n s i t i o n moments f o r t h e Am=±l t r a n s i t i o n s between t h e t h r e e l o w e s t energy s t a t e s o f 2.3a i s ( 1 0 / 6 ) 1 / 2 . F o r r e a l i s t i c v a l u e s o f B and S 4 A t h e e f f e c t i v e t r a n s v e r s e n u c l e a r moment can e a s i l y be 50 t i m e s t h e b a r e n u c l e a r moment. (The enhanced t r a n s v e r s e n u c l e a r moment has i m p o r t a n t p r a c t i c a l i m p l i c a t i o n s as i t g r e a t l y r e d u c e s t h e r f power needed f o r t h e e x p e r i m e n t s . N i n e t y degree p u l s e t i m e s o f 150ns a r e common a l l o w i n g t h e a p p l i c a t i o n o f s i m p l e p u l s e d NMR t e c h n i q u e s t o re s o n a n c e l i n e s o f l a r g e w i d t h ) . I f t h e r e a r e o t h e r n u c l e a r s p i n s i n t e r a c t i n g w i t h 5 4Mn n u c l e i t h r o u g h a magnetic d i p o l e i n t e r a c t i o n t h e s t r e n g t h o f t h e t r a n s v e r s e terms f o r t h i s c o u p l i n g w i l l a l s o be enhanced. F o r a 5 4 M n 2 + i m p u r i t y p r e s e n t i n an i n s u l a t i n g m a g n e t i c l a t t i c e t h e o r d e r i n g f i e l d f o r t h e moment has t h r e e s o u r c e s . There i s t h e exchange c o u p l i n g t o t h e ma g n e t i c l a t t i c e , t h e Zeeman c o u p l i n g t o t h e e x t e r n a l f i e l d , and t h e f o r c e s due t o a n i s o t r o p i c c r y s t a l f i e l d i n t e r a c t i o n s . F o r a two s u b l a t t i c e e asy a x i s c o l l i n e a r a n t i f e r r o m a g n e t w i t h t h e m a g n e t i c f i e l d a p p l i e d a l o n g t h e easy a x i s , t h e e x p r e s s i o n s f o r t h e energy d i f f e r e n c e between a d j a c e n t l e v e l s o f t h e l o w e s t h y p e r f i n e Q m u l t i p l e t a r e 14 E -5/2,m+1 - E -5/2,m = - ( 5 / 2 ) 5 4 A - 5 V B h + (l+2m)P n a + ( 5 / 2 ) 5 4 A 2 m (2.5a) g u b ( B £ + B a+ 4D/g E 5/2,m-1 - E 5/2,111 = - (5/2) 5 4 A + 5 4y B h + (l-2m)P n a ( 5 / 2 ) S 4 A 2 m (2.5b) g U b ( B £ - Ba+ 4D / g U f a ) E q u a t i o n 2.5a i s f o r t h e s u b l a t t i c e w i t h n e t moment p a r a l l e l t o t h e e x t e r n a l f i e l d and 2.5b i s f o r t h e s u b l a t t i c e w i t h n e t moment a n t i p a r a l l e l . The parameter D i s a c r y s t a l f i e l d p a r a m eter, P i s an e l e c t r i c q u a d r u p o l e i n t e r a c t i o n parameter and t h e e f f e c t i v e exchange f i e l d B e depends on t h e magnitude and s i g n o f t h e exchange i n t e r a c t i o n s between t h e i m p u r i t y e l e c t r o n i c moment and t h e n e i g h b o r i n g s p i n s o f t h e a n t i f e r r o m a g n e t , and a l s o on t h e e q u i l i b r i u m c o n f i g u r a t i o n o f t h e s e s p i n s . I f t h e i m p u r i t y i s 5 4 M n 2 + i n a 5 5Mn 2* i n s u l a t i n g magnet t h e n a mean f i e l d H a m i l t o n i a n s i m i l a r t o e q u a t i o n 2.1 i s n o t a p p r o p r i a t e f o r c a l c u l a t i n g t h e wave f u n c t i o n s o f t h e i m p u r i t y h o s t system because s t r o n g c o u p l i n g e x i s t s between t h e i m p u r i t y e l e c t r o n i c moment and t h e h o s t magnetic l a t t i c e . I n t h i s c a s e t h e e l e c t r o n i c components o f t h e n u c l e a r wave f u n c t i o n must be e x p r e s s e d i n terms o f el e m e n t a r y e x c i t a t i o n s o f t h e complete m a g n e t i c l a t t i c e . The e l e c t r o n i c component o f t h e 5 4Mn n u c l e a r wave f u n c t i o n s become d i s t r i b u t e d i n space i n a way w h i c h depends l a r g e l y on t h e bandwidth and gap o f t h e e l e m e n t a r y 15 >- 0.96 CO LU 0.92 Q LU ixi 0.88 o 0.84 N* 499 502 505 508 511 514 FREQUENCY (MHZ) 517 F i g u r e 2.1: The A x i a l NMRON Spectrum o f t h e A n t i f e r r o m a g n e t i c Phase o f MnCl 2.4H 20 T h i s f i g u r e shows t h e s i x pseudoquadrupole s p l i t Am±l re s o n a n c e l i n e s o f 5 4Mn o r i e n t e d i n MnCl 2.4H 20. The s p l i t t i n g s and res o n a n c e f r e q u e n c i e s a r e g i v e n by e q u a t i o n s 2.5a and 2.5b. T h i s s p e c t r u m i s t h e a x i a l spectrum r e c o r d e d u s i n g a d e t e c t o r w h i c h i s c o - a x i a l w i t h t h e n u c l e a r s p i n q u a n t i s a t i o n a x i s . T t i s l o n g as can be seen from t h e s l o w r e l a x a t i o n o f t h e a n i s o t r o p y f o l l o w i n g each r e s o n a n c e . The s i g n o f t h e a n i s o t r o p y change a t each t r a n s i t i o n can be c a l c u l a t e d u s i n g e q u a t i o n 2.20a (see page 2 3 ) . 16 >-r— I—i CO UJ r— • — i Q UJ 1.055 1.045 1.035 1.025 cr 1.015 -CrT O 1.005 h 499.0 501.0 503.0 505.0 FREQUENCY (MHZ) F i g u r e 2.2: The E q u a t o r i a l NMRON Spectrum o f t h e A n t i f e r r o m a g n e t i c Phase o f MnCl .4H O 2 2 T h i s f i g u r e shows t h e s i x pseudoquadrupole s p l i t Am±l re s o n a n c e l i n e s o f 5 4Mn o r i e n t e d i n MnCl 2.4H 20. The s p l i t t i n g s and reso n a n c e f r e q u e n c i e s a r e g i v e n by e q u a t i o n s 2.5a and 2.5b. T h i s s p ectrum i s an e q u a t o r i a l spectrum r e c o r d e d u s i n g a d e t e c t o r mounted p e r p e n d i c u l a r t o t h e n u c l e a r s p i n q u a n t i s a t i o n a x i s and l e v e l w i t h t h e sample. The s i g n o f t h e a n i s o t r o p y change a t each t r a n s i t i o n c an be c a l c u l a t e d from e q u a t i o n 2.20b. Note t h a t t h e r e i s z e r o change on t h e e q u a t o r i a l a n i s o t r o p y on s a t u r a t i n g t h e -3 t o -2 t r a n s i t i o n . 17 e x c i t a t i o n spectrum o f t h e magnetic l a t t i c e (see s e c t i o n 2.5). I n f i g u r e 2.1 and f i g u r e 2.2 t h e s i n g l e quantum, (Am=±l), CW NMRON spectrum o f 5 4Mn o r i e n t e d i n t h e ma g n e t i c l a t t i c e o f MnCl 2.4H 20 i s shown. These p i c t u r e s a r e an example o f t h e c l a s s i c NMRON l i n e s h a p e a r i s i n g from a p o l a r i s e d 5 4 M n 2 + i m p u r i t y when t h e n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t i m e i s e x c e e d i n g l y 9 l o n g . 2.3 S p i n Dynamics and y-Ray D e t e c t e d NMR The most g e n e r a l approach f o r c a l c u l a t i n g t h e e q u a t i o n s o f mo t i o n o f an i s o l a t e d 5 4Mn n u c l e a r s p i n under an a r b i t r a r y n u c l e a r s p i n H a m i l t o n i a n i n v o l v e s t h e s o l u t i o n o f L i o u v i l l e ' s 1 0 e q u a t i o n f o r a 7*7 d e n s i t y m a t r i x p ( T ) . A complete d e s c r i p t i o n o f t h e t i m e b e h a v i o r o f p(T) r e q u i r e s t h e knowledge o f t h e t i m e e v o l u t i o n o f t h e 48 independent components o f t h e d e n s i t y m a t r i x . F o r t u n a t e l y i n t h e e x p e r i m e n t s d e s c r i b e d i n c h a p t e r s 4 and 5 t h e use o f s i n g l e and do u b l e quantum s e l e c t i v e e x c i t a t i o n s e q u e n c e s 1 1 a l l o w a g r e a t s i m p l i f i c a t i o n o f t h i s d e s c r i p t i o n . A s e l e c t i v e e x c i t a t i o n sequence o n l y c o u p l e s two o f t h e l e v e l s o f t h e h y p e r f i n e m u l t i p l e t , and f o r t i m e s much s h o r t e r t h a n T t h e e v o l u t i o n o f t h e s p i n system f o l l o w i n g a t w o - l e v e l s e l e c t i v e e x c i t a t i o n sequence can be a d e q u a t l y t r e a t e d i n terms o f a f i c t i t i o u s s p i n - 1 / 2 system. The dynamics o f a two l e v e l system under a sequence o f r f p u l s e s i s d i s c u s s e d i n many p l a c e s and t h e f o r m a l i s m used i s a minor g e n e r a l i z a t i o n o f t h e s p i n o r 12 r o t a t i o n f o r m a l i s m The d e n s i t y m a t r i x a p p r o p r i a t e t o t h e f i c t i t i o u s s p i n 1/2 i s a 2*2 s u b m a t r i x o f p(T) d e f i n e d by 18 o-(T) = p ( T ) A ( T ) m+n n+m,m A ( T ) p ( T ) m,n+m m ( 2 . 6 ) H e r e p a n d p a r e t h e f r a c t i o n a l p o p u l a t i o n s o f t h e t w o e n e r g y l e v e l s c o u p l e d b y t h e s e l e c t i v e e x c i t a t i o n p u l s e , a n d t h e c o m p o n e n t s A ( T ) a n d A (T) a r e o f f - d i a g o n a l c o m p o n e n t s c x n , n + m ' n + m , n o f t h e f u l l d e n s i t y m a t r i x . T h e s e c o m p o n e n t s r e p r e s e n t a c o h e r e n t s u p e r p o s i t i o n o f t h e s t a t e s |m+n> a n d |n>. A s e l e c t i v e e x c i t a t i o n s e q u e n c e r e l i e s u p o n t h e f r e q u e n c y o f t h e t r a n s i t i o n o f i n t e r e s t b e i n g d i f f e r e n t f r o m t h a t o f a l l o t h e r t r a n s i t i o n s . I n t h e s y s t e m s s t u d i e d h e r e s e l e c t i v i t y i s a c h i e v e d b e c a u s e t h e Am=±l t r a n s i t i o n s a l l h a v e d i f f e r e n t f r e q u e n c i e s d u e t o t h e p s e u d o q u a d r u p o l e i n t e r a c t i o n . I t i s a l s o a n i m p o r t a n t r e q u i r e m e n t f o r s e l e c t i v i t y t h a t t h e s t r e n g t h o f t h e r f f i e l d , h w E , s h o u l d be s m a l l c o m p a r e d t o t h e e n e r g y d i f f e r e n c e b e t w e e n t h e t r a n s i t i o n b e i n g e x c i t e d a n d t h a t o f t h e o t h e r t r a n s i t i o n s . A n o t h e r e x a m p l e o f s e l e c t i v e e x c i t a t i o n i s t h e u s e o f a P i n e s " S o f t D o u b l e Quan tum P u l s e 1 1 " t h a t s e l e c t i v e l y e x c i t e s a t r a n s i t i o n b e t w e e n t h e m=-3 l e v e l t o t h e m = - l l e v e l o f t h e h y p e r f i n e m u l t i p l e t . T h i s i s a n NMRON e f f e c t o b s e r v e d f o r t h e f i r s t t i m e . T h e t h r e e l o w e s t e n e r g y l e v e l s i n e q u a t i o n 2 . 3 a h a v e t h e l e v e l s t r u c t u r e s h o w n i n f i g u r e 2 . 3 . I n t h e s o f t d o u b l e q u a n t u m p u l s e e x c i t a t i o n m e t h o d t h e y a r e s u b j e c t t o a t r a n s v e r s e o s c i l l a t i n g r f f i e l d w i t h a f r e q u e n c y , C J q , w h i c h i s o n e h a l f o f t h e s e p a r a t i o n o f t h e m=-3 a n d m = - l l e v e l s . T h e r e a r e t w o s i n g l e q u a n t u m t r a n s i t i o n s f o r w h i c h Am±l a t t h e f r e q u e n c i e s UQ- A a n d 19 I-1> *—*— I -2> |-3> F i g u r e 2.3: S e l e c t i v e S i n g l e and Double Quantum P u l s e Sequences T h i s f i g u r e shows t h e bottom t h r e e l e v e l s o f t h e 5 4Mn h y p e r f i n e m u l t i p l e t ( e q u a t i o n 2.3a). The dashed arrows r e p r e s e n t s i n g l e quantum t r a n s i t i o n s w i t h f r e q u e n c i e s UQ+ A and w -A, and t h e s o l i d arrow r e p r e s e n t s a two quantum t r a n s i t i o n o f f r e q u e n c y 2CJ . o 20 uQ+ A and when t h e s t r e n g t h o f t h e r f f i e l d w £ » A t h e major e f f e c t o f t h e i r r a d i a t i n g p u l s e i s t h e c r e a t i o n o f c o h e r e n t s u p e r p o s i t i o n s o f a d j a c e n t l e v e l s . I n t h e language o f M u l t i p l e Quantum NMR such s u p e r p o s i t i o n s o f s t a t e s a r e termed S i n g l e Quantum Coherence. When t J E < < A t h e s e f i r s t o r d e r , Am=±l, p r o c e s s e s become nonresonant and t h e i r r a d i a t i o n can o n l y produce a s m a l l component o f s i n g l e quantum co h e r e n c e from an i n i t i a l t h e r m a l e q u i l i b r i u m d e n s i t y m a t r i x . F o r t h i s s i t u a t i o n t h e dominant e f f e c t o f t h e i r r a d i a t i o n i n v o l v e s a r e s o n a n t , second o r d e r , two photon p r o c e s s w h i c h c o u p l e s t h e l e v e l |-3> t o t h e l e v e l | - 1 > - Such i r r a d i a t i o n i n d u c e s o r d e r i n t h e d e n s i t y m a t r i x p ( t ) w h i c h i s two o f f t h e d i a g o n a l and c a l l e d two quantum coher e n c e . I n t h e s m a l l ^A" 1 l i m i t i r r a d i a t i o n a t a f r e q u e n c y UQ can be t r e a t e d as an e f f e c t i v e i n t e r a c t i o n w h i c h c o u p l e s l e v e l s s e p a r a t e d by Am±2 and t h e m i d d l e m=-2 l e v e l , |-2>, may be i g n o r e d . The dynamics o f t h e s p i n system has been r e d u c e d t o t h a t o f an e f f e c t i v e two l e v e l system d e s c r i b e d by cr(t) w i t h m=-3 and m+n=-l. A c o n v e n i e n t o p e r a t o r b a s i s f o r t h e c a l c u l a t i o n o f t h e b e h a v i o r o f cr(t) under b o t h s i n g l e and d o u b l e quantum e x c i t a t i o n s i s p r o v i d e d by t h e P a u l i m a t r i c e s 0 1 0 - i 1 0 1 0 cr = y i 0 cr = z 0 -1 (2.7) F o r monochromatic s e l e c t i v e e x c i t a t i o n s o f f r e q u e n c y UQ and s t r e n g t h to E i t i s c o n v e n i e n t t o make t h e u s u a l t r a n s f o r m a t i o n t o a r e f e r e n c e frame r o t a t i n g about t h e q u a n t i s a t i o n a x i s w i t h a 21 f r e q u e n c y <Jq . The r o t a t i n g frame t r a n s f o r m a t i o n i s d e f i n e d by U = e x p ( - i (j o- t ) U exp( i (J <r t ) (2.8) r f ^ v 0 z ' lab r * 0 z ' where U i s a r o t a t i n g frame o p e r a t o r and U i s a l a b frame r f lab o p e r a t o r . The r o t a t i n g frame s p i n H a m i l t o n i a n d e s c r i b i n g e v o l u t i o n under a s e l e c t i v e p u l s e o f c o n s t a n t a m p l i t u d e w h i c h c o u p l e s .the s t a t e s |m> t o |m+n> i s g i v e n by H = finer + hcj cr cos(tf ) + hu> cr sin ( t f ) (2.9) r f z E x p E y P The a n g l e (# ) i s t h e phase o f t h e e x c i t a t i o n p u l s e r e l a t i v e t o p a s t a b l e r e f e r e n c e o f f r e q u e n c y UQ and f o r a l l sequences used i n t h e e x p e r i m e n t s and i n t h e f o l l o w i n g e x p r e s s i o n s & p = 0-P r e c e s s i o n a l m o t i o n due t o t h e e x c i t a t i o n p u l s e o c c u r s a t a fr e q u e n c y (J and f o r a s i n g l e quantum e x c i t a t i o n p u l s e a> depends on t h e s t r e n g t h o f t h e r f f i e l d and t h e t h e t r a n s i t i o n moment o f t h e e x c i t e d l e v e l s . F o r a system o f t h r e e e q u a l l e v e l s w i t h u n e q u a l t r a n s i t i o n moments t h e r e l a t i o n s h i p between s i n g l e and d o u b l e quantum f r e q u e n c i e s f o r p r e c e s s i o n i n t h e e f f e c t i v e r f f i e l d i s W E ° = 1 ( d E 2 a ) E f ^ ) " 1 (2.10) where w^0 i s t h e d o u b l e quantum p u l s e p r e c e s s i o n f r e q u e n c y , 1 U E i s t h e s i n g l e quantum p r e c e s s i o n f r e q u e n c y o f one p a i r o f l e v e l s and 2w E i s t h e s i n g l e quantum p r e c e s s i o n f r e q u e n c y o f t h e o t h e r p a i r . 22 The result of applying a selective pulse of length T to the nuclear spin described by an i n i t i a l f i c t i t i o u s spin 1/2 density matrix <r(0) i s c(Tl)= exp(-i/h H^T^ cr(0) exp( i/h H r fT t) = Qf <r(0) Qi (2.11) where Q* i s the Hermitian conjugate of Q and the matrix Q has elements given by a 0 • • 0 a (2.12) a = cos( 1/2 u T ) - i costf sin( 1/2 u T ) 1 v ' e i ' c v ' e \' |3 = - i sin i? sin(l/2 <J T ) i c e i . 2, ^2.1/2 0) = ( (J + Q ) e E ' = tan" 1 ( u n"1) c E n = ( n - m ) u - u (2.13) v ' 0 n , m + n v ' the result of a sequence of n pulses i s o-(T) = Q o-(0) Q (2.14) with Q = Q, — Q = 1 n a -0 0 a (2.15) The populations at the end of a pulse sequence are given by 23 P(T) = a*a p(0) + /3*/3 p(0) m+n m+n m p(T) = /3*0 P(°> + a * a P(°) m m m+ n m (2.16a) (2.16b) The use o f s e l e c t i v e p u l s e s has e n a b l e d t h e d e s c r i p t i o n o f s p i n dynamics t o be r e d u c e d t o a f i c t i t i o u s m a g n e t i s a t i o n v e c t o r p r e s s e s s i n g around an e f f e c t i v e m agnetic f i e l d . The g e n e r a l form f o r t h e a n i s o t r o p i c p a r t i c l e d i s t r i b u t i o n f u n c t i o n s a r i s i n g from t h e decay o f o r d e r e d r a d i o a c t i v e s p i n systems has been d i s c u s s e d (Chapter 2 o f r e f . 2 ) . F o r 5 4Mn o r i e n t e d i n an o r d e r e d magnet w i t h c o l l i n e a r s u b l a t t i c e s t h e gamma r a y i n t e n s i t y , n o r m a l i z e d t o t h e i s o t r o p i c y - r a y c o u n t , a t . 1 3 an a n g l e (tf) t o t h e o r d e r i n g a x i s i s W(tf) = E T? B U F P (costf) (2.17) v ' ^ k k k k k v ' v ' k The sum o v e r k o n l y i n c l u d e s k even, U^F^are p a r a m e t e r s r e l a t e d t o r a d i o a c t i v e decay, P (costf) a r e Legendre p o l y n o m i a l s , TJ i s a d e t e c t o r dependent s o l i d a n g l e c o r r e c t i o n and B^ a r e t h e o r i e n t a t i o n p a r a m e t e r s w h i c h a r e d e f i n e d by B = I (2k+l) C(I , k,I : m,0) p (2.18) k m m where C(I,k,I:m 90) a r e Clebsh-Gordan c o e f f i c i e n t s and t h e p a r e t h e d i a g o n a l elements o f p ( t ) . F o r S 4Mn, W(tf) i s g i v e n by 24 W(tf)=l-0.495 B 2P 2COS(#)- 0.447 B 4P 4COS(#) (2.19) E q u a t i o n 2.17 assumes t h a t t h e n u c l e a r s p i n ensemble p o s s e s s a x i a l symmetry about t h e l o c a l e l e c t r o n i c q u a n t i s a t i o n a x i s ; most measurements i n t h i s t h e s i s have an a x i a l l y symmetric t h e r m a l e q u i l i b r i u m n u c l e a r s p i n s t a t e and t h e gamma r a y c o u n t i n g t i m e s a r e much l o n g e r t h a n t h e s p i n p r e c e s s i o n p e r i o d making t h e use o f e q u a t i o n 2.17 a p p r o p r i a t e . The e x p r e s s i o n o f t h e a n i s o t r o p y p a t t e r n s i n terms o f g e n e r a l o r i e n t a t i o n t e n s o r s i s v e r y u s e f u l when a complete d y n a m i c a l d e s c r i p t i o n o f t h e n u c l e a r s p i n ensemble i s n e c e s s a r y . F o r p u l s e d NMRON ex p e r i m e n t s e m p l o y i n g s e l e c t i v e e x c i t a t i o n methods i t i s much more c o n v e n i e n t t o e x p r e s s W(tf) i n terms o f t h e n o r m a l i z e d p o p u l a t i o n s . The n o r m a l i z e d r - r a y i n t e n s i t y i n t h e a x i a l , tf=0, and e q u a t o r i a l I>=TT/2, d i r e c t i o n s i s The t i m e dependence o f t h e a n i s o t r o p y i n each o f t h e s e d i r e c t i o n s f o l l o w i n g a p u l s e sequence o r d u r i n g s p i n l a t t i c e r e l a x a t i o n c a n be c a l c u l a t e d by s u b s t i t u t i n g t h e v a l u e s o f p m o b t a i n e d from e q u a t i o n 2.16 o r e q u a t i o n 2.21 i n t o e q u a t i o n s 2.20. One u s e f u l f a c t about u s i n g b o t h t h e s i n g l e and d o u b l e quantum e x c i t a t i o n t e c h n i q u e s f o r p u l s e d NMRON on t h e 5 4Mn W(0 ) = l - ( p 3 + p _ 3 ) + 0.667(p 2+p_ 2)+ 0.333(p i+p_ 1) (2.20a) W(Tr / 2)=l+0.25(p 3+p_ 3)+0.25(p 2+p_ 2) - 0.25(p i+p_ i) - 0.5 p Q (2.20b) 25 system can be seen from equation 2.20a and 2.20b. Each method has i t s own signature; for example the single quantum pulse applied to the m=-3 to m=-2 t r a n s i t i o n changes only the a x i a l anisotropy, while a soft double quantum pulse coupling the |-3> state with the | -1> state changes both the equatorial and the a x i a l anisotropy. This observation forms an excellent diagnostic t o o l f o r set t i n g up pulse sequences and adjusting the strength of the applied r f f i e l d . 2.4 Spin L a t t i c e Relaxation 5 4Mn nuclear s p i n - l a t t i c e relaxation involves the transfer of energy between the nuclear spin hyperfine r e s e r v o i r and the thermal r e s e r v o i r formed by the l a t t i c e degrees of freedom. A coupling i n t e r a c t i o n H' f l i p s the nuclear spin between eigenstates of the s t a t i c hyperfine Hamiltonian and causes a simultaneous energy conserving change i n the state of the l a t t i c e . The e f f e c t i v e strength of H' must be weak compared to both the strength of the i n t r a - l a t t i c e interactions and the strength of the s t a t i c spin Hamiltonian, i f these conditions are s a t i s f i e d the relaxation process may be considered as a sum of uncorrelated processes involving a single f l i p of the nuclear spin between the nuclear hyperfine l e v e l s with a corresponding t r a n s i t i o n i n the l a t t i c e state. When the i n t e r n a l dynamics of the l a t t i c e occurs on a time scale much shorter than the nuclear spin precession times, termed the short c o r r e l a t i o n time l i m i t , memory of the l a t t i c e state a f t e r the relaxation process i s rap i d l y l o s t and the equations describing the time behavior of 26 the nuclear spin level populations reduce to a simple master equation: m m+1 m + l , m m m,m+l m m - 1 m-1 m-l,m The relaxation processes considered only connect states differing by Am=±l. Q are the transition rates from an energy m , n level m to an energy level n and can be defined in terms of a transition probability w"" and the latt i c e temperature TL by equations 2.22 Q m n = E W i r = ( 2 T r / h ) E | <n f I H' I im>| 28(E- E f -0) o n ) (2.22a) i f i f Om m 1 = Q m 1 « exp(AE/kT ) AE = E E m _ m m—1 (T ) _ 1= (I-m)(I+m+1)(2Q ) 1 m , m+1 (2.22b) (2.22c) (2.22d) In equation 2.22a i and f refer to i n i t i a l and f i n a l states of the la t t i c e and the sum is over a l l possible i n i t i a l and f i n a l states consistent with total energy conservation and the thermal state of the lat t i c e . For a given pair of nuclear spin states |m> and |m-l> the ratio of the upward transition rate to the downwards rate i s defined according to equations 2.22b and 2.22c. This ensures that the spin levels approach a state of thermal equilibrium defined by the lattice temperature T . The 27 s p i n - l a t t i c e r e l a x a t i o n r a t e d e f i n e d i n e q u a t i o n 2.22d i s an m-independent measure o f t h e r e l a x a t i o n p r o c e s s and i t c h a r a c t e r i s e s d y n a m i c a l p r o c e s s e s o f t h e l a t t i c e . To be c o n s i d e r e d an e f f e c t i v e s o u r c e o f s p i n - l a t t i c e r e l a x a t i o n , a t h e r m a l b a t h must c o u p l e t o t h e n u c l e a r s p i n d egrees o f freedom v i a an i n t e r a c t i o n w h i c h does n o t commute w i t h t h e s t a t i c s p i n H a m i l t o n i a n and i t s t h e r m a l m o t i o n s must modulate t h e c o u p l i n g a t t h e n u c l e a r r e s o n a n c e f r e q u e n c y . F o r a 5 4 M n 2 + i m p u r i t y moment t h e major n u c l e a r s p i n c o u p l i n g i s t h e i s o t r o p i c h y p e r f i n e i n t e r a c t i o n w h i c h i s g i v e n f o r a s p i n 1^ a t 14 s i t e 1 by H = AI«S = A I Z S 2 + A / 2 ( I + S " + I " S + ) (2.23) i i i i l ' v i i l l ' v '• When t h e e l e c t r o n i c moment i s h i g h l y p o l a r i z e d , <S >«S and z most o f t h e h y p e r f i n e f i e l d i s s t a t i c . S m a l l t h e r m a l m o t i o n s , e q u a t i o n 2.24a, o f t h e e l e c t r o n i c s p i n cause a m o d u l a t i o n o f b o t h t h e l o n g i t u d i n a l h y p e r f i n e i n t e r a c t i o n ( e q u a t i o n 2.24b) and t h e o f f - d i a g o n a l h y p e r f i n e i n t e r a c t i o n , ( e q u a t i o n 2.24c) S S ^ t ) = S ^ t ) - <S t> SH*(t) = AI*» S S * ( t ) SH*(t) = 5 4A/2 ( I + 6 S ; ( t ) + (2.24a) (2.24b) I + 5 S ~ ( t ) ) (2.24C) Here SS ( t ) i s t h e d e v i a t i o n o f t h e e l e c t r o n i c s p i n from t h e t h e r m a l e q u i l i b r i u m v a l u e , and t h e magnitude and power spectrum o f t h e s e d e v i a t i o n s w i l l depend on t h e c o u p l i n g o f t h e 28 e l e c t r o n i c s p i n t o t h e s u r r o u n d i n g s and t h e f l u c t u a t i o n spectrum o f t h e t h e r m a l b a t h . 5H*(t) governs p r o c e s s e s w h i c h cause a l o s s o f ensemble phase coherence f o r o f f - d i a g o n a l e l ements o f t h e ± s p i n d e n s i t y m a t r i x , i . e . T 2 p r o c e s s e s . SEt(t) g o v e r n s p r o c e s s e s w h i c h cause b o t h T g p r o c e s s e s and s p i n - l a t t i c e r e l a x a t i o n . The s p i n - l a t t i c e r e l a x a t i o n r a t e can be e x p r e s s e d i n terms o f t h e F o u r i e r T r a n s f o r m o f an e l e c t r o n i c s p i n c o r r e l a t i o n f u n c t i o n f o r t h e ' t r a n s v e r s e f l u c t u a t i o n s o f t h e e l e c t r o n i c moment -CO (T ) - 1= 1/2 ( A / h ) 2 f c o s ( u t ) < { 5 S + ( t ) 5S"(0)}> d t (2.25) 1 J o n 1 1 Here <{5S*(t) SS~(0)}> i s t h e t h e r m a l average o f a symmetrised e l e c t r o n i c s p i n c o r r e l a t i o n f u n c t i o n w h i c h i s d e f i n e d by <{5S*(t)5S~(0)}>=< 5 S + ( t ) SS~(0)+ 5S~(t) SS*(0)}> (2.26) The v a l i d i t y o f 2.25 a l s o depends on t h e c o u p l i n g i n d u c i n g t h e r e l a x a t i o n b e i n g weak and average e l e c t r o n i c m o t i o n s b e i n g much f a s t e r t h a n t h e n u c l e a r s p i n m o t i o n s . The c o r r e l a t i o n f u n c t i o n can be e v a l u a t e d by e x p r e s s i n g t h e s i t e e l e c t r o n i c s p i n o p e r a t o r s i n terms o f eigenmodes o f t h e l a t t i c e . A more complete d i s c u s s i o n o f c a l c u l a t i n g t h e f l u c t u a t i o n s o f t h e e l e c t r o n i c moment a r e g i v e n f o r t h e case when t h e o u t s i d e w o r l d i s a ma g n e t i c i n s u l a t o r , b u t f i r s t t h e magnetic e x c i t a t i o n s p ectrum o f a f e r r o m a g n e t w i l l be d i s c u s s e d . 29 2.5 The Magne t i c E x c i t a t i o n s o f a Ferromagnet The systems s t u d i e d are a n t i f e r r o m a g n e t i c i n s u l a t o r s but the q u a l i t a t i v e and most o f the q u a n t i t a t i v e f e a t u r e s o f t h e NMRON r e s u l t s i n t h e s e systems can be u n d e r s t o o d i n terms o f t h e t h e o r y o f NMR i n an i n s u l a t i n g f erromagnet . The H a m i l t o n i a n f o r a 5 5 M n 2 + f e r r o m a g n e t i c s p i n a r r a y . . 5 4 . . . . 15 c o n t a i n i n g a s m a l l number o f Mn i m p u r i t i e s i s H = - T J S °S - T J S °S -T J S os -y hB T S 2 - y hB T S z J J 11 1 1 J J JJ J J , j 1J 1 J e a ^ 1 "e a ^ J - 5 5 y h B £ I z + 5 4 y hB £ I 2 + 5 5 A £ I o S + 5 4 A £ I oS, ( 2 . 2 7 ) n a 1 n a J i i j J 1 J 1 J The terms o f e q u a t i o n 2.27 r e p r e s e n t r e s p e c t i v e l y the n e a r e s t n e i g h b o r f e r r o m a g n e t i c exchange energy between t h e e l e c t r o n i c s p i n s , t h e e l e c t r o n i c Zeeman i n t e r a c t i o n w i t h an e x t e r n a l magnet i c f i e l d B a d i r e c t e d a l o n g the z - a x i s , t h e n u c l e a r Zeeman i n t e r a c t i o n o f 5 5 M n and 5 4 M n , the i s o t r o p i c S 5 M n h y p e r f i n e i n t e r a c t i o n f o r n u c l e i a t s i t e i w i t h c o u p l i n g c o n s t a n t 5 5 A , and f i n a l l y t h e S 4 M n h y p e r f i n e c o u p l i n g w i t h c o u p l i n g c o n s t a n t 5 4 A f o r 5 4 M n i o n s a t s i t e j . E q u a t i o n 2.27 i s an a p p r o x i m a t i o n s i n c e i t i g n o r e s a n i s o t r o p i c c o u p l i n g s between t h e e l e c t r o n s and t h e l a t t i c e , s p i n - s p i n magnet ic d i p o l e i n t e r a c t i o n s and n u c l e a r e l e c t r i c q u a d r u p o l e i n t e r a c t i o n s . A n i s o t r o p i c f o r c e s promote o r d e r i n g o f the magnet a l o n g a p r e f e r r e d a x i s o r i n a g i v e n p l a n e , and f o r a x i a l l y a l i g n e d magnets t h e s e f o r c e s g i v e r i s e t o a gap i n t h e e l e c t r o n i c spec trum. In the H a m i l t o n i a n o f e q u a t i o n 2 . 2 7 b o t h o f t h e s e e f f e c t s a r e produced by the Zeeman c o u p l i n g 30 t o t h e e x t e r n a l magnetic f i e l d and t h e p r o p e r t i e s o f a system d e s c r i b e d by 2.27 a r e s i m i l a r t o t h o s e o f t h e r e a l systems o f i n t e r e s t . F o r a r b i t r a r y v a l u e s o f t e m p e r a t u r e and e x t e r n a l m a g n e t i c f i e l d t h e problem o f f i n d i n g t h e e i g e n v a l u e s and e i g e n f u n c t i o n s o f e q u a t i o n 2.27 r e p r e s e n t a f o r m i d a b l e many-body c a l c u l a t i o n . However i f t h e te m p e r a t u r e i s much l o w e r t h a n t h e f e r r o m a g n e t i c o r d e r i n g t e m p e r a t u r e , and i f t h e e l e c t r o n i c Zeeman i n t e r a c t i o n i s much l a r g e r t h a n t h e n u c l e a r h y p e r f i n e i n t e r a c t i o n t h e s y s t e m a t i c p r o c e d u r e s o f L i n e a r S p i n Wave (LSW) t h e o r y 1 6 and low o r d e r p e r t u r b a t i o n t h e o r y i n t h e o f f - d i a g o n a l h y p e r f i n e i n t e r a c t i o n p r o v i d e t h e n e c e s s a r y t o o l s t o a t t a c k t h e problem. The a n a l y s i s o f t h e abundant s p i n systems i n e q u a t i o n 2.27, i . e . t h e e l e c t r o n i c s p i n s and t h e 5 SMn n u c l e a r s p i n s can be f u r t h e r s i m p l i f i e d by i g n o r i n g t h e 5 4Mn n u c l e i . The v a l i d i t y o f t h e a p p r o x i m a t i o n r e s u l t s from t h e 5 4Mn s p i n s b e i n g v e r y d i l u t e and t h e 5 4Mn n u c l e i b e i n g non-resonant w i t h t h e 5 5Mn system due t o t h e d i f f e r e n c e i n h y p e r f i n e f r e q u e n c i e s . W i t h t h i s a p p r o x i m a t i o n 2.27 becomes H = - I J S oS - y hB £ S * - 5 5 y h B £ I * + 5 5 A £ I °S (2.28) kl i k e a 1 n a 1 1 1 1 k 1 1 i The f i r s t s t e p i n s o l v i n g 2.28 i s t h e a p p l i c a t i o n o f LSW t h e o r y t o t h e e l e c t r o n i c H a m i l t o n i a n ; t h e p r o c e d u r e i s w e l l known arid o n l y b r i e f l y d e s c r i b e d h e r e f o r t h e purpose o f i n t r o d u c i n g n o t a t i o n . 17 U s i n g t h e H o l s t e m - P r i m a k o f f t r a n s f o r m a t i o n t h e s i t e - d e p e n d e n t s p i n o p e r a t o r s S a r e e x p r e s s e d i n terms o f 31 s i t e - d e p e n d a n t Bose o p e r a t o r s a^ and a^ as S* = ( 2 5 - a ' a ^ 1 / 2 a t (2.29a) S* = S - a*a t (2.29c) s; = a* ( 2 S - a * S i ) 1 / 2 (2.29b) [ 3 * 3 ^ = 5 ^ (2.29d) A t low t e m p e r a t u r e s t h e N e l e c t r o n i c s p i n s a r e a l m o s t c o m p l e t e l y o r d e r e d , i . e . <a*a >«0, and t h e t r a n s f o r m a t i o n can be l i n e a r i s e d l i by s e t t i n g <a a >=0 y i e l d i n g S += 2 S 1 / 2 a 4 (2.30a) a*=N~ 1 / 2£ a* e x p ( - i k o r i ) (2.30d) k S~ = 2 S 1 / 2 a * (2.30b) a = N 1 / 2 £ a f eexp( i k o r t ) (2.30e) = 2S (2.30c) [a a 1 = 6 L k k ' J k k ' (2.30f) I n (2.30d, e, f ) t h e i n d e x k r e f e r s t o one o f t h e N w a v e v e c t o r s from t h e f i r s t B r i l l o u i n zone o f t h e r e c i p r o c a l m a g n e t i c l a t t i c e . The e l e c t r o n i c H a m i l t o n i a n o f e q u a t i o n 2.29 i s l i n e a r i s e d by r e p l a c i n g t h e s p i n o p e r a t o r s w i t h t h e s i t e dependent Bose o p e r a t o r s as d e f i n e d by e q u a t i o n s 2.30a 2.30b and 2.30c, and t h e n s u b s t i t u t i n g t h e s p i n wave o p e r a t o r s 2.30d and 2.30e f o r a* and a . A f t e r d i s c a r d i n g terms w h i c h a r e n o t b i l i n e a r i n t h e s p i n wave o p e r a t o r s t h e f o l l o w i n g e x p r e s s i o n i s o b t a i n e d : 32 H = H + H ' (2.31a) o H = ( - y hB - A S ) I I , + I hto a a (2.31b) 0 n a " 1 k k k i k H ' = 5 5 A N _ 1 £ l * a * a e x p ( i ( k - k ' ) r ) + k * k i 5 5 A / 2 ( 2 S / N ) 1 / 2 I ( I j a * e x p ( i k o r j ) + ( I + a k e x p ( - i k o ^ ) ) ( 2 . 3 l c ) J k The f i r s t t e r m o f H q i s t h e sum o f t h e s t a t i c h y p e r f i n e i n t e r a c t i o n and t h e n u c l e a r Zeeman i n t e r a c t i o n , and i t pro d u c e s t h e b a s i c l e v e l s t r u c t u r e o f t h e 5 4Mn n u c l e a r s p i n energy l e v e l s . The second term i s a d i a g o n a l q u a d r a t i c form i n t h e s p i n wave o r magnon a n n i h i l a t i o n and c r e a t i o n o p e r a t o r s a* and a k . These o p e r a t o r s c r e a t e and d e s t r o y n o n - i n t e r a c t i n g Bose e x c i t a t i o n s o f t h e magnetic l a t t i c e w i t h Wave v e c t o r k and energy htd k. F o r t h e a x i a l l y symmetric f e r r o m a g n e t t h e s e e x c i t a t i o n s c a r r y a z - p r o j e c t i o n o f a n g u l a r momentum o f ±h. The s p e c t r a l p r o p e r t i e s o f t h e e l e c t r o n i c e x c i t a t i o n s o f t h e ferr o m a g n e t a r e d e s c r i b e d by t h e d i s p e r s i o n r e l a t i o n s h i p w k. As an example f o r a one d i m e n s i o n a l f e r r o m a g n e t w i t h n e a r e s t n e i g h b o r exchange we have ho = E + 2 I J I S ( 1 - c o s ( k a ) ) (2.32) k g 1 1 T h i s spectrum d e s c r i b e s a band o f e x c i t a t i o n s w i t h a bandwidth g i v e n by E = ho = 2JS and a gap o f E = ho = hy H S (see f i g u r e b b g 0 e 2.1) . 33 The e f f e c t s o f H' on t h e e l e c t r o n i c s p ectrum a r e s m a l l p r o v i d e d E » hio = 5 5 A S ; t h e t h e r m a l average h y p e r f i n e g n i n t e r a c t i o n s i m p l y adds a s m a l l term, dependent on t h e n u c l e a r p o l a r i s a t i o n , t o a l l s p i n wave e n e r g i e s , and t h e o f f - d i a g o n a l terms o f H' i n t r o d u c e s m a l l energy s h i f t s and admix a s m a l l n u c l e a r s p i n component i n t o t h e e l e c t r o n i c wave f u n c t i o n s . A l t h o u g h t h e p r o p e r t i e s o f t h e e l e c t r o n i c magnons a r e l i t t l e a f f e c t e d by t h e n u c l e a r s p i n s t h e same i s n o t t r u e f o r t h e r e v e r s e s i t u a t i o n . The p o l a r i s a b l e e l e c t r o n i c l a t t i c e p r o v i d e s a medium f o r t h e i n t e r a c t i o n o f n u c l e i a t d i f f e r e n t l a t t i c e s i t e s . 18 19 T h i s i n t e r a c t i o n , c a l l e d t h e Suhl-Nakamura ' (SN) i n t e r a c t i o n , i s a "second o r d e r i n d i r e c t i n t e r a c t i o n " i n w h i c h a n u c l e a r s p i n a t one l a t t i c e s i t e f l i p s e x c i t i n g a v i r t u a l magnon from t h e e l e c t r o n i c ground s t a t e which i s s u b s e q u e n t l y r e a b s o r b e d by a n u c l e a r s p i n a t a d i f f e r e n t l a t t i c e s i t e . The SN i n t e r a c t i o n can be e x p r e s s e d as an e f f e c t i v e H a m i l t o n i a n i n v o l v i n g o n l y t h e n u c l e a r s p i n s . The e f f e c t i v e H a m i l t o n i a n i s d e r i v e d from second 15 o r d e r p e r t u r b a t i o n t h e o r y i n H' and i s H = 1/2 T U I I " (2.33a) SN i j I J 1 J U = -SA 2/N I (ho ) _ 1 e x p ( i k ( r - r ) (2.33b) J k J A t low t e m p e r a t u r e t h e p o l a r i s a b i l i t y o f t h e m a g n e t i c l a t t i c e i s a n i s o t r o p i c ; i t i s l a r g e i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e o r d e r i n g a x i s and v e r y c l o s e t o z e r o i n a d i r e c t i o n p a r a l l e l t o t h e e l e c t r o n i c s p i n s . The f u l l e f f e c t i v e H a m i l t o n i a n f o r t h e 5 5Mn n u c l e a r s p i n s i n c l u d i n g t h e s t a t i c h y p e r f i n e i n t e r a c t i o n 34 and t h e Zeeman i n t e r a c t i o n i s g i v e n by 55 H= - 5 5 ( J n £ I * + 5 5A 2(S/2N ) E (ha> k) _ 1 I [ ( I x ) 2+ ( I * ) 2 ] (2.34a) U = 5 5 A 2 S / 2 N £ (h'w )" -1 (2.34b) h 5 5 w = ( 5 5 A S + hr B ) n n a ( 2 . 3 4 C ) The second term i n e q u a t i o n 2.34a d e s c r i b e s t h e v i r t u a l e m i s s i o n and r e a b s o r p t i o n o f magnons by t h e same n u c l e a r s p i n , and i s c a l l e d t h e magnetic pseudoquadrupole i n t e r a c t i o n . ( T h i s i n t e r a c t i o n has been d i s c u s s e d i n s e c t i o n 2.2). The i n t e r a c t i o n between two d i f f e r e n t s p i n s l o c a t e d a t s i t e s i and j i s e x p r e s s e d i n t h e f i n a l term o f 2.34a by U^, w i t h t h e upper l i m i t t o t h i s i n t e r - s p i n i n t e r a c t i o n s t r e n g t h b e i n g g i v e n by t h e s i n g l e s p i n pseudoquadrupole i n t e r a c t i o n U^ . I n a h i g h l y p o l a r i z e d , c o n c e n t r a t e d n u c l e a r s p i n system a n u c l e u s a t s i t e i f e e l s t h e e f f e c t s o f a h i g h l y c o r r e l a t e d sum o f t h e i n t e r a c t i o n s from many near n e i g h b o r s , and t h i s l e a d s t o f r e q u e n c y s h i f t s i n t h e e x c i t a t i o n spectrum g r e a t l y e x c e e d i n g t h o s e due t o t h e ps e u d o q u a d r u p o l a r s e l f - i n t e r a c t i o n . The r e s u l t i s t h a t t h e f i n a l t e r m o f e q u a t i o n 2.34a dominates when i s l o n g - r a n g e d and c o u p l e s many s p i n s a t d i f f e r e n t l a t t i c e s i t e s . F o r t h e d i l u t e , w e a k l y - c o u p l e d 5 4Mn n u c l e i t h e pseudoquadrupole i n t e r a c t i o n i s t h e dominant cause o f t h e s p l i t t i n g s i n t h e 35 r e s o n a n c e spectrum (see f i g u r e 2.2 and s e c t i o n 2.4). F o r t h e fe r r o m a g n e t t h e range f u n c t i o n U has an a p p r o x i m a t e a n a l y t i c f o r m 1 5 U(R ) = - AS 2(4TrhJSR ) _ 1 a exp( v 1 j ' x l y o c v b = a ( E b / E g ) 1 / 2 0 o R U = l r i - r j l Here a^ i s t h e mag n e t i c l a t t i c e s p a c i n g and r ^ a r e t h e p o s i t i o n v e c t o r s o f t h e n u c l e i and b Q i s t h e e f f e c t i v e range o f t h e i n t e r a c t i o n , see f i g u r e 2.1. A major f e a t u r e d e t e r m i n i n g t h e range i s t h e r a t i o o f t h e bandwidth o f t h e e l e c t r o n i c magnons t o t h e gap i n t h e magnon spectrum. I f t h i s r a t i o i s l a r g e t h e s c r e e n i n g l e n g t h f o r t h e p o l a r i z a t i o n i n d u c e d by t h e h y p e r f i n e i n t e r a c t i o n i s l o n g and t h e i n t e r a c t i o n i s l o n g - r a n g e d . I f t h e r a t i o i s s m a l l t h e d i s t o r t i o n o f t h e mag n e t i c l a t t i c e i s v e r y l o c a l and t h e i n t e r a c t i o n i s s h o r t - r a n g e d . From 2.35b t h e e x a c t range f u n c t i o n i s p r o p o r t i o n a l t o t h e F o u r i e r t r a n s f o r m o f (h ( J k ) " 1 . Note t h a t a n i s o t r o p y i n t h e magnon spectrum causes a n i s o t r o p y i n t h e range f u n c t i o n . A u s e f u l way t o d e r i v e t h e s p e c t r a l p r o p e r t i e s o f t h e abundant n u c l e a r s p i n system i s t o e x p r e s s t h e s i t e - d e p e n d e n t n u c l e a r s p i n o p e r a t o r s i n e q u a t i o n 2.34 i n terms o f t h e i r 20 F o u r i e r t r a n s f o r m s d e f i n e d by - b"XR ) (2.35a) (2.35b) (2.35c) 36 I * = Nf E i ; exp ( - i k o r i ) (2.36a) i 1+ = N " 1 / 2 E l | exp( + ikor t) (2.36b) I [ I " I*]= - N " 1 / 2 I Z (2.36c) q k k - q A f t e r making t h e a p p r o p r i a t e s u b s t i t u t i o n s e q u a t i o n 2.34 becomes 5 5H = - f i 5 5 t O n N 1 / 2 I z - 1/2 (h 5 5w^ 5A) E ( h w k) \ (2.37) n n k The n u c l e a r s p i n wave o p e r a t o r s I * a r e v e r y s i m i l a r t o t h e e l e c t r o n i c magnon o p e r a t o r s a f e and a f e and f o r low-mode occupancy t h e y w i l l obey Bose s t a t i s t i c s s i n c e t h e low t e m p e r a t u r e t h e r m a l e x p e c t a t i o n v a l u e o f 2.3 6c i s < [ ] > ; s 5 k q • T n e n u c l e a r magnon o p e r a t o r s a r e n o t e i g e n o p e r a t o r s o f 5 5 H as can be seen by c a l c u l a t i n g t h e i r e q u a t i o n s o f mo t i o n from t h e H e i s e n b e r g e q u a t i o n : I * = i / h [ 5 5H, I * ] (2.38) A f t e r c a r r y i n g o u t t h e a p p r o p r i a t e commutations one f i n d s 37 I * = - i n I * + iu> A N ' 1 / 2 V of 1 ( I z - <I Z >) I* (2.39a) k k k n u a s k-q k-q ' q 5 5 55. = (J (1 - A<I >/(J ) k n v i ' k' (2.39b) The e x c i t a t i o n s o f t h e 5 SMn n u c l e a r s p i n system can be r e g a r d e d as a s e t o f s p i n - w a v e - l i k e e x c i t a t i o n s c a l l e d n u c l e a r magnons w h i c h a r e c r e a t e d and d e s t r o y e d by a p p l y i n g t h e o p e r a t o r s I * t o t h e f u l l y p o l a r i s e d n u c l e a r ground s t a t e . The energy o f an e x c i t a t i o n w i t h wave v e c t o r k i s g i v e n by n^, and t h e l i f e t i m e i s d e t e r m i n e d by n u c l e a r magnon-nuclear magnon s c a t t e r i n g p r o c e s s e s d e s c r i b e d by t h e second t e r m o f 2.39a. From 2.39b i t can be seen t h a t t h e f r e q u e n c y o f a n u c l e a r magnon o f wave v e c t o r k i s p u l l e d by an amount w h i c h depends on t h e n u c l e a r p o l a r i z a t i o n <I Z >» a n d t h e energy o f t h e c o r r e s p o n d i n g e l e c t r o n i c magnon w i t h t h e same wave v e c t o r . As shown i n f i g u r e 2.4 t h e n u c l e a r magnon d i s p e r s i o n r e l a t i o n s h i p n^ shows t h e same k-dependent t r e n d s as t h e e l e c t r o n i c magnon d i s p e r s i o n r e l a t i o n s h i p , w i t h t h e w i d t h sn = 5 5 u 5 5 A <I > u (CJ ( w + (J ) ) _ 1 (2.40) n z b cj b g o f t h e e x c i t a t i o n band b e i n g d e t e r m i n e d by b o t h t h e gap and t h e bandwidth o f t h e e l e c t r o n i c magnon spectrum. The n u c l e a r magnon bandwidth i n c r e a s e s w i t h d e c r e a s i n g gap and f o r d e c r e a s i n g t e m p e r a t u r e . The dynamic p r o p e r t i e s o f t h e n u c l e a r s p i n system show a g r a d u a l change from t h e h i g h t e m p e r a t u r e regime w i t h c o mplete n u c l e a r s p i n d i s o r d e r when t h e e x c i t a t i o n s c o n s i s t o f 38 s i n g l e n u c l e a r s p i n f l i p s o f energy h 5 5 t o n , t o t h e low t e m p e r a t u r e regime where t h e n u c l e a r s p i n s a r e c o m p l e t e l y p o l a r i z e d by t h e h y p e r f i n e i n t e r a c t i o n , and t h e e x c i t a t i o n s a r e most a c c u r a t e l y d e s c r i b e d by n u c l e a r magnons w i t h e n e r g i e s s p r e a d o v e r a bandwidth g i v e n by e q u a t i o n 2.40. F i g u r e 2.4 shows t h e low t e m p e r a t u r e e x c i t a t i o n s p e c t r u m o f t h e 1 - D f e r r o m a g n e t . There a r e two e x c i t a t i o n b r a n c h e s : t h e h i g h f r e q u e n c y b r a n c h i s p r e d o m i n a n t l y e l e c t r o n - l i k e and has a d i s p e r s i o n r e l a t i o n s h i p <Jk; t h e low f r e q u e n c y b r a n c h has a l a r g e n u c l e a r component t o t h e e x c i t a t i o n wave f u n c t i o n and a d i s p e r s i o n r e l a t i o n s h i p fik. The e l e c t r o n i c e x c i t a t i o n s a r e * c r e a t e d by a p p l y i n g t h e o p e r a t o r c*k t o t h e o r d e r e d g r o u n d s t a t e (see e q u a t i o n 2.40a), and t h e n u c l e a r e x c i t a t i o n s a r e c r e a t e d by t h e o p e r a t o r /3fc a c t i n g on t h e g r o u n d s t a t e (see e q u a t i o n 2.40b) a*= a * c o s h ( 0 ) - l * s i n h ( 0 ) (2.41a) 0*= a k s i n h ( 0 ) - l k c o s h ( 0 ) (2.41b) t a n h ( 0 ) = - 2 F ( A k + B) _ 1 (2.41c) A =E - 2 J S ( l - c o s ( k a ) ) ; B=h 5 5cj ; F= 5 5 A ( < I Z > S ) 1 / 2 (2.41d) k g n» The s m a l l e l e c t r o n i c magnon component o f t h e n u c l e a r magnons l e a d s t o some r a d i c a l l y a l t e r e d p r o p e r t i e s such as an enhanced t r a n s v e r s e n u c l e a r m a g n e t i c moment o f t h e u n i f o r m n u c l e a r mode and a magnon medi a t e d c o u p l i n g t o o t h e r n u c l e i i n t h e sample. A t low t e m p e r a t u r e s t h e e x c i t a t i o n s o f b o t h b r a n c h e s obey Bose s t a t i s t i c s and t h e d i s p e r s i o n r e l a t i o n s h i p s f o r b o t h branches 3 9 CJ ( k ) k Figure 2.4: Magnetic E x c i t a t i o n Spectrum For A Ferromagnet The upper e x c i t a t i o n branch i s for the e l e c t r o n i c magnons and the lower branch i s f o r the nuclear magnons. Also shown i s the 5 4Mn resonance frequency 5 4CJ . The SN c o r r e l a t i o n radius B , n 0 the e l e c t r o n i c magnon gap CJ , the e l e c t r o n i c magnon bandwidth g CJ and the nuclear magnon bandwidth SQ. 4 0 have a f i n i t e gap. I n c l u s i o n o f magnon s c a t t e r i n g i n t e r a c t i o n s cause b o t h b r a n c h e s t o have a t h e r m a l f l u c t u a t i o n spectrum w h i c h e x t e n d s t o • . 5 4 z e r o f r e q u e n c y o f t e n w i t h s u f f i c i e n t power a t t h e Mn reso n a n c e f r e q u e n c y , 5 4 o , t o be a major cause o f 5 4Mn s p i n l a t t i c e n r e l a x a t i o n . 2.6 S p i n - L a t t i c e R e l a x a t i o n i n Ma g n e t i c I n s u l a t o r s H a v i n g d e s c r i b e d t h e s t r u c t u r e o f t h e r a d i o a c t i v e i m p u r i t y p robe and t h e e x c i t a t i o n s o f t h e h o s t l a t t i c e , t h e d i s c u s s i o n now t u r n s t o t h e mechanisms o f 5 4Mn s p i n - l a t t i c e r e l a x a t i o n i n mag n e t i c i n s u l a t o r s . The f i r s t r e l a x a t i o n p r o c e s s e s c o n s i d e r e d a r e t h o s e due t o t h e s c a t t e r i n g o f e l e c t r o n i c magnons v i a t h e h y p e r f i n e 21 i n t e r a c t i o n . The p a r t i c u l a r p r o c e s s e s o f i n t e r e s t a r e t h o s e w h i c h o c c u r i n systems where t h e gap i n t h e e l e c t r o n i c magnon spectrum i s much l a r g e r t h a n t h e l e v e l s p l i t t i n g s o f t h e probe n u c l e u s , i . e . E »h 5 4<j , and t h e l a t t i c e t e m p e r a t u r e i s such g n t h a t k b T L « E ^ . I n t h i s s i t u a t i o n t h e r e a r e v e r y few t h e r m a l l y e x c i t e d e l e c t r o n i c magnons and t h e r e l a x a t i o n p r o c e s s e s can be d e s c r i b e d i n terms o f a n u c l e a r s p i n f l i p w i t h t h e c o n c u r r e n t s c a t t e r i n g o f a s m a l l number o f magnons. The e l e c t r o n i c magnons o f t h e p r e v i o u s s e c t i o n a r e l i n e a r i s e d eigenmodes o f t h e e l e c t r o n i c H a m i l t o n i a n and t h e y do n o t i n t e r a c t w i t h each o t h e r w i t h i n t h e LSW a p p r o x i m a t i o n . The magnon s c a t t e r i n g i n t e r a c t i o n r e q u i r e d f o r t h e above r e l a x a t i o n p r o c e s s e s i s a c t u a l l y d e s c r i b e d by terms d i s c a r d e d i n t h e l i n e a r i s a t i o n p r o c e d u r e . A s i m p l e way t o r e - i n t r o d u c e t h e r e q u i r e d n o n - l i n e a r i t i e s i s t o 41 expand the e l e c t r o n i c spin variables of the impurity hyperfine i n t e r a c t i o n i n terms of the l i n e a r i s e d magnons. The r e s u l t of such a procedure f o r the i s o t r o p i c hyperfine i n t e r a c t i o n i s 54 lA I Z S Z = 5 4A I 4 Z ( S - N [ e x p ( i ( k - k ' J r , ) a ^ , ) (2.42a) 54 k (4SN) 1 I exp ( i ( k - k ' - k M ) r ) a a , a „ + . . . ] (2.42b) E q u a t i o n 2.42a i n d u c e s a T 2 p r o c e s s i n w h i c h an e l e c t r o n i c magnon s c a t t e r s o f f t h e n u c l e a r s p i n and modulates t h e s t r e n g t h of t h e s t a t i c h y p e r f i n e i n t e r a c t i o n . I n e q u a t i o n 2.42b o n l y t h e f i r s t two terms o f t h e e x p a n s i o n a r e shown. I n t h e f i r s t t e r m t h e n u c l e a r s p i n f l i p s c r e a t i n g an e l e c t r o n i c magnon and i t o n l y c o n t r i b u t e s t o r e l a x a t i o n when t h e magnon spectrum o v e r l a p s t h e n u c l e a r spectrum. The second term d e s c r i b e s a r e l a x a t i o n p r o c e s s i n v o l v i n g t h e s c a t t e r i n g o f t h r e e magnons and t h e f l i p o f a s i n g l e n u c l e a r s p i n . The second p r o c e s s can o c c u r even when t h e r e i s a l a r g e gap i n t h e magnon spectrum p r o v i d e d t h e magnon bandwidth i s s u f f i c i e n t l y wide t o a b s o r b t h e n u c l e a r s p i n f l i p e nergy. A r e l a x a t i o n mechanism i n v o l v i n g a two magnon Raman p r o c e s s i n w h i c h a t h e r m a l magnon o f wave v e c t o r k f l i p s a s p i n and becomes a magnon o f wave v e c t o r k' w i t h energy h u k = f i ( u k + 5 4 c t ) n ) , does n o t appear i n e q u a t i o n 2.38b. T h i s i s a r e s u l t o f t h e i m p u r i t y h o s t system h a v i n g a x i a l symmetry. I n t h i s c a s e t h e z - p r o j e c t i o n o f a n g u l a r momentum i s c o n s e r v e d and t h e Raman 42 p r o c e s s i s d i s a l l o w e d . In r e a l systems s m a l l d e p a r t u r e s from a x i a l symmetry a r e common so t h a t n o n - c o l l i n e a r i t y o f the e l e c t r o n i c and n u c l e a r q u a n t i s a t i o n axes o r e l e c t r o n n u c l e a r d i p o l e - d i p o l e i n t e r a c t i o n s a l l o w the Raman p r o c e s s e s t o o c c u r . The g e n e r a l form f o r a c o u p l i n g i n d u c i n g a Raman p r o c e s s i s H ; = a I ( I " a k a k , + I a ^ , ) (2.43) kk ' Here a i s a c o e f f i c i e n t de termined by the i n t e r a c t i o n which d e s t r o y s t h e a x i a l symmetry o f the sys tem, and f o r a Raman p r o c e s s e q u a t i o n 2 .22d becomes T ; 1 = 2rr/h a 2 I n (n f l ) S ( E ^ E - . o J (2.44) kk " Here n i s a Bose d i s t r i b u t i o n f u n c t i o n k n k = <a*a k> = ( exp / 3 E k - l ) _ 1 0= ( k ^ ) " 1 (2.45) The t emperature dependence o f the Raman p r o c e s s depends on t h e form o f t h e magnon d i s p e r s i o n r e l a t i o n s h i p s , and the r e l a t i v e magnitudes o f k T and the gap i n t h e magnon spec trum. F o r an a n t i f e r r o m a g n e t i c i n s u l a t o r , making t h e s m a l l k a p p r o x i m a t i o n f o r u and assuming T « T where k T =E , the k L A E b A E g . 14 t e m p e r a t u r e dependence o f the r e l a x a t i o n r a t e i s ( T j ) " 1 - C T 2 exp ( - T ^ T ^ 1 ) (2.46) 43 The c o n s t a n t C i s a parameter r e l a t e d t o t h e symmetry b r e a k i n g i n t e r a c t i o n s . A l l h i g h o r d e r magnon s c a t t e r i n g p r o c e s s e s e x h i b i t an e x p o n e n t i a l l y d i m i n i s h i n g c o n t r i b u t i o n t o t h e r e l a x a t i o n r a t e as T L approaches z e r o . T h i s i s s i m p l y a m a n i f e s t a t i o n o f t h e gap i n t h e e l e c t r o n i c e x c i t a t i o n spectrum w h i c h f o r b i d s d i r e c t r e l a x a t i o n p r o c e s s e s because o f energy c o n s e r v a t i o n . As t h e t e m p e r a t u r e d e c r e a s e s from T, = E k" 1, t h e t h e r m a l L g b f l u c t u a t i o n s o f t h e e l e c t r o n i c b a t h c e a s e , and t h e n e x t t h e r m a l r e s e r v o i r o f magn e t i c e x c i t a t i o n s w i t h a h i g h d e n s i t y o f s t a t e s and r e l a t i v e l y s t r o n g c o u p l i n g t o t h e 5 4Mn n u c l e i i s t h a t o f t h e 5 5Mn n u c l e a r magnons. R e l a x a t i o n t o n u c l e a r magnons i s c o m p l i c a t e d because, a t t h e t e m p e r a t u r e s o f i n t e r e s t , t h e occupancy o f a l l n u c l e a r magnon modes i s o f t h e o r d e r o f 1 and m u l t i p l e n u c l e a r magnon s c a t t e r i n g abounds. The s i m p l e s t r e l a x a t i o n p r o c e s s i n v o l v e s a 5 4Mn s p i n - f l i p w i t h t h e c r e a t i o n o f a n u c l e a r magnon |k>. The e x c e s s energy i s p r o v i d e d by m u l t i p l e s c a t t e r i n g o f t h e r m a l n u c l e a r magnons and t h e s e e v e n t s a r e d e s c r i b e d by t h e s c a t t e r i n g terms o f 2.39a . Whatever t h e e x a c t n a t u r e o f such a h i g h o r d e r r e l a x a t i o n p r o c e s s e s t h e major f a c t o r s d e t e r m i n i n g t h e r e l a x a t i o n r a t e w i l l be t h e r a t i o o f t h e n u c l e a r magnon bandwidth hSu t o t h e energy d i f f e r e n c e hAu=h( 5 4td - fi ) , and t h e s t r e n g t h o f t h e SN i n t e r a c t i o n . When n k 50., (see f i g u r e 2.4), i s s m a l l v e r y h i g h o r d e r s c a t t e r i n g p r o c e s s e s a r e n e c e s s a r y t o absorb t h e e x t r a energy and t h e s p i n l a t t i c e r e l a x a t i o n r a t e w i l l be c o r r e s p o n d i n g l y s m a l l . A f u r t h e r c o m p l i c a t i o n i n t h e t h e o r y o f d i r e c t 5 4Mn t o 5 SMn r e l a x a t i o n i s due t o t h e l o n g range o f t h e SN i n t e r a c t i o n . Each 5 4Mn n u c l e u s 44 i s c o u p l e d t o many 5 5Mn n u c l e i and t h e p r e s e n c e o f s t r o n g i n t e r a c t i o n s w i t h i n t h e S 5Mn s p i n system means t h a t t h e l o c a l f i e l d f l u c t u a t i o n s produced by d i f f e r e n t 5 5Mn s p i n s on a g i v e n 5 4Mn s p i n a r e s t r o n g l y c o r r e l a t e d . The r e l a x a t i o n r a t e f o r a 5 4Mn c o u p l e d t o t h e 5 5Mn s p i n b a t h t h r o u g h t h e SN i n t e r a c t i o n i s (by a n a l o g y w i t h e q u a t i o n 2.25) (T 1)~ 1=h~ 2j , 8°^ I U ^ I ^ t ) ! U * t r(0) c o s ( S 4 O n t ) d t (2.47) Terms o f 2.47 where i * j e x p r e s s t h e e f f e c t s o f c o r r e l a t e d m o t i o n o f d i f f e r e n t 5 5Mn s p i n s and when t h e dominant r e l a x a t i o n p r o c e s s e s i n v o l v e multimagnon s c a t t e r i n g t h e e v a l u a t i o n o f t h e r e l a x a t i o n r a t e from e q u a t i o n 2.47 becomes v e r y d i f f i c u l t . 5 4 M n - n u c l e a r magnon d i r e c t p r o c e s s r e l a x a t i o n i s p o s s i b l e i f t h e 5 4Mn n u c l e a r s p i n s a r e c o u p l e d t o a system c a p a b l e o f • . 54 • a b s o r b i n g t h e energy d i f f e r e n c e hAw = f i ( f i k ~ <*>n) and i n c h a p t e r 5 such a p r o c e s s i s d i s c u s s e d f o r t h e case when t h e o t h e r system i s a p r o t o n w i t h a Zeeman s p l i t t i n g e q u a l t o hAu. 5 4Mn r e l a x a t i o n p r o c e s s e s o p e r a t i v e a t T L = 0 i n v o l v e spontaneous e m i s s i o n r e l a x a t i o n e v e n t s , and such p r o c e s s e s must o c c u r between t h e s p i n and an e x c i t a t i o n o f energy h 5 4 o . I n n i n s u l a t o r s w i t h a l a r g e gap i n t h e magnon spectrum a good 22 c a n d i d a t e f o r such an e x c i t a t i o n i s a phonon , s i n c e t h e phonon s p e c t r a e x t e n d t o z e r o energy, a l b e i t t h a t t h e c o u p l i n g t o t h e s p i n s i s v e r y weak. An a p p r o p r i a t e form f o r t h e H a m i l t o n i a n i n d u c i n g a d i r e c t s p i n - f l i p phonon p r o c e s s g i v e n by 45 H = T r ( I + b +I~b*) (2.48) PH k k k v ' k Here b* and b k c r e a t e and d e s t r o y phonons, o f wave v e c t o r k and an energy e q u a l t o n t J k H , a n d * k i s a n e f f e c t i v e c o u p l i n g c o n s t a n t w h i c h i s d e t e r m i n e d by t h e i n t e r a c t i o n c o u p l i n g t h e n u c l e i t o t h e phonons. The phonon n u c l e a r c o u p l i n g may be due t o an e l e c t r i c q u a d r u p o l e i n t e r a c t i o n o r i t may o c c u r v i a an i n t e r m e d i a r y system such as t h e e l e c t r o n i c magnons. I n t h e l a t t e r c a s e t h e f u l l p r o c e s s i n v o l v e s t h e n u c l e a r s p i n f l i p p i n g c r e a t i n g , v i a t h e h y p e r f i n e i n t e r a c t i o n , a v i r t u a l magnon wh i c h t h e n decays t o a phonon v i a a m a g n e t o e l a s t i c c o u p l i n g . The e f f e c t i v e c o u p l i n g c o n s t a n t 7 k f o r t h e d i r e c t p r o c e s s H a m i l t o n i a n o f e q u a t i o n 2.48 can be c a l c u l a t e d by t h e same second o r d e r p e r t u r b a t i o n p r o c e d u r e s used t o d e r i v e t h e i n d i r e c t s p i n - s p i n c o u p l i n g o f e q u a t i o n 2.3 3a t h i s l e a d s t o t h e f o l l o w i n g 23 e x p r e s s i o n 1 * G 5 4 A ( u - 5 4 u ) _ 1 (2.49) k k v k n' v ' h e r e (*>k i s t h e energy o f t h e v i r t u a l i n t e r m e d i a t e magnon and i s a magnon phonon i n t e r a c t i o n c o n s t a n t w h i c h d e s c r i b e s t h e decay o f a magnon o f wave v e c t o r k i n t o a phonon o f t h e same wave v e c t o r . The number and wave v e c t o r s o f i n t e r m e d i a t e magnons i n v o l v e d i n t h e above d e s c r i b e d p r o c e s s depends on t h e p a r t i c u l a r phonons whose energy l i e s w i t h i n t h e 5 4Mn l i n e w i d t h . A n o t h e r way o f d e s c r i b i n g t h e above r e l a x a t i o n p r o c e s s i s as d i r e c t r e l a x a t i o n t o a mixed magnon phonon mode. The amount o f magnon admixed i n t o a phonon mode o f wave v e c t o r k w i l l be 46 p r o p o r t i o n a l t o r k ( 5 4 A ) - 1 and t h e d i r e c t r e l a x a t i o n r a t e t o 23 t h e s e low energy modes i s g i v e n by ( T i ) " 1 = C i (1+ ( e x p ( x ) - l ) " 1 ) (2.50a) x = ( h 5 4 u ) ( k T ) _ 1 (2.50b) n b L C = A 2 p ( 5 4 w ) h _ 1 (2.50c) 1 n Here A i s t h e s t r e n g t h o f t h e i n t e r a c t i o n c o u p l i n g t h e n u c l e a r s p i n s t o t h e c o u p l e d magnon phonon modes and p( 5 4w n) i s t h e d e n s i t y o f s t a t e s o f t h e s e modes a t t h e n u c l e a r r e s o n a n c e f r e q u e n c y . The d e s c r i b e d p r o c e s s i s b u t one o f many p o s s i b l e j o i n t magnon-phonon d i r e c t n u c l e a r s p i n r e l a x a t i o n p r o c e s s e s and i t i s r a r e l y t h e d o m i n a t i n g p r o c e s s . Other low l y i n g m a g n e t i c e x c i t a t i o n s such as t h o s e caused by magnon s c a t t e r i n g o f f i m p u r i t i e s o r c r y s t a l b o u n d a r i e s can a l s o g i v e r i s e t o d i r e c t r e l a x a t i o n p r o c e s s e s . I f t h e phonon-spin c o u p l i n g v a n i s h e s and t h e s p e c t r a o f a l l o t h e r e x c i t a t i o n s have a T L=0 energy gap b i g g e r t h a n t h e 5 4Mn h y p e r f i n e s p l i t t i n g s t h e o b s e r v e d l i m i t i n g r e l a x a t i o n p r o c e s s f o r 5 4Mn i s r a d i o a c t i v e decay w i t h a h a l f l i f e o f 2 . 6 * l 0 7 s . 47 Chapter 3 E x p e r i m e n t a l Techniques 3 . 1 I n t r o d u c t i o n NMRON i s an e x p e r i m e n t a l l y c h a l l e n g i n g low t e m p e r a t u r e NMR t e c h n i q u e . The sample must be m a i n t a i n e d a t t e m p e r a t u r e s o f t h e o r d e r o f m i l l i k e l v i n s w h i l e s i m u l t a n e o u s l y b e i n g i n t e r r o g a t e d by f r e q u e n t b u r s t s o f CW i r r a d i a t i o n o r sequences o f v e r y h i g h power r f p u l s e s . The e x p e r i m e n t s can t a k e many h o u r s and t h e i n t e g r a t e d h e a t i n p u t t o t h e c r y o s t a t f o r a s i n g l e e x p e r i m e n t can e a s i l y be o f t h e o r d e r o f a hundred o f m i l l i j o u l e s . F o r an a p p a r a t u s c a p a b l e o f p e r f o r m i n g t h e f u l l r a nge o f o r i e n t e d n u c l e i r e s o n a n c e t e c h n i q u e s a c o n t i n u o u s l y c o o l i n g d i l u t i o n r e f r i g e r a t o r i s t h e o n l y v i a b l e c h o i c e f o r t h e c o o l i n g s t a g e . An e x c e l l e n t d i s c u s s i o n o f many o f t h e t e c h n i c a l r e q u i r e m e n t s o f p u l s e d and CW NMRON a p p a r a t u s e s can be found i n t h e modern ' b i b l e ' o f NO and NMRON "Low Temperature N u c l e a r O r i e n t a t i o n " (see r e f . 2 ) . The CW NMRON resonance method i n v o l v e s a p p l y i n g an r f f i e l d t o t h e sample and sweeping t h e r f f r e q u e n c y i n s t e p s t h r o u g h t h e reso n a n c e f r e q u e n c y range. The y - r a y e m i s s i o n p a t t e r n i s measured f o r each f r e q u e n c y s t e p and when re s o n a n c e o c c u r s t h e y - r a y e m i s s i o n p a t t e r n undergoes a change. The d w e l l t i m e a t each c h a n n e l may be l o n g , s ay 100s, o r i t may be s h o r t and t h e sweep r e p e a t e d many t i m e s w i t h t h e r e s u l t s o f many r u n s added up t o g i v e t h e r e q u i r e d c o u n t i n g s t a t i s t i c s . The r f power may be 48 a p p l i e d w i t h g r e a t v a r i e t y , b o t h w i t h and w i t h o u t f r e q u e n c y m o d u l a t i o n , and a t v a r i o u s power l e v e l s . T h i s v a r i e t y i s t h e s p i c e o f CW NMRON: by a j u d i c i o u s c h o i c e o f r f f i e l d p a r a m e t e r s some o f t h e s e c r e t s o f t h e NMRON l i n e s h a p e can be deduced. As an example, t h e n a t u r e o f t h e i n t e r a c t i o n s r e s p o n s i b l e f o r t h e l i n e shape may o f t e n be e l u c i d a t e d by a comparison o f t h e o b s e r v e d l i n e s h a p e s and s i g n a l i n t e n s i t i e s o b t a i n e d from s u c c e s s i v e r u n s , p e r f o r m e d w i t h and w i t h o u t f r e q u e n c y m o d u l a t i o n . I f t h e res o n a n c e l i n e w i d t h i s m a i n l y due t o an inhomogeneous b r o a d e n i n g mechanism t h e r u n w i t h o u t f r e q u e n c y m o d u l a t i o n w i l l show d e c r e a s e d i n t e n s i t y . The r f f r e q u e n c y s o u r c e s h o u l d have a s t a b l e a m p l i t u d e and f r e q u e n c y c o n t r o l and a good a t t e n u a t o r w i t h f i n e t u n i n g . I f t h e r f power i s a p p l i e d i n p u l s e s t h e p u l s e r i s e t i m e s h o u l d be such t h a t t h e f r e q u e n c y spectrum o f t h e p u l s e f a l l s w i t h i n t h e f r e q u e n c y s t e p o f s u c c e s s i v e a c q u i s i t i o n c h a n n e l s . Sharp edges on t h e p u l s e s can g i v e s u f f i c i e n t power t o s a t u r a t e a l o n g T reson a n c e l i n e l o n g b e f o r e t h e c e n t e r f r e q u e n c y o f t h e p u l s e c o i n c i d e s w i t h t h e resonance f r e q u e n c y o f t h e re s o n a n c e l i n e . Computer c o n t r o l f a c i l i t a t e s b o t h t h e v a r i a t i o n o f e x p e r i m e n t a l p a r a m e t e r s and d a t a a c q u i s i t i o n d u r i n g t h e e x p e r i m e n t a l r u n s . The o b s e r v a t i o n o f a resonance s i g n a l u s i n g CW NMRON o c c u r s o n l y when t h e a p p l i e d r f f i e l d s i g n i f i c a n t l y p e r t u r b s t h e p o p u l a t i o n s o f t h e n u c l e a r s p i n energy l e v e l s . When T i s s h o r t l a r g e v a l u e s o f r f f i e l d a r e r e q u i r e d t o s a t u r a t e t h e t r a n s i t i o n s and t h e r e i s o f t e n a c o m p e t i t i o n between t h e r e s o n a n t and non-resonant d e s t r u c t i o n o f y - r a y a n i s o t r o p y . The r e s o n a n t d e s t r u c t i o n i s due t o t h e s a t u r a t i o n o f t h e r a d i o a c t i v e 49 n u c l e a r s p i n t r a n s i t i o n s and t h e non-resonant d e s t r u c t i o n i s due t o h e a t i n g caused by energy d e p o s i t e d by t h e r f f i e l d i n t h e sample and t h e sample c o l d f i n g e r . To r e d u c e non-resonant h e a t i n g t h e amount o f m a t e r i a l i n s i d e t h e res o n a n c e c o i l s h o u l d be m i n i m i s e d . I n t h e systems s t u d i e d h e r e t h e range o f T a b l e 7 t o be measured was from 5s t o 2.6*10 s. Thermal NMR i s a l s o a c o n t i n u o u s wave t e c h n i q u e i n which r e s o n a n t l y d e p o s i t e d energy i n t h e s t a b l e i s o t o p e s p i n b a t h f l o w s i n t o t h e l a t t i c e t h r o u g h t h e p r o c e s s e s o f s p i n - l a t t i c e r e l a x a t i o n . The r e s u l t a n t h e a t i n g o f t h e l a t t i c e warms t h e n u c l e a r thermometer and t h e resonance appears as a change i n t h e ob s e r v e d y - r a y a n i s o t r o p y . Many o f t h e above comments on CW NMRON a p p l y t o t h i s t e c h n i q u e as w e l l , b u t one i m p o r t a n t p r a c t i c a l d i f f e r e n c e i s t h e range o f T amenable t o s t u d y by t h e method. S h o r t s p i n - l a t t i c e r e l a x a t i o n t i m e s a r e n o t an a b s o l u t e r e q u i r e m e n t f o r t h e method, but when T i s l e s s t h a n t h e d w e l l t i m e used f o r t h e f r e q u e n c y sweep, t h e method becomes much s i m p l e r and more g e n e r a l l y a p p l i c a b l e . The method can produce d i s t o r t i o n s o f t h e l i n e s h a p e , b u t i f c a r e i s t a k e n t o o p t i m i z e sweep r a t e s and t h e r m a l t i m e c o n s t a n t s i t can g i v e v e r y u s e f u l l i n e s h a p e i n f o r m a t i o n . Thermal NMR c a p t u r e s t h e s i m p l i c i t y o f CW NMRON e x p e r i m e n t s and has some a d d i t i o n a l v e r y a t t r a c t i v e f e a t u r e s . The method can be a p p l i e d t o r e s o n a n c e s w i t h q u i t e b r o a d l i n e w i d t h and can be u t i l i z e d t o s t u d y systems w i t h s h o r t T v a l u e s . I P u l s e d NMRON i s perhaps t h e most i n t r i c a t e and demanding o f t h e e x p e r i m e n t a l methods. The r f s e c t i o n s h o u l d be e x t r e m e l y s t a b l e w i t h r e g a r d t o b o t h f r e q u e n c y and a m p l i t u d e o f t h e r f 50 p u l s e s and t h e r f t r a n s m i t t e r must be c a p a b l e o f p r o d u c i n g h i g h power, sub-microsecond p u l s e s t o e x c i t e b r o a d NMRON r e s o n a n c e s . E x t r a c a r e s h o u l d be t a k e n t o ens u r e a h i g h degree o f r f i s o l a t i o n between t h e t r a n s m i t t e r s t a g e s and t h e f r e q u e n c y s y n t h e s i z e r when T i s l o n g as v e r y s m a l l r f f i e l d s can e a s i l y s a t u r a t e a l o n g T resonance l i n e . The advantage o f p u l s e d e x p e r i m e n t s i s t h a t s p i n - l a t t i c e r e l a x a t i o n t i m e s down t o 100ms can be measured and r e l a x a t i o n measurements can be pe r f o r m e d a t t e m p e r a t u r e s as h i g h as t o 6 t i m e s t h e h y p e r f i n e s p l i t t i n g . 3.2 The NMRON Ap p a r a t u s A b l o c k diagram o f t h e major components o f t h e NMRON a p p a r a t u s i s shown i n f i g u r e 3.1a. The r f power s o u r c e i s a computer c o n t r o l l e d M a r c o n i I n s t r u m e n t s 2022C f r e q u e n c y s y n t h e s i z e r , and t h e r f p u l s e s a r e formed by a h i g h i s o l a t i o n W a t k i n s J o h n s t o n H - l r f g a t e . The p u l s e s a r e a m p l i f i e d t o t h e r e q u i r e d l e v e l by a c h a i n o f 3 a m p l i f i e r u n i t s t h e f i r s t o f whi c h i s a c l a s s A M i n i c i r c u i t s ZHL-2 lw a m p l i f i e r . The ZHL-2 d r i v e s a c l a s s C s t r i p l i n e a m p l i f i e r b u i l t from a 19w M o t o r o l a MHW 710-3 h y b r i d u n i t and a 60w MPF 330 r f power t r a n s i s t o r . The f i n a l s t a g e i s a r e t u n e d Henry R a d i o 1002 c l a s s - A grounded g r i d t r i o d e power a m p l i f i e r . A t y p i c a l 90° p u l s e l e n g t h i s 250ns and t h e p u l s e has a 50ns r i s e t i m e . The peak power o u t p u t o f t h e f i n a l t r a n s m i t t e r a t a f r e q u e n c y o f 500MHz i s 600 w a t t s . The NMRON probe s h o u l d be d e s i g n e d t o produce f a s t r i s e t i m e , h i g h power p u l s e s and i t s h o u l d be t u n a b l e o v e r a wide range o f f r e q u e n c y . The probe used f o r t h e e x p e r i m e n t s i s b u i l t 51 D i l u t i o n Cry o s t a t L 1 C 1 1 1 : 1 1 - C 2 L 2 Nal A x l a 1 Dete c t o r Syst e m P o w e r A m p l i f i e r r f g a t e R e s i s t a n c e B r i d g e T e m p e r a t u r e R e g u l a t o r M a g n e t P o w e r S u p p l y P u l s e P r o g r a m m e r M a r c o n i F r equ ency S y n t h es i ser C o r o n a P C 2 1 C e n t r a l C o n t r o l C o m p u t e r B l u e C h i p PC Com put er N a l E q u a t o r i a l D e t e c t o r S y s t e m T r a c o r N o r t h e r n TN 17 10 F i g u r e 3.1: B l o c k Diagrame o f t h e NMRON A p p a r a t u s 52 i n t o t h e l o w e r p o r t i o n o f t h e IK h e a t s h i e l d o f an SHE DRI-236 d i l u t i o n r e f r i g e r a t o r . I t i s r e m o t e l y t u n a b l e o v e r t h e range 350 t o 600 MHz and has a f i x e d LC ma t c h i n g network c o n s i s t i n g o f a 4mm*2mm copper s t r i p , L l (see f i g 3 . 1 ) i n p a r a l l e l w i t h an ATC 30pf c e r a m i c c a p a c i t o r , C l . Because t h e NMRON s i g n a l i s d e t e c t e d by m o n i t o r i n g changes i n t h e r - r a y i n t e n s i t y , good m a t c h i n g o v e r t h e complete t u n i n g range i s u n n e c e s s a r y and poor m a t c h i n g can be e a s i l y compensated f o r by i n c r e a s i n g t h e t r a n s m i t t e r power. The sample c o i l , L2, i s made from t h r e e t u r n s o f b r a s s f o i l w i t h a t o t a l volume o f 1 cm 3, and t h e t u n i n g c a p a c i t o r c o n s i s t s o f two f l a t 1 cm 2 copper p l a t e s w i t h a s p a c i n g w h i c h can be a d j u s t e d r e m o t e l y a t room t e m p e r a t u r e . The Q o f t h e r e s o n a n t c i r c u i t i s v e r y low v a r y i n g between 10 and 15 o v e r t h e t u n i n g range. A low Q i s i m p o r t a n t when f a s t p u l s e r i s e t i m e s a r e needed. NMRON resonance f r e q u e n c i e s e n c o u n t e r e d i n t h e work p r e s e n t e d h e r e a r e w i t h i n t h e range o f 400 t o 550 MHz, and i t i s i m p o r t a n t t o d e s i g n t h e t u n e d c i r c u i t components o f t h e probe i n o r d e r t o m i n i m i s e s t r a y i n d u c t a n c e s . More co m p l e t e diagrams o f t h e a p p a r a t u s can be found i n appendix A. I t i s u s e f u l t o mount a s m a l l p i c k u p c o i l c l o s e t o t h e t r a n s m i t t e r c o i l i n o r d e r t o m o n i t o r b o t h t h e t u n e d c i r c u i t r e s o n a n c e c u r v e , and t h e h i g h power p u l s e s . The p i c k - u p c o i l a l l o w s t h e phase and a m p l i t u d e o f t h e p u l s e s t o be m o n i t o r e d . T h i s i s o f t h e utmost i m p o r t a n c e because p u l s e i n s t a b i l i t i e s can e a s i l y l e a d t o e r r o n e o u s r e s u l t s t h e r e b y w a s t i n g c o n s i d e r a b l e t i m e and money. The hardware used i n t h e p u l s e d e x p e r i m e n t s i s a l s o used f o r 53 t h e CW NMRON e x p e r i m e n t s . I n our CW e x p e r i m e n t s t h e probe i s r e c o n n e c t e d t o t h e o u t p u t o f t h e f i r s t a m p l i f i e r i n t h e r f power t r a i n , and t h e r f g a t e c o n t r o l l i n e i s c o n n e c t e d t o t h e o u t p u t of a p u l s e - w i d t h m o d u l a t i o n t e m p e r a t u r e c o n t r o l l e r d i s c u s s e d below ( I t i s v e r y i m p o r t a n t t o p e r f o r m t h i s sequence o f o p e r a t i o n s i n t h e c o r r e c t o r d e r ) . The sample t e m p e r a t u r e i s measured d i r e c t l y from t h e n u c l e a r o r i e n t a t i o n s i g n a l w h i l e t h e measurement o f t h e c o l d f i n g e r t e m p e r a t u r e was a c h i e v e d u s i n g b o t h s t a n d a r d r e s i s t a n c e thermometry and NO thermometry. I n CW NMRON o r t h e r m o m e t r i c NMR ex p e r i m e n t s t h e t e m p e r a t u r e was s t a b i l i z e d u s i n g a f e e d b a c k - c o n t r o l l e d , p u l s e - w i d t h m o d u l a t i o n u n i t . The c o n t r o l s i g n a l came from a r e s i s t a n c e b r i d g e w h i c h m o n i t o r e d t h e r e s i s t a n c e o f a r e s i s t a n c e thermometer on t h e sample c o l d f i n g e r . The o u t p u t o f t h e mo d u l a t o r d r i v e s t h e r f g a t e and h e a t i n g o f t h e c o l d f i n g e r i s a c h i e v e d by eddy c u r r e n t h e a t i n g from t h e r e s u l t i n g v a r i a b l e l e n g t h r f p u l s e s . T h i s method o f te m p e r a t u r e r e g u l a t i o n a l l o w s r e l a t i v e l y l a r g e f i e l d a m p l i t u d e s i n CW NMRON resonance s e a r c h e s . D u r i n g t h e p u l s e d e x p e r i m e n t s t h e o u t p u t o f t h e m o d u l a t o r i s f e d d i r e c t l y t o a h e a t e r r e s i s t o r mounted on t h e c o l d f i n g e r . A f i n a l i m p o r t a n t r e q u i r e m e n t r e l a t e d t o t e m p e r a t u r e r e g u l a t i o n i s t h e i n c l u s i o n o f an r f r e l a y between t h e power t r a n s m i t t e r and th e c r y o s t a t . The r e l a y and i t s a s s o c i a t e d c o n t r o l e l e c t r o n i c s a c t as a p r o t e c t i o n mechanism w h i c h , i n t h e e v e n t o f an e x c e s s i v e l y l o n g p u l s e , d i s c o n n e c t s t h e t r a n s m i t t e r from t h e c r y o s t a t . T h i s d e v i c e p r o t e c t s t h e system from o v e r h e a t i n g and e x p e l l i n g t h e m i x t u r e from t h e d i l u t i o n u n i t . 54 Two main magnets were used: t h e one was a 4T 2" bore Magnion s u p e r c o n d u c t i n g s o l e n o i d , and t h e o t h e r was a 1" bore 10T O x f o r d I n s t r u m e n t s NbSn h i g h homogeneity NMR magnet. The magnet c u r r e n t i s s u p p l i e d t h r o u g h removable v a p o u r - c o o l e d c u r r e n t p r o b e s by a computer c o n t r o l l e d I n t e r m a g n e t i c s 75A power s u p p l y . The NMRON s i g n a l was d e t e c t e d u s i n g two m o d i f i e d B i c r o n model 4H4-3LP N a l y - r a y s c i n t i l l a t i o n d e t e c t o r s . One d e t e c t o r i s mounted a x i a l l y , a l o n g t h e a p p l i e d f i e l d , w h i l e t h e o t h e r d e t e c t o r i s mounted p e r p e n d i c u l a r t o t h e a p p l i e d f i e l d and h o r i z o n t a l l y l e v e l w i t h t h e sample. To re d u c e p h o t o m u l t i p l i e r g a i n changes produced by magnetic f i e l d s a lm l i g h t p i p e was p l a c e d between t h e p h o t o m u l t i p l i e r t u b e and t h e N a l s c i n t i l l a t i o n c r y s t a l . T h i s m o d i f i c a t i o n a l s o i n c o r p o r a t e s a te m p e r a t u r e r e g u l a t e d LED l i g h t p u l s e spectrum s t a b i l i z e r w h i c h h e l p s t o c o n t r o l t h e r e m a i n i n g m a g n e t i c f i e l d i n d u c e d p h o t o m u l t i p l i e r g a i n changes and compensates f o r t h e r m a l l y i n d u c e d d r i f t s i n t h e g a i n o f t h e d e t e c t o r e l e c t r o n i c s . The s i g n a l s f r o m . t h e d e t e c t o r s a r e p r o c e s s e d by a c h a i n o f a m p l i f i e r s , spectrum s t a b i l i z e r s and p u l s e h e i g h t windows, and t h e d a t a i s f i n a l l y d i s p l a y e d and c o l l e c t e d on a T r a c o r N o r t h e r n 1710 N u c l e a r a c q u i s i t i o n system, and/or an O r t e c ACE M u l t i c h a n n e l A n a l y z e r and P u l s e H e i g h t A n a l y z e r . The l a t t e r i s i n s t a l l e d on an IBM c l o n e B l u e C h i p PC computer. The e x p e r i m e n t a l p r o c e d u r e s f o r p u l s e d NMRON i n c l u d e complex, p r e c i s e l y t i m e d sequences i n v o l v i n g m a g n e t i c f i e l d sweeps, t h e a p p l i c a t i o n o f p u l s e t r a i n s and t h e s e q u e n t i a l i n c r e m e n t a t i o n o f t h e f r e q u e n c y and a m p l i t u d e o f t h e r f f i e l d . 55 The c o m p l e x i t y o f t h e e x p e r i m e n t a l p r o c e d u r e s means t h a t a c e n t r a l i z e d computer c o n t r o l i s e s s e n t i a l . The system c o n t r o l computer i s a Corona PC21 r u n n i n g w i t h c u s t o m - w r i t t e n , menu-driven s o f t w a r e . T h i s computer c o n t r o l s t h e magnet and a s s o c i a t e d h e a t s w i t c h , t h e p u l s e programmer, t h e f r e q u e n c y s y n t h e s i z e r and t h e TN-1710. The s o f t w a r e f o r b o t h CW and p u l s e d NMRON must p o s s e s s a h i g h degree o f o p e r a t i o n a l s i m p l i c i t y a l l o w i n g t h e independent c o n t r o l o f each o f t h e a f o r e m e n t i o n e d components. T h i s f e a t u r e i s i m p o r t a n t f o r d e v e l o p i n g and c h a n g i n g e x p e r i m e n t a l sequences d u r i n g e x p e r i m e n t a l r u n s . 3.3 Sample p r e p a r a t i o n . 3 MnCl 2.4H zO samples were grown by p l a c i n g a s m a l l (<lmm ) seed c r y s t a l i n a t r o u g h 2mm wide and 1mm deep. A s m a l l g l a s s c o v e r s l i p was p l a c e d o v e r t h e seed c r y s t a l and s e a l e d t o t h e body o f t h e t r o u g h w i t h s i l i c o n g r e a s e . A s m a l l q u a n t i t y o f a s a t u r a t e d r a d i o a c t i v e MnCl .4H O s o l u t i o n was t h e n p u t i n t o t h e 2 2 t r o u g h i n t h e r e g i o n c o v e r e d by t h e g l a s s . T h i s sample c e l l was l e f t u n d i s t u r b e d and, as t h e s o l u t i o n e v a p o r a t e d , t h e seed c r y s t a l grew i n t o a shape d e f i n e d by t h e t r o u g h , w i t h an o r i e n t a t i o n d e t e r m i n e d by t h e placement o f t h e seed c r y s t a l . The method i s an e c o n o m i c a l way o f p r o d u c i n g s m a l l h i g h a c t i v i t y samples because most o f t h e r a d i o a c t i v e s o l u t i o n i s u sed i n t h e growth o f t h e sample. Mn(COOCH.) .4H 20 was grown by a n a l o g o u s m i n i a t u r e beaker methods but problems a s s o c i a t e d w i t h s p u r i o u s n u c l e a t i o n a t t h e a i r w a t e r i n t e r f a c e r e q u i r e d t h a t t h e samples be grown by t h e s l o w c o o l i n g o f a m i n i a t u r e beaker c o n t a i n i n g a seed c r y s t a l p l a c e d i n a s m a l l drop o f 56 s u p e r s a t u r a t e d s o l u t i o n immersed i n m i n e r a l o i l (see a p p endix A f o r diagrams o f t h e sample growth methods). The samples used f o r t h e p u l s e d measurements were t y p i c a l l y lmm*2mm*3mm and c o n t a i n e d 5uCi o f 5 4Mn a c t i v i t y . Samples w i t h 5uCi a c t i v i t y c o u l d be c o o l e d t o 30mK, w h i l e a 40uCi sample o f s i m i l a r s i z e c o o l e d o n l y t o 80mK due t o r a d i o a c t i v e h e a t i n g . I t i s i m p o r t a n t t o make t h e samples as s m a l l as p o s s i b l e "since t h i s f a c i l i t a t e s r a p i d c o o l i n g , (due t o t h e r e d u c e d h e a t c a p a c i t y ) , h e l p s t o keep t h e r f power l e v e l s r e q u i r e d f o r t h e p u l s e d NMRON e x p e r i m e n t s t o minimum, and red u c e s non-resonant power i n p u t because a c o l d f i n g e r o f s m a l l s i z e can be used. P u l s e d e x p e r i m e n t s e m p l o y i n g a s i n g l e 180° p u l s e and a 40s r e p e t i t i o n t i m e can be pe r f o r m e d on t h e af o r e m e n t i o n e d samples w i t h t h e sample t e m p e r a t u r e b e i n g m a i n t a i n e d a t 30mK. I n a s i m i l a r e x p e r i m e n t p e r f o r m e d a t 120mK a 2 second r e p e t i t i o n r a t e can be t o l e r a t e d . The samples were a t t a c h e d t o t h e c o l d f i n g e r o f t h e d i l u t i o n r e f r i g e r a t o r u s i n g e i t h e r A p i e s i o n N g r e a s e o r s i l i c o n vacuum g r e a s e as a c o n t a c t agent. The samples were s e c u r e d t o t h e c o l d f i n g e r by a l a y e r o f my l a r f o i l w h i c h a l s o f u n c t i o n s as a h e r m e t i c s e a l t o p r o t e c t t h e samples from d e g r a d a t i o n by a t m o s p h e r i c m o i s t u r e . The v a l u e s o f T were o b t a i n e d by f i t t i n g a n u m e r i c a l s i m u l a t i o n o f t h e r e l a x a t i o n p r o c e s s t o t h e measured r e l a x a t i o n c u r v e s . The n u m e r i c a l s i m u l a t i o n i s based on t h e ma s t e r e q u a t i o n 2.21 w i t h t h e d e f i n i t i o n s o f T g i v e n i n e q u a t i o n s 2.22d. The f i t t i n g p r o c e d u r e a d j u s t s t h e f o u r f r e e p a r a m e t e r s t o m i n i m i z e t h e v a l u e o f c h i squared f o r t h e measured and s i m u l a t e d d a t a 57 p o i n t s . The a d j u s t a b l e p arameters a r e t h e i n i t i a l t e m p e r a t u r e o f t h e sample, t h e a m p l i t u d e o f t h e res o n a n c e , t h e s p i n - l a t t i c e r e l a x a t i o n t i m e T , and t h e resonance l i n e w i d t h . The l i n e w i d t h parameter i s r e l e v a n t o n l y f o r CW NMRON res o n a n c e e x p e r i m e n t s s i n c e p u l s e d T measurements g i v e an i n s t a n t a n e o u s e x c i t a t i o n o f t h e r e s o n a n c e l i n e a t a w e l l d e t e r m i n e d t i m e c h a n n e l . F o r a l l measurements t h e 5 4Mn spectrum c o n s i s t e d o f s i x w e l l spaced t r a n s i t i o n s and t h e r e l a x a t i o n c u r v e s were a c c u r a t e l y f i t t e d t o a m u l t i - e x p o n e n t i a l r e l a x a t i o n p r o c e s s . 3 . 4 S e t t i n g Up A P u l s e d NMRON Experiment The d e t e r m i n a t i o n o f t h e f r e q u e n c y o f a h y p e r f i n e r e s o n a n c e can p r e s e n t a major problem. F o r NMRON h y p e r f i n e r e s o n a n c e s an i n i t i a l e s t i m a t e can o f t e n come from a measurement o f t h e y - r a y a n i s o t r o p y . When t h e s p i n t e m p e r a t u r e o f t h e r a d i o a c t i v e n u c l e i and t h e o r i e n t i n g i n t e r a c t i o n i s w e l l known a c a r e f u l measurement o f t h e a n i s o t r o p y can l o c a t e t h e r e s o n a n c e r e g i o n t o w i t h i n a few MHz. For n u c l e i o r i e n t e d i n o r d e r e d magnets t h i s method r e q u i r e s t h a t t h e magn e t i c s t r u c t u r e be u n d e r s t o o d and t h a t t h e h y p e r f i n e resonance spectrum be r e a s o n a b l y narrow. The NO measurement can t h e n be f o l l o w e d by a CW NMRON res o n a n c e s e a r c h t o l o c a t e t h e resonance e x a c t l y . The t r a n s m i t t e r i s t h e n t u n e d t o t h e a p p r o p r i a t e f r e q u e n c y and p u l s e d NMRON measurements can b e g i n . S e t t i n g up a p u l s e d NMRON expe r i m e n t r e q u i r e s knowledge o f t h e s t r e n g t h o f t h e i n t e r a c t i o n o f t h e r f f i e l d w i t h t h e n u c l e a r s p i n s o f i n t e r e s t . T h i s i n f o r m a t i o n i s r e q u i r e d i n o r d e r t o s e t t h e l e n g t h o f t h e p u l s e s used i n t h e p u l s e 58 >-CO U J 0.98 Q LU cr o 0.94 0.90 i ' i i i i i i i 1 i » i . 1 1 I . I . I I " i i i ' 0 3 6 9 12 15 TIME (US) F i g u r e 3.2: S i n g l e Quantum R o t a t i o n P a t t e r n The a x i a l a n i s o t r o p y , W(0), i s p l o t t e d as a f u n c t i o n o f p u l s e l e n g t h t . F o r t h i s e x p e r i m e n t a 180° p u l s e i s 500ns l o n g and c a u s e s a complete i n v e r s i o n o f t h e m=-3 t o m=-2 l e v e l s . The b a s e l i n e i s a measurement o f t h e t h e r m a l e q u i l i b r i u m a n i s o t r o p y a f t e r each magnon c o o l i n g c y c l e . The i n c r e a s e i n sample t e m p e r a t u r e i n d i c a t e d by t h e r i s i n g b a s e l i n e i s due t o e x c e s s i v e sample h e a t i n g caused by l o n g r f p u l s e s . 59 sequences. I n p r i n c i p l e t h e r f f i e l d s t r e n g t h c o u l d be measured from a c o n v e n t i o n a l p u l s e d NMR ex p e r i m e n t on an abundant n u c l e u s i n t h e sample, and f o r t h e e x a c t measurement o f an enhancement f a c t o r s uch a c a l i b r a t i o n o f t h e f i e l d s t r e n g t h would be i m p o r t a n t . F o r most e x p e r i m e n t s t h e NMRON s i g n a l i s t h e b e s t c a n d i d a t e f o r t h e s e t up p r o c e d u r e and t h e most u s e f u l s e t - u p e x p e r i m e n t i s t h e measurement o f an NMRON r o t a t i o n p a t t e r n , (see f i g u r e 3.2) f o r a s i n g l e quantum r o t a t i o n p a t t e r n ) . The p u l s e l e n g t h c o r r e s p o n d i n g t o t h e f i r s t maximum i n t h e a n i s o t r o p y change i n f i g u r e 3.2 i s c a l l e d a s i n g l e quantum 180° p u l s e and a s i n g l e quantum 90°pulses g i v e h a l f o f t h e maximum a n i s o t r o p y change, b u t g e n e r a t e s a maximum amount o f o f f - d i a g o n a l o r d e r i n t h e s p i n d e n s i t y m a t r i x . F i g u r e 3.2 a l s o i l l u s t r a t e s t h e u n d e s i r a b l e e f f e c t s o f e x c e s s i v e h e a t i n g caused by t h e l o n g e r r f p u l s e s , i . e . a d r i f t i n g b a s e - l i n e . 3 . 5 P u l s e Sequences and M u l t i p l e Quantum NMRON NMRON p u l s e sequences a r e al m o s t i d e n t i c a l t o c o n v e n t i o n a l NMR p u l s e sequences and f o r a good d i s c u s s i o n o f t h e s e s e e 1 . The o b s e r v a b l e i n c o n v e n t i o n a l NMR i s t h e p r e c e s s i n g t r a n s v e r s e m a g n e t i z a t i o n w h i c h i s an o f f - d i a g o n a l component o f t h e s p i n d e n s i t y m a t r i x . The NMRON o b s e r v a b l e i s t h e a n i s o t r o p i c y - r a y d i s t r i b u t i o n p a t t e r n w h i c h , f o r t i m e s l o n g compared t o T 2, i s r e l a t e d t o t h e d i a g o n a l elements o f t h e s p i n d e n s i t y m a t r i x . T h i s means t h a t most NMRON p u l s e sequences must c o n t a i n an e x t r a " r e a d p u l s e " . T h i s f i n a l r e a d p u l s e c o n v e r t s t h e e v o l v i n g n o n - d i a g o n a l components o f t h e s p i n d e n s i t y m a t r i x i n t o d i a g o n a l e l e m e n t s . The a m p l i t u d e and phase o f t h e o f f - d i a g o n a l components 60 become encoded as t h e magnitude o f i n v a r i a n t s o f t h e s t a t i c s p i n H a m i l t o n i a n . R e p e a t i n g a p u l s e sequence w i t h i n c r e m e n t e d " r e a d p u l s e " t i m e s s e q u e n t i a l l y maps t h e t i m e e v o l u t i o n o f t h e o f f - d i a g o n a l e l e m e n t s . One p o t e n t i a l problem w i t h t h e measurement o f s p i n e v o l u t i o n by such p r o c e d u r e s i s t h a t t h e d i a g o n a l e l e m e n t s a r e o n l y i n v a r i a n t s o f t h e s t a t i c s p i n H a m i l t o n i a n and t h e y a r e s u b j e c t t o change t h r o u g h t h e p r o c e s s e s o f s p i n - l a t t i c e r e l a x a t i o n . T h i s means t h a t t h e y - r a y d i s t r i b u t i o n p a t t e r n W(tf) r e l a x e s back towards i t s t h e r m a l e q u i l i b r i u m v a l u e d u r i n g t h e y - r a y c o u n t i n g p e r i o d and t h i s l e a d s t o a d i s t o r t i o n o f t h e o b s e r v e d s p i n p r e c e s s i o n s i g n a l s . The i d e a l e x p e r i m e n t a l c i r c u m s t a n c e i s a system w i t h an i n f i n i t e T d u r i n g each y - r a y c o u n t i n g p e r i o d , and a T o f a few seconds between p u l s e sequences t o a l l o w t h e r a p i d r e s t o r a t i o n o f t h e r a d i o a c t i v e s p i n ensemble t o a r e p r o d u c i b l e i n i t i a l c o n d i t i o n . I n b o t h MnCl .4H 0 and ^ 2 2 Mn(COOCH 3) 2.4H 20 s p i n l a t t i c e i n t e r a c t i o n s s t r o n g l y depend on f i e l d and p r o v i d e a means o f a c h i e v i n g t h i s i d e a l . F o r measurements i n t h e a n t i f e r r o m a g n e t i c phase o f M n C l 2 . 4 H 2 0 t h e g 'magnon c o o l i n g ' can be used t o r a p i d l y r e s e t t h e i n i t i a l c o n d i t i o n s a f t e r a p u l s e sequence. T h i s method i s a t e c h n i q u e i n wh i c h r e s o n a t e d 5 4Mn o r i e n t e d i n MnCl 2 - 4 H 2 0 can be r a p i d l y c o o l e d by d r i v i n g t h e sample t h r o u g h t h e a n t i f e r r o m a g n e t i c - t o - s p i n - f l o p phase t r a n s i t i o n . The s p i n - l a t t i c e r e l a x a t i o n t i m e o f 5 4Mn d e c r e a s e s by 7 o r d e r s o f magnitude when t h e f i e l d , a p p l i e d a l o n g t h e easy a x i s , i s changed from OT t o 0.7T. The a v a i l a b i l i t y o f a magnon c o o l i n g t e c h n i q u e i s n o t 61 e s s e n t i a l f o r t h e measurement FIDs, s p i n echoes and r o t a t i o n p a t t e r n s , b u t t o o b t a i n s i g n a l s u n d i s t o r t e d by e f f e c t s t h e y- r a y c o u n t i n g p e r i o d s h o u l d be much l e s s t h a n T and t h e t i m e between p u l s e s s h o u l d be a t l e a s t 5!^. R o t a t i o n p a t t e r n s , f r e e i n d u c t i o n decays and echoes have a l l been o b t a i n e d when T i s o f t h e o r d e r o f 5s, b u t t h e s i g n a l s l a c k t h e h i g h f i d e l i t y o f t h e p u l s e d NMRON s i g n a l s produced u s i n g magnon c o o l i n g u n l e s s s i g n a l a v e r a g i n g o v e r l o n g t i m e s i s used. A s i m p l e example o f a s i n g l e c y c l e o f a p u l s e d NMRON exp e r i m e n t i n c o r p e r a t i n g magnon c o o l i n g i s : 1. Measure t h e t h e r m a l e q u i l i b r i u m gamma r a y a n i s o t r o p y W(#). 2. Increment t h e p u l s e s p a c i n g s and/or p u l s e l e n g t h s . 3. A p p l y t h e p u l s e t r a i n . 4. Measure W(tf) a f t e r t h e p u l s e sequence. 5. Magnon c o o l t o r e s e t t h e i n i t i a l c o n d i t i o n s and go t o 1. Measurement o f W(tf) a f t e r each magnon c o o l i n g p r o v i d e s a b a s e l i n e o f y - r a y measurements o f t h e sample t e m p e r a t u r e . T h i s i s q u i t e i m p o r t a n t f o r r e s o l v i n g e x p e r i m e n t a l problems such as a g r a d u a l l y i n c r e a s i n g sample t e m p e r a t u r e due t o acc u m u l a t e d h e a t l o a d e f f e c t s (see f i g . 3 . 2 ) , and i t a l s o p r o v i d e s a good r e f e r e n c e l i n e i n p r e l i m i n a r y v i s u a l a t t e m p t s t o d i f f e r e n t i a t e a s i g n a l from t h e n a t u r a l s t a t i s t i c a l v a r i a t i o n o f t h e y - r a y c o u n t s . P u l s e sequences f o r whi c h good r e s u l t s have been o b t a i n e d a r e : two p u l s e s i n g l e quantum FIDs, t h r e e p u l s e s i n g l e quantum Hahn echoes, s i n g l e p u l s e s i n g l e quantum T measurements, two p u l s e d o u b l e quantum FID, t h r e e p u l s e d o u b l e quantum Hahn echoes, d o u b l e quantum r o t a t i o n p a t t e r n s , and s i n g l e p u l s e d o u b l e quantum T measurements. 62 Double quantum r o t a t i o n p a t t e r n s have been o b t a i n e d f o r 5 4Mn o r i e n t e d i n t h e a n t i f e r r o m a g n e t i c phase o f Mn C l 2 - 4 H 2 0 and t h e s e p a t t e r n s a r e shown i n f i g u r e s 3.3 and 3.4. I n t h i s sequence t h e p u l s e t r a i n i n s t e p 2 o f t h e magnon c o o l i n g sequence i s a s i n g l e p u l s e w i t h a l e n g t h w h i c h i s i n c r e m e n t e d a c o n s t a n t amount f o r each s u c c e s s i v e c y c l e . The s o f t d o u b l e quantum p u l s e c o u p l e s t h e m=-3 and m=-l l e v e l s and produces a p e r i o d i c m o d u l a t i o n o f b o t h t h e - a x i a l and t h e e q u a t o r i a l a n i s o t r o p y . A s i n g l e quantum r o t a t i o n p a t t e r n f o r t h e m=-3 t o m=-2 t r a n s i t i o n changes t h e a x i a l a n i s o t r o p y , b u t g i v e s no change o f e q u a t o r i a l a n i s o t r o p y . I n f i g u r e 3.3 and 3.4 t h e f i r s t p u l s e l e n g t h used was 250ns and f o r each s u c c e s s i v e s i g n a l p o i n t t h e p u l s e l e n g t h was in c r e m e n t e d by 250ns. The maximum a n i s o t r o p y change o b s e r v e d o c c u r s f o r a 180° p u l s e and t h e a x i a l a n i s o t r o p y i s d r i v e n w e l l above 1 f o r t h e ex p e r i m e n t shown i n f i g u r e 3.3. A s e l e c t i v e d o u b l e quantum f r e e i n d u c t i o n decay i s shown i n f i g u r e 3.5. The s i g n a l was o b t a i n e d u s i n g a 90-t-90 sequence and t h e e x p e r i m e n t was performed o f f r e s o n a n c e by 50KHz. The n e x t r e s u l t s d i s c u s s e d a r e t h e f i r s t use o f s e l e c t i v e s i n g l e and d o u b l e quantum s p i n echoes i n NMRON. S i n g l e and do u b l e quantum Hahn s p i n echoes have been used t o measure t h e z e r o f i e l d s p i n - s p i n r e l a x a t i o n t i m e f o r 5 4Mn o r i e n t e d i n MnC l 2 . 4 H 2 0 . P r e v i o u s measurements o f t h e a n t i f e r r o m a g n e t i c phase 7 2 CW NMRON spectrum and o f t h e s i n g l e quantum FID have shown an inhomogeneously broadened resonance l i n e w i t h a l i n e w i d t h o f 35KHz. I n t h e e x p e r i m e n t s d e s c r i b e d h e r e a 90-t- 1 8 0 - t - 9 0 Hahn s p i n echo was used t o r e f o c u s t h e d e p h a s i n g e f f e c t s o f t h e s t a t i c m a g n e t i c i n h o m o g e n e i t i e s . The v a r i a t i o n o f t h e h e i g h t o f 63 >_ 1.10 Lu 1.02 2 0.98 R 0.94 0.90 0.86 cc o 0.82 • i i • 1 1 1 0.0 2.0 4.0 6.0 8.0 TIME (US) F i g u r e 3.3: A x i a l Double Quantum R o t a t i o n P a t t e r n The p e r i o d i c m o d u l a t i o n o f t h e a x i a l a n i s o t r o p y i s produced by a p p l y i n g a s o f t d o u b l e quantum p u l s e o f l e n g t h x t o t h e m=-3 t o m=-l l e v e l s o f 5 4Mn o r i e n t e d i n MnCl 2.4H 20. F o r t h i s measurement t h e l e n g t h o f a 180° p u l s e i s 1250ns. 64 >-r— i — i CO LU 1.06 1.02 § 0.98 cr o 0.94 1,1 ••11 •. • • 1 1 ••'•"i1 B f •1 • • • • • I • ' 1 1 1 ' 1 1 III 0.0 11" I • I I I I V I 1 'I I I I I I I I I I 2.0 4.0 6.0 TIME (US) ' l l ' 1 , 1 I 8.0 F i g u r e 3 .4: E q u a t o r i a l Double Quantum R o t a t i o n P a t t e r n The p e r i o d i c m o d u l a t i o n o f t h e a x i a l a n i s o t r o p y i s produc e d by a p p l y i n g a S o f t Double Quantum p u l s e o f l e n g t h x t o t h e m=-3 t o m=-l l e v e l s o f 5 4Mn o r i e n t e d i n MnCl 2.4H 20. The l e n g t h o f a 180° p u l s e i s 1250ns, and t h i s p u l s e p r o d u c e s an 8% change i n t h e o b s e r v e d a n i s o t r o p y . 65 >-r— CO 1 ^ 1.00 1 - 1 0.96 o rtj 0.92 ex 0.88 o 0.84 i i i » i i 1 , 1 i ' , ' ' i i • -I L. 0 4 8 12 16 20 TIME (US) F i g u r e 3.5: S o f t Double Quantum F r e e I n d u c t i o n Decay T h i s Double Quantum F r e e I n d u c t i o n Decay was o b t a i n e d u s i n g a 90-t-90 p u l s e sequence. The l e n g t h o f t h e 90° p u l s e i s 750ns and t h e s i g n a l i s o f f r e s o n a n c e by 50KHz. 66 t h e peak o f t h e echo w i t h p u l s e s p a c i n g , t , r e v e a l s t h e r a t e o f coherence l o s s due t o i r r e v e r s i b l e T 2 p r o c e s s e s . The r e s u l t s o f a s i n g l e quantum Hahn echo p e r f o r m e d on t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn o r i e n t e d i n MnCl .4H 0 i s shown 2 2 i n f i g u r e 3.6. As d i s c u s s e d i n s e c t i o n 4.3, t h e r e l a x a t i o n t i m e s a t z e r o f i e l d i n t h e a n t i f e r r o m a g n e t i c phase a r e e x c e e d i n g l y l o n g , so t h a t i n t h e s e e x p e r i m e n t s magnon c o o l i n g must be used. There a r e two r e f e r e n c e measurements; t h e b a s e l i n e i s a measurement o f t h e t h e r m a l e q u i l i b r i u m a n i s o t r o p y and r e p r e s e n t s t h e sample t e m p e r a t u r e a f t e r each magnon c o o l i n g c y c l e , and t h e upper r e f e r e n c e l i n e i s t h e a n i s o t r o p y r e s u l t i n g from an NMRON Hahn echo w i t h o u t t h e f i n a l r e a d p u l s e . T h i s 90-t-180 sequence does form a m a g n e t i z a t i o n echo i n t h e t r a n s v e r s e p l a n e , b u t , w i t h o u t t h e f i n a l r e a d p u l s e , t h e echo i s unobserved and t h e a n i s o t r o p y i s t h a t r e s u l t i n g from a s i n g l e 90° p u l s e . When t h e p u l s e sequence has been c o r r e c t l y s e t up t h e s i g n a l from t h e complete NMRON Hahn echo p u l s e sequence s h o u l d be a s y m p t o t i c t o t h e upper r e f e r e n c e l i n e f o r t » T 2 « The phases o f t h e t h r e e p u l s e s a r e i d e n t i c a l and f o r t=0 t h e sequence i s e q u i v a l e n t t o a 360 degree r o t a t i o n . Such a r o t a t i o n r e t u r n s t h e a n i s o t r o p y t o i t s i n i t i a l t h e r m a l e q u i l i b r i u m v a l u e . F o r t h e measurement shown i n f i g u r e 3.6, t h e t v a l u e f o r t h e f i r s t s i g n a l p o i n t i s lOus and s u c c e s s i v e p o i n t s have t i n c r e m e n t e d by l O u s . The echo i s seen t o d e c r e a s e t o h a l f i t s maximum v a l u e a t t=60us g i v i n g an e s t i m a t e d w i d t h o f 17kHz f o r t h e n o n - r e f o c u s a b l e s i n g l e quantum l i n e w i d t h . From t h e d o u b l e quantum FID o f f i g u r e 3.5 a d o u b l e quantum l i n e w i d t h o f 70kHz can be deduced. A two quantum Hahn echo 67 >-h— t—t CO LU Q LU CC O 0.96 0.92 0.88 0.84 0.80 , I I i I , , , 1 I l | I , l i l I I ' I i I I • I » i , I » I , I I I I , i , i i i l 0 100 200 300 400 TIME (US) F i g u r e 3.6: Decay o f t h e S i n g l e Quantum S p i n Echo A m p l i t u d e The decay c u r v e f o r t h e peak o f a s i n g l e quantum s p i n echo p e r f o r m e d on t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn i s shown above. The upper r e f e r e n c e l i n e g i v e s t h e a n i s o t r o p y r e s u l t i n g from a 90-t-180 p u l s e sequence, t h e m i d d l e p o i n t s r e s u l t from a 9 0 - t - 1 8 0 - t - 9 0 p u l s e sequence and t h e b a s e l i n e i s a measurement o f t h e t h e r m a l e q u i l i b r i u m a n i s o t r o p y . 68 _ 1.02 CO Lu 0.98 o UJ 0.94 0.90 cr 0.86 o 0.82 i i • i i 1 i i 1 i 1 , i I I I I | I I 1 ' I I 1 I I 1 ' 10 20 30 TIME (US) 40 F i g u r e 3.7: Decay o f t h e Double Quantum S p i n Echo A m p l i t u d e The decay c u r v e f o r t h e peak o f a d o u b l e quantum s p i n echo p e r f o r m e d on t h e m=-3 t o m=-l t r a n s i t i o n o f 5 4Mn i s shown above. The upper r e f e r e n c e l i n e g i v e s t h e a n i s o t r o p y r e s u l t i n g from a 90-t-180 p u l s e sequence, t h e m i d d l e p o i n t s r e s u l t from a 90-t-180-t-90 p u l s e sequence and t h e b a s e l i n e i s a measurement o f t h e t h e r m a l e q u i l i b r i u m a n i s o t r o p y . 69 e x p e r i m e n t was performed on t h e l e v e l s m=-3 t o m=-l, and t h e r e s u l t i n g t i m e decay o f t h e echo a m p l i t u d e i s shown i n f i g u r e 3.7. The decay t i m e i s 30us g i v i n g an e s t i m a t e f o r t h e n o n - r e f o c u s a b l e two quantum l i n e w i d t h o f 33kHz. A s e l e c t i v e 90° p u l s e c r e a t e s o f f - d i a g o n a l o r d e r i n t h e s p i n d e n s i t y m a t r i x . D i r e c t l y a f t e r t h e p u l s e t h i s o f f - d i a g o n a l o r d e r i s u n i f o r m l y phased f o r a l l s p i n s i n t h e sample. As t i m e p r o g r e s s e s t h i s phase coherence i s g r a d u a l l y l o s t . The mechanism f o r t h e l o s s o f ensemble phase coherence can be due t o a v a r i a t i o n o f t h e n u c l e a r energy l e v e l s p l i t t i n g s t h r o u g h o u t t h e sample. T h i s k i n d o f l i n e b r o a d e n i n g mechanism i s s t a t i c and i t can always be r e f o c u s e d by t h e a p p r o p r i a t e s e l e c t i v e e x c i t a t i o n Hahn s p i n echo. A n o t h e r mechanism i n v o l v e s i n t e r a c t i o n w i t h t h e o t h e r degrees o f freedom o f t h e sample. These i n t e r a c t i o n s may cause a s l o w m o d u l a t i o n o f t h e s p i n energy l e v e l s o r t h e o c c a s i o n a l s p i n f l i p . Such p r o c e s s e s g i v e r i s e t o a homogeneously broadened l i n e shape and t h e y u s u a l l y cause an i r r e v e r s i b l e l o s s o f phase coherence. A c o m p a r i s o n o f t h e r a t e o f coherence l o s s f o r phase c o h e r e n t s u p e r p o s i t i o n s o f d i f f e r e n t p a i r s o f l e v e l s can g i v e i n f o r m a t i o n on t h e n a t u r e o f b o t h c l a s s e s o f b r o a d e n i n g mechanism. I f t h e T 2 mechanism i n v o l v e s an a d i a b a t i c m o d u l a t i o n o f t h e energy l e v e l s and i t i s o f m a g n e t i c o r i g i n t h e n d o u b l e quantum coherence s h o u l d decay a t t w i c e t h e r a t e o f s i n g l e quantum coherence. The r e s u l t s o f t h e above e x p e r i m e n t s i n d i c a t e t h a t b o t h t h e s t a t i c and dynamic T 2 mechanisms a r e o f m a g n e t i c o r i g i n because t h e r a t e o f c o h e r e n c e l o s s f o r t h e s i n g l e quantum t r a n s i t i o n i s h a l f t h a t o f t h e d o u b l e quantum t r a n s i t i o n i n b o t h t h e FID e x p e r i m e n t , and t h e 70 s p i n echo a m p l i t u d e decay. The w i d t h o f t h e s i n g l e quantum 5 4Mn reson a n c e l i n e i s c o n s i s t e n t w i t h t h a t due t o a c o m b i n a t i o n o f t h e s t a t i c 5 4 h e t e r o n u c l e a r d i p o l e - d i p o l e i n t e r a c t i o n between Mn and t h e s u r r o u n d i n g p r o t o n s i n t h e w a t e r s o f h y d r a t i o n , and t h e magn e t i c b r o a d e n i n g due t o i m p u r i t i e s i n t h e magn e t i c l a t t i c e . I f t h e mechanism o f i r r e v e r s i b l e T 2 i s a t t r i b u t e d t o d i p o l e - d i p o l e c o u p l i n g t o t h e p r o t o n b a t h t h e n t h e c o r r e l a t i o n t i m e f o r p r o t o n s p i n f l i p s , deduced from t h e s i n g l e quantum r e f o c u s e d l i n e w i d t h o f 5 4Mn, i s o f t h e o r d e r o f 15ns. T h i s e s t i m a t e d c o r r e l a t i o n t i m e i s c o n s i s t e n t w i t h t h e second moment o f t h e p r o t o n r e s o n a n c e l i n e s due t o t h e p r o t o n homonuclear d i p o l e - d i p o l e i n t e r a c t i o n . The v a l u e o f p r o t o n second moment i s s m a l l because t h e s t r o n g homonuclear d i p o l e i n t e r a c t i o n n o r m a l l y f ound i n such c o n c e n t r a t e d p r o t o n systems i s g r e a t l y r e d u c e d due t o t h e l a r g e d i f f e r e n c e i n resonance f r e q u e n c i e s o f m a g n e t i c a l l y n o n e q u i v a l e n t p r o t o n s . A c o m b i n a t i o n resonance s e a r c h and T measurement f o r 5 4Mn I o r i e n t e d i n Mn(COOCH.) 2.4H 20 i s shown i n f i g u r e 3.8. I n t h i s e x p e r i m e n t t h e r f f r e q u e n c y i s s t e p p e d t h r o u g h a sequence o f v a l u e s and a s i n g l e p u l s e i s a p p l i e d a t each f r e q u e n c y s t e p . When t h e p u l s e i s r e s o n a n t w i t h e i t h e r a s i n g l e o r a d o u b l e quantum t r a n s i t i o n a l a r g e change i n t h e measured a n i s o t r o p y o c c u r s . The subsequent r e l a x a t i o n o f t h e a n i s o t r o p y back t o i t s t h e r m a l e q u i l i b r i u m v a l u e i s m o n i t o r e d f o r s e v e r a l t i m e c h a n n e l s f o l l o w i n g t h e p u l s e . I n f i g u r e 3.8 t h e f i r s t l a r g e jump i n t h e a n i s o t r o p y o c c u r s when t h e p u l s e i s r e s o n a n t w i t h t h e s i n g l e quantum m=-3 t o m=-2 t r a n s i t i o n a t a f r e q u e n c y o f 475.2MHz, and 71 t h e second l a r g e r jump i s due t o a d o u b l e quantum t r a n s i t i o n between t h e m=-3 and m=-l l e v e l s a t a f r e q u e n c y o f 475.9MHz. The p u l s e used was 1000ns i n l e n g t h and t h e bandwidth o f t h e p u l s e i s e q u a l t o 1 MHz. T h i s p u l s e bandwidth i s chosen t o be g r e a t e r t h a n t h e f r e q u e n c y s t e p o f 0.7 MHz used f o r t h e re s o n a n c e sweep because t h i s e nsure a complete coverage o f t h e f r e q u e n c y range. The s m a l l s t e p i n t h e a n i s o t r o p y a t 476.6 MHz i s due t o t h e combined e x c i t a t i o n o f t h e . m=-2 t o m=-l t r a n s i t i o n , a t 476.6MHz, and t h e o f f resonance e x c i t a t i o n o f t h e m=-3 t o m=-l t r a n s i t i o n , a t 475.9 MHz. T h i s combined s i n g l e and d o u b l e quantum e x c i t a t i o n i s l a b e l e d -3 -» -2 + -3-» -1 i n f i g u r e 3.8. The s i g n o f t h e a n i s o t r o p y change i s p o s i t i v e because t h e o f f res o n a n c e e x c i t a t i o n o f t h e -3 t o -1 t r a n s i t i o n dominates t h e s i g n a l , ( T h i s due t o t h e l a r g e i n i t i a l p o p u l a t i o n o f t h e m=-3 l e v e l ) . Note t h a t t h e a n i s o t r o p y change l a b l e d d e s i g n a t e d a -3 t o -2. t r a n s i t i o n i n f i g 3.8 a l s o i s a f f e c t e d by t h e c l o s e p r o x i m i t y o f t h e -3 t o -1 t r a n s i t i o n . When c o n d u c t i n g p u l s e d r e s o n a n c e s e a r c h e s t h e oc c u r a n c e o f such o v e r l a p i n g e x c i t a t i o n s w i l l be common because o f t h e r e q u i r e m e n t o f a l a r g e p u l s e bandwidth. The a n i s o t r o p y i s r e c o r d e d f o r 50 c h a n n e l s f o l l o w i n g each p u l s e and t h u s t h e r e l a x a t i o n t i m e i s a l s o measured. A complete sequence o f f r e q u e n c i e s i s r e p e a t e d many t i m e s and t h e r e s u l t s s i g n a l averaged. The method i s v e r y u s e f u l f o r f i n d i n g a res o n a n c e w i t h a w h i c h i s t o o s h o r t t o e n a b l e d e t e c t i o n by c o n v e n t i o n a l CW NMRON. An i m p o r t a n t f e a t u r e o f t h e s o f t d o u b l e quantum e x c i t a t i o n e x p l i c i t l y shown by t h i s f i g u r e i s t h a t i t prod u c e s a much b i g g e r a n i s o t r o p y change i n 5 4Mn t h a n t h e s i n g l e 72 quantum e x c i t a t i o n . One o f t h e most u s e f u l p u l s e d NMRON sequences i s t h e one used f o r t h e measurement o f T . I n t h i s measurement a s i n g l e 180° p u l s e i s used t o produce a maximum p e r t u r b a t i o n o f t h e a n i s o t r o p y and t h e subsequent r e l a x a t i o n i s m o n i t o r e d and b i n n e d i n t i m e i n t e r v a l s w h i c h a r e s h o r t compared t o T . The whole r e l a x a t i o n p r o c e s s i s m o n i t o r e d e v e r y p u l s e r e p e t i t i o n making t h i s p u l s e sequence t h e most e f f i c i e n t sequence o f t h e p u l s e d methods. A c c u r a t e measurements o f s p i n - l a t t i c e r e l a x a t i o n t i m e s as s h o r t as 100ms have been o b t a i n e d u s i n g s i g n a l a v e r a g i n g t i m e s w h i c h a r e o f t h e o r d e r o f 6 h o u r s . F i g u r e 3.9 shows t h e r e l a x a t i o n c u r v e f o r such a measurement i n Mn(C00CH.) .4H O a t v 3 7 2 2 z e r o a p p l i e d f i e l d . 73 >- 0.770 I— ^ 0.750 LU z 0.730 S 0.710 0.690 CE ct: o 0.670 0 10 20 30 TIME (MS) 40 F i g u r e 3.8: P u l s e d Resonance S e a r c h T h i s f i g u r e i l l u s t r a t e s a p u l s e d r e s o n a n c e s e a r c h . T h i s method i s p a r t i c u l a r l y u s e f u l f o r f i n d i n g r e s o n a n c e l i n e s when t h e s p i n - l a t t i c e r e l a x a t i o n t i m e i s t o o s h o r t t o a l l o w d e t e c t i o n by c o n v e n t i o n a l CW methods. 74 F i g u r e 3.9: P u l s e d S p i n L a t t i c e R e l a x a t i o n Time Measurement A p u l s e d T i measurement on t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn o r i e n t e d i n Mn(COOCH 3) .4H 20. A 250ns 180° p u l s e was used and a v a l u e o f 100ms was o b t a i n e d f o r T . I 75 Chapter 4 NMRON i n Manganese C h l o r i d e T e t r a h y d r a t e 4.1 The M a g n e t i c P r o p e r t i e s o f MnCl 2.4H 20 Manganese c h l o r i d e t e t r a h y d r a t e ( M n C l 2 . 4 H 2 0 ) has been t h e s u b j e c t " o f many NO and NMRON s t u d i e s . The s i m p l i c i t y o f i t s c r y s t a l p r e p a r a t i o n , and i t s e a s i l y a c c e s s i b l e phase b o u n d a r i e s have made i t an e x c e l l e n t system f o r t h e development o f CW, p u l s e d and t h e r m a l NMRON i n magnetic i n s u l a t o r s . M n C l 2 . 4 H 2 0 i s a f o u r s u b l a t t i c e , easy a x i s a n t i f e r r o m a g n e t w i t h b i a x i a l s i n g l e i o n a n i s o t r o p y and i n z e r o f i e l d i t o r d e r s a t T«1.6K. The c r y s t a l s t r u c t u r e i s m o n o c l i n i c (£=99.7) and n t h e m a g n e t i c space group i s P2J/a ( C 2 h ) . The i o n i c p o s i t i o n s and . 3 c o n f i g u r a t i o n s have been d e t e r m i n e d by x - r a y a n a l y s i s and by n e u t r o n d i f f r a c t i o n 4 . The magnetic s t r u c t u r e o f t h e 5 a n t i f e r r o m a g n e t i c phase has been s t u d i e d by NMR , n e u t r o n 6 7 d i f f r a c t i o n and n u c l e a r o r i e n t a t i o n . Fo r f i e l d s a p p l i e d a l o n g t h e easy a x i s and a t t e m p e r a t u r e s below t h e b i c r i t i c a l p o i n t M n C l 2 . 4 H 2 0 e x h i b i t s t h r e e w e l l d e f i n e d f i e l d dependent phases (see f i g u r e 4 . 1 a ) . The a n t i f e r r o m a g n e t i c phase i s s t a b l e up t o B a=B s f«0.7T where a f i r s t o r d e r phase t r a n s i t i o n t o t h e s p i n f l o p phase o c c u r s , and t h e s p i n f l o p phase i s s t a b l e up t o B =B «1.85T where a second a p o r d e r phase t r a n s i t i o n t o t h e p a r a m a g n e t i c phase o c c u r s . The e l e c t r o n i c magnon spectrum has f o u r b ranches o f a l m o s t e q u a l energy and a l a r g e energy gap f o r z e r o a p p l i e d f i e l d . As t h e 76 F i g u r e 4.1: The Phase Diagram ( a ) , and M a g n e t i c U n i t C e l l (b) o f MnCl .4H o 2 2 I n a) r e g i o n s o f t h e phase d i a g r a m a c c e s s i b l e t o s t u d y by NMRON a r e t h o s e t o t h e l e f t o f t h e dashed l i n e , b) The arrangement o f e l e c t r o n i c s p i n s ( s o l i d arrows) and n u c l e a r s p i n s (dashed arrows) i n t h e magnetic u n i t c e l l o f M n C l 2 . 4 H 2 0 . 7 7 a p p l i e d f i e l d approaches t h e s p i n f l o p f i e l d t h e e x c i t a t i o n gap i n one o f t h e branches approaches z e r o , and t h i s v a n i s h i n g magnon gap i s r e s p o n s i b l e f o r t h e magnon c o o l i n g e f f e c t d i s c u s s e d i n s e c t i o n 3.3. I n t h e p a r a m a g n e t i c phase t h e r e a r e f o u r b r a n c h e s w i t h t h e gap i n t h e e l e c t r o n i c magnon spectrum b e i n g g i v e n by E =gu S(B -B ). g b a p The e x a c t magnitude o f t h e n e a r e s t n e i g h b o r exchange c o u p l i n g i s unknown, but each s p i n e x p e r i e n c e s f e r r o m a g n e t i c c o u p l i n g s from two near n e i g h b o r s and a n t i f e r r o m a g n e t i c c o u p l i n g s from t h e r e m a i n i n g f o u r near n e i g h b o r s (see f i g u r e 4.1b). A u s e f u l model f o r MnCl 2.4H 20 i s a two s u b l a t t i c e u n i a x i a l a n t i f e r r o m a g n e t i n w h i c h t h e e f f e c t s o f t h e b i a x i a l s i n g l e - i o n a n i s o t r o p y a r e r e p l a c e d by an e f f e c t i v e u n i a x i a l i n t e r a c t i o n . F o r f i e l d s a p p l i e d a l o n g t h e easy a x i s t h e u n i a x i a l a n t i f e r r o m a g n e t shows t h e same t h r e e f i e l d dependant phases as 9 MnCl . 4H 0 . A t z e r o f i e l d t h e r e a r e two d e g e n e r a t e 2 2 a n t i f e r r o m a g n e t i c magnon branches c h a r a c t e r i z e d by a gap a t wave v e c t o r k=0 o f magnitude E^«gub ( 2 B A B £ ) 1 7 2 , and a bandwidth o f magnitude git B . F o r MnCl . 4H 0 t h e e f f e c t i v e exchange f i e l d i s b E 2 2 B £«1T and t h e e f f e c t i v e a n i s o t r o p y f i e l d i s B A«1.4T. I n t h e p a r a m a g n e t i c phase t h e r e i s o n l y one b r a n c h as a l l s p i n s a r e m a g n e t i c a l l y e q u i v a l e n t and t h i s b r a n c h has an energy gap o f magnitude E =gu (B -B ) and a bandwidth e q u a l t o 2gu B . The g b a p b E energy gap v a n i s h e s a t B a=B p and magnons w i t h t h e l o w e s t energy have a wave v e c t o r w i t h a magnitude e q u a l t o T r / a Q , where a Q i s t h e m a g n e t i c l a t t i c e c o n s t a n t I n z e r o a p p l i e d f i e l d t 6 8 r e s o n a n c e spectrum o f b o t h s i t e s i s i d e n t i c a l ' . There a r e two h e r e a r e two S 4Mn s i t e s , and t h e 78 5 5Mn n u c l e a r magnon branches and t h e branches have i d e n t i c a l d i s p e r s i o n r e l a t i o n s h i p s . Upon a p p l y i n g a ma g n e t i c f i e l d a l o n g 5 4 t h e easy a x i s o f t h e magnet t h e degeneracy o f b o t h t h e Mn 8 • resona n c e l i n e s , and t h e n u c l e a r magnon d i s p e r s i o n r e l a t i o n s h i p s 5 4 i s removed. I n t h e par a m a g n e t i c phase t h e r e i s o n l y one Mn s i t e and a s i n g l e n u c l e a r magnon b r a n c h (see f i g u r e 4.12). 4.2 S p i n - L a t t i c e r e l a x a t i o n i n t h e A n t i f e r r o m a g n e t i c Phase N u c l e a r s p i n - l a t t i c e r e l a x a t i o n s t u d i e s o f o r d e r e d a n t i f e r r o m a g n e t i c i n s u l a t o r s have been t h e s u b j e c t o f e x t e n s i v e 21 14 15 s t u d y i n t h e p a s t ' ' . The aim o f t h e s e s t u d i e s was t h e measurement o f t h e te m p e r a t u r e and f i e l d dependence o f t h e s p i n - l a t t i c e r e l a x a t i o n r a t e f o r regimes o f t e m p e r a t u r e where t h e dominant r e l a x a t i o n p r o c e s s e s i n v o l v e m u l t i p l e magnon s c a t t e r i n g e v e n t s . Here t h e r e s u l t s o f a s t u d y o f t h e v e r y low te m p e r a t u r e regime i n whi c h t h e s e p r o c e s s e s become v e r y weak i s p r e s e n t e d . The measurements a r e a good example o f t h e use o f NMRON f o r measuring e x c e e d i n g l y l o n g r e l a x a t i o n t i m e s and t h e u s e f u l n e s s e s o f p u l s e d methods i n such measurements. P u l s e d e x c i t a t i o n methods produce l a r g e a n i s o t r o p y changes and t h e use of t h e s e methods can g r e a t l y r e d u c e t h e t i m e s f o r s i g n a l a c q u i s i t i o n . The s t u d y i n v o l v e d s e v e r a l measurements o f a t d i f f e r e n t t e m p e r a t u r e s i n t h e range o f 35mK t o 90mK and a b r i e f d e s c r i p t i o n o f t h e t e c h n i q u e i s now g i v e n . The r e l a x a t i o n t i m e s were measured by f i r s t c o o l i n g t h e c r y s t a l t o t h e t e m p e r a t u r e o f i n t e r e s t , u s i n g t h e magnon c o o l i n g t e c h n i q u e , and t h e n r e t u r n i n g t o z e r o f i e l d and r e s o n a t i n g t h e S 4Mn m=-3 t o m=-2 t r a n s i t i o n 79 u s i n g a c o n t i n u o u s wave r f f i e l d o r by u s i n g a 180 s i n g l e quantum p u l s e . A f t e r t h e e x c i t a t i o n p r o c e s s t h e r e t u r n o f t h e gamma r a y a n i s o t r o p y t o i t s e q u i l i b r i u m v a l u e was m o n i t o r e d as a f u n c t i o n o f t i m e . The r e s u l t s o f t h e measurements o f t h e s p i n l a t t i c e r e l a x a t i o n r a t e f o r t e m p e r a t u r e s between 35mK and 90mK a t z e r o a p p l i e d f i e l d i s shown i n f i g u r e 4.2. There a r e two r a n g e s o f t e m p e r a t u r e w h i c h show a v e r y d i f f e r e n t t e m p e r a t u r e dependence f o r T j 1 * There i s a s h a r p change i n t h e s l o p e o f t h e t e m p e r a t u r e dependence o f T"1 a t about 65mK. T h i s i n d i c a t e s t h a t t h e n a t u r e o f t h e dominant r e l a x a t i o n p r o c e s s has changed a t t h i s t e m p e r a t u r e . From 65mK t o 90mK t h e dominant r e l a x a t i o n p r o c e s s has s t r o n g e x p o n e n t i a l b e h a v i o r i n d i c a t i n g t h a t t h e r e l a x a t i o n mechanism i n v o l v e s e x c i t a t i o n s w i t h an energy much g r e a t e r t h a n k T . The b L r e l a x a t i o n p r o c e s s i s i n t e r p r e t e d as a Raman p r o c e s s and a v a l u e o f T =0.8(2)K i s o b t a i n e d from a f i t o f t h e d a t a i n t h i s A E X ' r e g i o n t o e q u a t i o n 2.42. T h i s v a l u e o f T a e i s c o n s i s t e n t w i t h t h e z e r o f i e l d gap o f T A £=1K o b t a i n e d from a n t i f e r r o m a g n e t i c r e s o n a n c e e x p e r i m e n t s . Below 60mK a n o t h e r p r o c e s s becomes t h e d o m i n a t i n g r e l a x a t i o n p r o c e s s . T h i s p r o c e s s has a weak t e m p e r a t u r e dependence i n d i c a t i n g t h a t i t i n v o l v e s e x c i t a t i o n s w i t h an energy o f t h e o r d e r o f k T . The two most l i k e l y c a n d i d a t e s f o r t h e e x c i t a t i o n b L a r e t h e phonon b a t h o r t h e 5 5Mn n u c l e a r s p i n b a t h . I f t h e l i m i t i n g p r o c e s s i n v o l v e s r e l a x a t i o n t o phonons t h e n t h e spin-phonon i n t e r a c t i o n mechanism i s most l i k e l y an i n d i r e c t p r o c e s s i n v o l v i n g v i r t u a l i n t e r m e d i a t e e x c i t a t i o n s o f t h e 80 10 -4 -= 1 0 " 5 | = 10 -6 -10 -7 H i 20 i i 1 40 60 80 TEMPERATURE (mK) 100 F i g u r e 4.2: The t e m p e r a t u r e Dependence o f T"1 i n t h e A n t i f e r r o m a g n e t i c Phase o f MnCl 2.4H 20 Between 65 mK and 90 mK t h e dominant r e l a x a t i o n p r o c e s s i s an e l e c t r o n i c magnon Raman p r o c e s s . F o r t e m p e r a t u r e s below 65 mK t h e dominant p r o c e s s i s a d i r e c t p r o c e s s . 81 m a g n e t i c l a t t i c e s i m i l a r t o t h e p r o c e s s d i s c u s s e d i n s e c t i o n 2.6. T h i s s u g g e s t i o n i s s u p p o r t e d by t h e b e h a v i o r o f t h e r e l a x a t i o n t i m e o f 5 4Mn measured a t h i g h f i e l d s i n t h e pa r a m a g n e t i c phase o f MnCl 2.4H 20. These measurements show t h a t t h e u l t i m a t e 5 4Mn l i m i t i n g r e l a x a t i o n p r o c e s s , i . e . r a d i o a c t i v e decay, c o r r e s p o n d i n g t o T 1=2.6*10 7s i s r e a c h e d a t an a p p l i e d f i e l d o f 4T. D i r e c t n u c l e a r - s p i n phonon r e l a x a t i o n m e d i a t e d by t h e e l e c t r i c q u a d r u p o l e i n t e r a c t i o n i s ind e p e n d e n t o f t h e mag n e t i c s t r u c t u r e , and i f t h i s p r o c e s s was t h e d i r e c t p r o c e s s o b s e r v e d i n t h e a n t i f e r r o m a g n e t i c phase t h e n t h i s same p r o c e s s would be o p e r a t i v e i n t h e par a m a g n e t i c phase.The f a c t t h a t t h e l i m i t i n g r e l a x a t i o n r a t e i s so d i f f e r e n t f o r t h e two phases s u g g e s t s t h a t t h e l i m i t i n g r e l a x a t i o n p r o c e s s e s i n t h e a n t i f e r r o m a g n e t i c phase do n o t i n v o l v e t h e e l e c t r i c q u a d r u p o l e mechanism. A n o t h e r p o s s i b l e mechanism w h i c h depends on t h e a p p l i e d f i e l d i s a d i r e c t r e l a x a t i o n p r o c e s s t o t h e 5 5Mn s p i n s ystem; i n f a v o r o f t h i s mechanism i s t h e h i g h d e n s i t y o f n u c l e a r magnon s t a t e s c l o s e t o t h e 5 4Mn reso n a n c e f r e q u e n c y , and t h e l a r g e SN c o u p l i n g o f s t r e n g t h 3MHz between 5 4Mn and 5 5Mn. A p o i n t a g a i n s t d i r e c t r e l a x a t i o n t o t h e n u c l e a r magnon system i s t h a t t h e f r e q u e n c y d i f f e r e n c e between t h e n u c l e a r magnons and t h e 5 4Mn re s o n a n c e , ( f i k - 5 4 t d n ) [2n)-1=13 0MHz, i s l a r g e compared t o t h e bandwidth o f t h e n u c l e a r magnons, 5Q=4MHz. These v a l u e s o f f r e q u e n c y d i f f e r e n c e and magnon bandwidth i m p l y a r e l a x a t i o n p r o c e s s e s i n v o l v i n g o f t h e o r d e r o f 40 magnons, and t h u s v e r y h i g h o r d e r p r o c e s s e s a r e r e q u i r e d t o a b s o r b t h e energy o f a f l i p p i n g 5 4Mn s p i n . I n p r i n c i p l e e q u a t i o n 2.46 c o u l d be used t o c a l c u l a t e t h e r e l a x a t i o n r a t e , b u t t h e c a l c u l a t i o n would be v e r y 82 d i f f i c u l t . Y e t a n o t h e r p o s s i b i l i t y i n v o l v i n g t h e n u c l e a r magnon system i s a p r o c e s s s i m i l a r t o t h e phonon mechanism d i s c u s s e d f o r t h e e l e c t r o n i c magnons. I n t h i s c a s e t h e e x p r e s s i o n f o r r k a n a l o g o u s t o e q u a t i o n 2.44 i s y k«sinh(e)G kU(n k- 5 4cj n) _ 1 (4.1) Where s i n h ( 8 ) i s d e f i n e d i n e q u a t i o n 2.40b and i t i s t h e e l e c t r o n i c magnon a d m i x t u r e c o e f f i c i e n t f o r t h e n u c l e a r magnon wave f u n c t i o n o f wave v e c t o r k. G k i s t h e magnetophonon c o u p l i n g c o n s t a n t f o r t h e e l e c t r o n i c magnon o f wave v e c t o r k and U i s t h e s t r e n g t h o f t h e SN i n t e r a c t i o n c o u p l i n g t h e n u c l e a r magnons t o t h e 5 4Mn n u c l e i . The v a l u e o f U(Q - 5 4<j ) - 1 i s o f t h e same o r d e r k n as 5 4 A ( c a k - 5 4 w n ) ~ 1 and sinh(0)«l and a l t h o u g h t h i s p r o c e s s w i l l g i v e a c o n t r i b u t i o n t o T i t w i l l be dominated by t h e c o r r e s p o n d i n g e l e c t r o n i c p r o c e s s . Due t o t h e l a c k o f d a t a on magnon phonon c o u p l i n g c o n s t a n t s i n MnCl . 4H 0 no c o n c l u s i v e c a l c u l a t i o n o f t h e magnon m e d i a t e d 2 2 phonon p r o c e s s can be made. The o n l y r e a s o n a b l e c o n c l u s i o n i s t h a t t h e p r o c e s s shows a s t r o n g dependence on b o t h t h e magn e t i c s t r u c t u r e and t h e magnon energy gap i m p l y i n g i n v o l v e m e n t o f e l e c t r o n i c and/or n u c l e a r magnons, and t h a t t h e o b s e r v e d l i m i t i n g r e l a x a t i o n p r o c e s s i s a d i r e c t p r o c e s s due t o i t s weak t e m p e r a t u r e dependence (see e q u a t i o n 2.45a f o r t h e t e m p e r a t u r e dependence o f a d i r e c t r e l a x a t i o n p r o c e s s ) . 4.3 The Spectrum of the Paramagnetic Phase CW NMRON has been observed for the f i r s t time in the paramagnetic phase of MnCl2.4H20 and this section discusses the line shape and f i e l d dependence of the resonances. . . 5 4 The resonance line for the m=-3 to m=-2 transition of Mn oriented in MnCl2.4H20 at a temperature of 40mK and a value of applied-field of 2.6T is shown in figure 4.5. The CW resonance experiment was performed both with and without frequency modulation of the applied r f f i e l d . The intensity of the resonance without modulation was observed to decrease to one half of that observed with frequency modulation. This approximate decrease in signal amplitude indicates that the main cause of the observed line width i s a static broadening mechanism. The 300KHz line width i s consistent with that due to the variation of the local magnetic f i e l d caused by electronic dipole interactions and sample shape dependent demagnetizing • . 5 4 . . . f i e l d s . The maximum Mn frequency shift due to interactions with neighboring electronic moments i s 1 MHz and the net magnetisation in the paramagnetic phase i s 0.04T, (54Mn has an NMR resonance frequency of 8.4 MHz/T). A careful measurement of the f i e l d dependence of the lowest three resonances of the 54Mn hyperfine multiplet was undertaken to determine the value of the S4Mn hyperfine f i e l d < 5 4 A S > The results of these measurements at f i e l d values above 1.85T i s shown in figure 4.6. For applied fields above 2.15T the behavior of the resonance lines i s well described by equation 2.5a. Table 1 gives the values of the hyperfine f i e l d < 5 4 A S > and the 84 >-r— t - H CO LU Q LU 0.94 0.90 0.86 0.82 0.78 I 1 I 1 I I I I I I ) I | I | I 484 485 485 485 486 486 FREQUENCY (MHZ) Figure 4.3: A CW NMRON Resonance Line i n the Paramagnetic Phase o f MnCl .4H O 2 2 This figure shows the m=-3 to m=-2 t r a n s i t i o n of 5 4Mn at an applied f i e l d of 2.6T. 85 500 2.5 3 3.5 F IELD [T] - 3 - > - 2 # - 2 - > -1 ^ -1 - > 0 F i g u r e 4 . 4 : F i e l d Dependence o f t h e P a r a m a g n e t i c Phase Resonance F r e q u e n c i e s . The f i e l d dependence o f t h e resonance f r e q u e n c y f o r l o w e s t t h r e e r e s o n a n c e l i n e s o f 5 4Mn i s shown. The s o l i d l i n e i s a f i t t o t h e d a t a u s i n g e q u a t i o n 2.5a. Below 2.15 T e q u a t i o n 2.5a i s no l o n g e r v a l i d and h i g h e r o r d e r p e r t u r b a t i o n c o r r e c t i o n s a r e n e c e s s a r y t o f i t t h e d a t a . 86 sum of the exchange and anisotropy fields B£+ 40/g/i^ obtained from numerical f i t s of the f i e l d dependence of the lowest three resonance frequencies to equation 2.5a. In the table m and m' label the energy levels involved and the value of " P " (see equation 2.5a), the electric quadrupole coupling constant, used in the f i t s was 0.15MHz8. The average value of <54AS>^h obtained from the data i s -513.63(3) MHz. A value for (BE+4D/g^b) can also be obtained from the data. From f i t s to the m=-3 -> m=-2 and m=-2 m=-l transitions a value of (BE+4D/gfib)=0.95 (5) T i s obtained. The same parameter measured from f i t s to the f i e l d dependence of the resonance lines in the antiferromagnetic phase i s (BE+4D/g|nb) =1.355 (25) T. In the antif erromagnetic phase the exchange f i e l d BE equals the sum of the ferromagnetic, F A F B , and antiferromagnetic, B , exchange fi e l d s . In the E E A F F paramagnetic phase B i s equal to the difference of B and B . E E E From the values of (BE+4D/g/ib) obtained in both phases the total difference between the antiferromagnetic and ferromagnetic contributions to the exchange f i e l d i s estimated to be 2(BF-BAF)=0.20 (1) T. E E 87 m m' < 5 4 A S > / h [MHz] (B E +4D/gu f a ) [T] -3 -2 -513 .3 ± 0 . 2 0 . 8 9 ± 0 . 0 4 -2 -1 -513 .9 ± 0 . 3 1 . 0 1 ± 0 . 0 5 -1 0 -513 .9 ± 0 . 3 0.56+0.25 T a b l e 1 Measurements o f the Paramagnet i c Phase H y p e r f i n e C o u p l i n g C o n s t a n t s F o r v a l u e s o f a p p l i e d f i e l d l e s s t h a n 2.15 T e q u a t i o n 2 .16a i s no l o n g e r v a l i d and a h i g h e r o r d e r p e r t u r b a t i o n e x p a n s i o n i s n e c e s s a r y t o d e s c r i b e the f i e l d dependent b e h a v i o r o f the re sonance l i n e s . 4.4 Zero P o i n t M o t i o n i n the A n t i f e r r o m a g n e t i c Phase F o r an M n 2 + s p i n o r d e r e d a l o n g the z - a x i s the s t a t i c 5 4 M n h y p e r f i n e H a m i l t o n i a n i s H = 5 4 A S o l = h 5 4 u I (4.2) s z z n z The maximum v a l u e o f < 5 4A S > i s o b t a i n e d f o r a f r e e Mn 2* i o n z and t h i s v a l u e i s d e c r e a s e d upon i n c o r p o r a t i o n o f t h e i o n i n a s o l i d . The r e d u c t i o n i n 5 4 C J i s due t o a d e c r e a s e i n <S > o r a n z d e c r e a s e i n 5 4 A . The reduced v a l u e o f 5 4 A i n a s o l i d i s caused by the p a r t i a l c o v a l e n t bonding o f M n 2 + t o o t h e r atoms i n t h e s o l i d which l e a d s t o a d e c r e a s e d e l e c t r o n i c s p i n d e n s i t y a t t h e i o n i c s i t e . The v a l u e o f <S z> i s m o d i f i e d by c r y s t a l f i e l d e f f e c t s and s p i n - d e v i a t i o n s caused by the t h e r m a l and quantum 88 m e c h a n i c a l z e r o p o i n t m o t i o n o f t h e e l e c t r o n i c s p i n . The ground s t a t e o f an a n t i f e r r o m a g n e t e x h i b i t i n g l o n g range N e e l o r d e r has a n e t s p i n S=0 and an a p p r o x i m a t i o n t o t h e z e r o p o i n t s p i n d e v i a t i o n 1 0 can be c a l c u l a t e d from t h e sum o f t h e a m p l i t u d e s o f t h e z e r o p o i n t m o t i o n o f each spin-wave mode. The v a l u e o b t a i n e d exceeds t h a t c a l c u l a t e d f o r t h e c o r r e s p o n d i n g f e r r o m a g n e t due t o t h e l a r g e c o n t r i b u t i o n t o t h e z e r o p o i n t m o t i o n coming from t h e l o n g wave l e n g t h a n t i f e r r o m a g n e t i c spin-waves. I f i t i s assumed t h a t 5 4A i s t h e same i n b o t h phases t h e n t h e z e r o p o i n t s p i n d e v i a t i o n i n t h e a n t i f e r r o m a g n e t i c phase o f MnCl .4H 0 can be e x p r e s s e d as 2 2 AS=(< 5 4AS> P-< 5 4AS> A F) ( ^ W ) " 1 (4.3) Here < 5 4AS> P i s t h e par a m a g n e t i c phase h y p e r f i n e f i e l d and < 5 4AS> A F i s t h e a n t i f e r r o m a g n e t i c phase h y p e r f i n e f i e l d . As d i s c u s s e d above t h e z e r o p o i n t m o t i o n i s dependent upon t h e s t r u c t u r e o f t h e o r d e r e d s t a t e and s h o u l d be d i f f e r e n t f o r t h e a n t i f e r r o m a g n e t i c and p a r a m a g n e t i c phases o f MnCl 2.4H zO. I n t h e a n t i f e r r o m a g n e t i c phase * 5 4AS> A F/h=-509.4(1) MHz 8 and a com p a r i s o n w i t h t h e v a l u e o f < S 4AS> P/h=-513.6(3) MHz o b t a i n e d i n t h e p r e v i o u s s e c t i o n g i v e s an a n t i f e r r o m a g n e t i c phase z e r o p o i n t m o t i o n o f AS=0.0084(5). Note t h a t t h e r e a r e a l s o c o n t r i b u t i o n s t o t h e 5 4Mn reso n a n c e f r e q u e n c y from l o c a l d i p o l e f i e l d s w h i c h a r e d i f f e r e n t i n b o t h phases b u t t h e s e e f f e c t s a r e s m a l l , (<1 MHz), compared t o t h e d i f f e r e n c e i n 5 4o n=< 5 4AS>/h o f t h e r e s p e c t i v e p h a s e s , «5 MHz. The z e r o p o i n t s p i n d e v i a t i o n has been c a l c u l a t e d f o r MnCl .4H O 1 1. The c a l c u l a t i o n assumes a s i m p l i f i e d c u b i c 2 2 2 s u b l a t t i c e model o f MnCl .4H O and a v a l u e o f AS=0.024 was 89 o b t a i n e d f o r t h e z e r o p o i n t s p i n d e v i a t i o n . The s m a l l v a l u e o f t h e o b s e r v e d s p i n d e v i a t i o n , AS=0.0084(5), i s a t t r i b u t e d t o t h e pr e s e n c e o f f e r r o m a g n e t i c a l l y a l i g n e d near n e i g h b o r s p i n s i n t h e mag n e t i c u n i t c e l l . These i n t e r a c t i o n s were n o t i n c l u d e d i n t h e c a l c u l a t i o n o f r e f . 34. 4.5 S p i n - L a t t i c e R e l a x a t i o n i n t h e Pa r a m a g n e t i c Phase The f i e l d dependence o f t h e 5 4Mn s p i n l a t t i c e r e l a x a t i o n t i m e f o r f i e l d s a p p l i e d a l o n g t h e easy a x i s and f o r v a l u e s o f f i e l d above t h e s p i n - f l o p p a r a m a g n e t i c phase t r a n s i t i o n has been measured and t h e r e s u l t s a r e shown i n f i g u r e s 4.5 and 4.6. F i g u r e 4.5 shows t h e f i e l d dependence o f T a t 35mK w h i l e f i g u r e 4.6 shows t h e f i e l d dependence a t 55mK. Bo t h c u r v e s d i s p l a y a s i m i l a r f i e l d dependent b e h a v i o r w i t h t h e l o w e r t e m p e r a t u r e measurements y i e l d i n g l o n g e r v a l u e s o f r e l a x a t i o n t i m e . A t h i g h f i e l d s t h e r e l a x a t i o n t i m e becomes v e r y l o n g and T r e a c h e s t h e r a d i o a c t i v e decay l i m i t o f 2.6*10 7s a t a f i e l d o f 4T. As B i s d e c r e a s e d t h e c u r v e s show a br o a d f l a t minimum i n a T t c e n t e r e d a t B a=2.65T, and a r a p i d l y d e c r e a s i n g T as t h e a p p l i e d f i e l d approaches t h e par a m a g n e t i c s p i n - f l o p t r a n s i t i o n f i e l d o f B «1.85T. T h i s r a p i d d e c r e a s e i s due t o t h e v a n i s h i n g gap i n t h e p a r a m a g n e t i c phase magnon spectrum. A p l a u s i b l e mechanism f o r t h e T minimum i n v o l v e s t h e o t h e r n u c l e a r s p i n s p e c i e s p r e s e n t i n t h e c r y s t a l . A t a f i e l d o f 2.65T t h e sum o f t h e average p r o t o n Zeeman r e s o n a n c e f r e q u e n c y and t h e 5 4Mn h y p e r f i n e f r e q u e n c y e q u a l s t h e gap i n t h e 5 SMn n u c l e a r magnon spectrum. A r e l a x a t i o n p r o c e s s i n v o l v i n g b o t h a 5 4Mn n u c l e a r s p i n f l i p and a p r o t o n n u c l e a r s p i n f l i p w i t h t h e 90 g e n e r a t i o n o f a n u c l e a r magnon can o c c u r q u i t e f r e e l y s i n c e a l l t h r e e systems a r e m u t u a l l y c o u p l e d by t h e i r n u c l e a r m a g n e t i c d i p o l e - d i p o l e c o u p l i n g s and t h e SN i n t e r a c t i o n . T h i s mechanism has been d i s c u s s e d i n s e c t i o n 2.6 and an e x p l i c i t c a l c u l a t i o n o f t h e r e l a x a t i o n r a t e f o r t h e above p r o c e s s i s g i v e n i n s e c t i o n 5.9. The p r o t o n s i n t h e MnCT 2.4H 20 u n i t c e l l have d i f f e r e n t r e s o n a n c e f r e q u e n c i e s due t o t h e d i f f e r e n c e s i n t h e i r t r a n s f e r r e d h y p e r f i n e i n t e r a c t i o n s and m a g n e t i c d i p o l e i n t e r a c t i o n s w i t h t h e Mn 2 + l o c a l moments. These l o c a l f i e l d s s p r e a d t h e p r o t o n r esonance spectrum o v e r a f r e q u e n c y range o f 29 16 MHz and t h e p r o t o n spectrum i s c e n t e r e d a t 130 MHz when B =2.65 T. A t t h e same f i e l d t h e w i d t h o f t h e n u c l e a r magnon band SQ, (see e q n u a t i o n 2.40), has a v a l u e o f 10MHz and t h e band i s c e n t e r e d a t 611 MHz. As t h e a p p l i e d f i e l d i s d e c r e a s e d from a v a l u e f a r above t h e T minimum t h e p r o t o n r e s o n a n c e f r e q u e n c i e s d e c r e a s e and b o t h t h e gap i n t h e n u c l e a r magnon spectrum, and t h e 5 4Mn reso n a n c e f r e q u e n c y i n c r e a s e . The l e v e l c r o s s i n g p r o c e s s d i s c u s s e d above o c c u r s a t about 2.65 T and t h e w i d t h o f t h e T minimum can be e x p l a i n e d by t h e range o f f i e l d v a l u e s f o r w h i c h t h e p r o t o n s pectrum o v e r l a p s t h e n u c l e a r magnon band. The t e m p e r a t u r e dependence o f t h e r e l a x a t i o n r a t e was measured i n t h e r e g i o n o f t h e T minimum and t h e r e s u l t o f one su c h measurement a t B a = 3 T i s shown i n f i g u r e 4.7. The r e l a x a t i o n r a t e has an a p p r o x i m a t e l y l i n e a r t e m p e r a t u r e dependence t h r o u g h o u t t h e r e g i o n o f t h e minimum and t h i s b e h a v i o r i s c o n s i s t e n t w i t h a r e l a x a t i o n mechanism w h i c h i n v o l v e s e x c i t a t i o n s w i t h energy o f t h e o r d e r o f k T . The b L t e m p e r a t u r e dependence o f t h e r e l a x a t i o n r a t e was a l s o measured 91 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 FIELD [T] F i g u r e 4.5: The F i e l d Dependence o f T i n t h e P a r a m a g n e t i c Phase o f MnCl .4H 0 a t 35 mK 2 2 5 4 The f i e l d dependence o f t h e s p i n l a t t i c e r e l a x a t i o n r a t e o f Mn i n t h e p a r a m a g n e t i c phase o f MnCl 2.4H 20 a t a t e m p e r a t u r e o f 35mK i s shown f o r f i e l d s between 2.15T and 3T. Below 2.3T t h e r a t e i s dominated by r e l a x a t i o n t o t h e e l e c t r o n i c magnons, w h i l e i n t h e r e g i o n o f t h e T minimum t h e dominant p r o c e s s i n v o l v e s t h e p r o t o n and 5 5Mn s p i n systems. 92 1400 1200 1000 1 1 800 </) H 600 400 200 0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 FIELD [T] 3.1 3.2 F i g u r e 4 . 6 : The F i e l d Dependence o f T i n t h e P a r a m a g n e t i c Phase o f MnCl .4HO a t 55mK 93 10 9 8 in 1 O o o ^ 6 " 5 30 35 40 45 50 55 60 T E M P E R A T U R E [mK] Figure 4.7: The Temperature Dependence of T^1 i n the Paramagnetic phase for Ba=3 T The dependence of T^1 on temperature at an applied f i e l d of 3T i s l i n e a r . This indicates that the relaxation mechanism involves excitations with an energy of the order of k bT L. 94 35 40 45 50 55 60 65 T E M P E R A T U R E [mK] F i g u r e 4.8: The Temperature Dependence of T"1 i n t h e P a r a m a g n e t i c phase for Ba=2.1T The dependence o f l n ( T ~ 1 ) on t e m p e r a t u r e a t an a p p l i e d f i e l d o f 2. IT has a l i n e a r t e m p e r a t u r e dependence i n d i c a t i n g t h a t t h e r e l a x a t i o n mechanism i n v o l v e s e x c i t a t i o n s w i t h energy much g r e a t e r t h a n k T . b L 95 a t a f i e l d o f 2. 2T i n o r d e r t o i n v e s t i g a t e t h e n a t u r e o f t h e r e l a x a t i o n p r o c e s s below t h e l e v e l c r o s s i n g minimum. The r e s u l t , shown i n f i g u r e 4.8, i s t h a t t h e r e l a x a t i o n r a t e has an e x p o n e n t i a l t e m p e r a t u r e dependence s i m i l a r t o t h a t g i v e n i n e q u a t i o n 2.42 w i t h T =160mK. The v a l u e o f k T i s e q u a l t o ^ AE b AE ^ t h e gap p r e s e n t i n t h e par a m a g n e t i c magnon spectrum a t t h i s v a l u e o f f i e l d and t h e r e l a x a t i o n mechanism i s most l i k e l y an e l e c t r o n i c magnon Raman s c a t t e r i n g p r o c e s s s i m i l a r t o t h a t d i s c u s s e d i n s e c t i o n 2.6. 4.6 Thermal NMR i n t h e Para m a g n e t i c Phase The t h e r m a l d e t e c t i o n o f 5 5Mn NMR i n t h e a n t i f e r r o m a g n e t i c 7 phase o f MnCl 2.4H 20 was f i r s t p e r f o rmed by K o t l i c k i and T u r r e l l . The z e r o f i e l d r e s o n a n c e was o b s e r v e d by a magnon c o o l i n g i n d u c e d c r o s s r e l a x a t i o n between t h e 'hot' r e s o n a t e d 5 5Mn s p i n system and 5 4Mn s p i n s . The reso n a n c e was a l s o o b s e r v e d a t a f i e l d c l o s e t o t h e a n t i f e r r o m a g n e t i c s p i n - f l o p phase t r a n s i t i o n where T was s u f f i c i e n t l y s h o r t t o o b s e r v e t h e re s o n a n c e t h r o u g h c r o s s r e l a x a t i o n w i t h out u s i n g magnon c o o l i n g . I n t h i s s e c t i o n t h e r e s u l t s o f a 5 5Mn t h e r m a l r e s o n a n c e e x p e r i m e n t i n t h e par a m a g n e t i c phase o f MnCl 2-4H 20 a r e p r e s e n t e d and a d i s c u s s i o n o f t h e l i n e s h a p e g i v e n . The r e s u l t o f a t h e r m a l r e s o n a n c e r u n a t B =2.IT i s shown i n f i g u r e 4.9. The a p p l i e d r f f i e l d c o u p l e s t o t h e k=0 5 5Mn n u c l e a r mode and h e a t s t h e 5 5Mn s p i n b a t h t h r o u g h t h e magnon-magnon s c a t t e r i n g and t h e l a t t i c e o f t h e c r y s t a l v i a s p i n - l a t t i c e r e l a x a t i o n . F o r t h i s v a l u e o f a p p l i e d f i e l d t h e 5 4Mn s p i n - l a t t i c e r e l a x a t i o n t i m e i s s h o r t and t h e t h e r m a l r e s o n a n c e 96 i s d e t e c t e d w i t h o u t t h e need f o r f i e l d i n d u c e d c r o s s r e l a x a t i o n . A t low t e m p e r a t u r e s t h e 5 5Mn e x c i t a t i o n s a r e t h e n u c l e a r s p i n waves d i s c u s s e d i n s e c t i o n 2.5 and a dia g r a m o f t h e wave v e c t o r dependence o f t h e e l e c t r o n i c magnon and n u c l e a r magnon d i s p e r s i o n r e l a t i o n s h i p s f o r wave v e c t o r s a l o n g t h e (1,1,1) d i r e c t i o n i s shown i n f i g u r e 4.10. The wave v e c t o r o f t h e n u c l e a r magnon w i t h t h e l a r g e s t t e m p e r a t u r e dependent f r e q u e n c y p u l l i n g o c c u r s a t t h e edge o f t h e B r i l l o u i n zone and t h e maximum v a l u e o f t e m p e r a t u r e dependent s h i f t f o r t h e s e n u c l e a r magnons i s 50MHz. The k=0 mode e x h i b i t s a v e r y s m a l l t e m p e r a t u r e dependent f r e q u e n c y p u l l i n g o f maximum v a l u e 5MHz, t h i s s m a l l s i z e o f t h e f r e q u e n c y p u l l i n g i s due t o t h e h i g h energy o f t h e k=0 e l e c t r o n i c magnon (see e q u a t i o n 2.13b). When t h e a p p l i e d f i e l d i s swept up t h r o u g h t h e k=0 n u c l e a r magnon f r e q u e n c y t h e s p i n system b e g i n s t o abs o r b energy from t h e f i e l d and h e a t s up. As t h e t e m p e r a t u r e i n c r e a s e s t h e a b s o r p t i o n spectrum o f t h e n u c l e a r system broadens and e v e n t u a l l y c o v e r s a range o f f r e q u e n c i e s d e t e r m i n e d by t h e magnetic pseudoquadrupole spectrum o f an i s o l a t e d 5 5Mn n u c l e u s . The s p i n system c o n t i n u e s t o ab s o r b power from t h e r f f i e l d u n t i l t h e f r e q u e n c y o f t h e a p p l i e d r f has swept t h r o u g h t h i s whole range. F o r t h e re s o n a n c e l i n e shown i n f i g u r e 4.11 t h i s range i s 20 MHz. The o b s e r v e d w i d t h o f 3 7 MHz i s somewhat l a r g e r t h a n t h e sum o f t h e maximum low t e m p e r a t u r e f r e q u e n c y p u l l i n g , 5 MHz, and t h e t o t a l w i d t h o f t h e pseudoquadrupole s p l i t spectrum, 20 MHz. T h i s c o u l d be due t o a l o n g t h e r m a l t i m e c o n s t a n t g o v e r n i n g t h e c o o l i n g r a t e o f t h e c r y s t a l and g i v i n g an ob s e r v e d l i n e w i d t h l a r g e r t h a n t h e 9 7 t r u e v a l u e . The s t a r t f r e q u e n c y o f t h e t h e r m a l l y d e t e c t e d a b s o r p t i o n band i s 606MHz and t h i s v a l u e i s c l o s e t o t h a t c a l c u l a t e d from t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn. There may be an u n d e r l y i n g pseudoquadrupole s t r u c t u r e t o t h e r e s o n a n c e l i n e , b u t i t s d e t e c t i o n would r e q u i r e c a r e f u l o p t i m i z a t i o n o f t h e r f f i e l d sweep r a t e and t h e r f f i e l d a m p l i t u d e . 9 8 >- 0.96 CO LU 0.92 Q LU rvi 0.88 CC o 0.84 lll'li , nlll'l'll'1!!"!!,,!! II II II "Win 'III ll ll',l 580 600 620 640 660 FREQUENCY (MHZ) F i g u r e 4.9: Thermal NMR L i n e i n t h e P a r a m a g n e t i c Phase o f MnCl .4H0 2 2 99 (*)( k) i 1 : 1—> k -TT TT F i g u r e 4.10: The P a r a m a g n e t i c Phase Magnon Spectrum. The e l e c t o n i c and n u c l e a r e x c i t a t i o n s p ectrum a l o n g t h e (1,1,1) d i r e c t i o n f o r a two s u b l a t i c e u n i a x i a l a n t i f e r r o m a g n e t i n an a p p l i e d f i e l d above t h e s p i n - f l o p t o p a r a m a g n e t i c phase t r a n s i t i o n f i e l d , B . 100 Chapter 5 NMRON in Manganese Acetate Tetrahydrate 5 . 1 NMRON in Manganese Acetate Tetrahydrate An i m p o r t a n t r e q u i r e m e n t f o r a s u c c e s s f u l NMRON s t u d y o f any m a t e r i a l i s t h a t t h e r a d i o a c t i v e n u c l e a r ensemble c o o l , and t h a t t h e c o o l i n g t i m e be s u f f i c i e n t l y s h o r t t o make NMRON e x p e r i m e n t s p r a c t i c a l . F o r r a d i o a c t i v e n u c l e i i m p l a n t e d i n m e t a l s t h e h i g h d e n s i t y o f c o n d u c t i o n e l e c t r o n s a t t h e Fermi s u r f a c e p r o v i d e t h e n e c e s s a r y f l u c t u a t i n g h y p e r f i n e f i e l d s t o r e l a x t h e n u c l e i . The c o n d u c t i o n e l e c t r o n s a r e a l s o t h e major t h e r m a l c a r r i e r s w h i c h t r a n s p o r t t h e energy from t h e r e l a x i n g n u c l e i i n t o t h e c o l d f i n g e r o f t h e d i l u t i o n r e f r i g e r a t o r . I n o r d e r e d M n 2 + magnetic i n s u l a t o r s t h e major t h e r m a l r e s e r v o i r s a r e t h e 5 5Mn n u c l e a r s p i n b a t h , t h e e l e c t r o n i c magnon b a t h , t h e phonon b a t h and t h e 5 4Mn n u c l e a r s p i n system. The e l e c t r o n i c magnon and phonon b a t h s a r e k e p t i n t h e r m a l e q u i l i b r i u m by magnon-phonon s c a t t e r i n g p r o c e s s e s . These p r o c e s s e s a r e r a p i d compared t o t h e r a t e o f h e a t t r a n s p o r t from t h e sample t o t h e c o l d f i n g e r and so t h e magnon and phonon systems a r e always a t t h e same t e m p e r a t u r e . T h e r m a l i s a t i o n o f th e n u c l e a r s p i n systems w i t h t h e phonon b a t h o c c u r s v i a much weaker s p i n - l a t t i c e r e l a x a t i o n p r o c e s s e s o f t h e t y p e d i s c u s s e d i n s e c t i o n 2.6. The e x c i t a t i o n s w h i c h c a r r y t h e h e a t from t h e sample i n t o t h e c o l d f i n g e r a r e phonons w h i l e c a r r i e r s 101 r e s p o n s i b l e f o r t h e r m a l t r a n s p o r t w i t h i n t h e sample a r e t h e l a t t i c e phonons and t h e m agnetic e x c i t a t i o n s . The i n i t i a l NMRON e x p e r i m e n t s on MnCl 2. 4 H 20 showed t h a t t h e n u c l e a r s p i n t e m p e r a t u r e o n l y r e a c h e d 85 mK i f t h e sample was s i m p l y mounted on t h e c o l d f i n g e r and l e f t t o c o o l . As d e s c r i b e d i n s e c t i o n 3.3 t h e magnon c o o l i n g t e c h n i q u e can be used t o red u c e t h e n u c l e a r s p i n t e m p e r a t u r e t o 30 mK b u t w i t h o u t t h e a p p l i c a t i o n o f t h i s c o o l i n g method i t would t a k e months f o r t h i s t o happen. 35 Mn(C00CH 3) 2.4H 20 has a complex c r y s t a l s t r u c t u r e and t h e magnon and phonon s p e c t r a a r e h i g h l y a n i s o t r o p i c . The z e r o f i e l d magnon energy gap i s c l o s e t o one h a l f o f t h e MnCl 2.4H 20 magnon energy gap and one might e x p e c t s i m i l a r z e r o f i e l d c o o l i n g b e h a v i o r f o r b o t h systems. T h i s does n o t o c c u r and t h e n u c l e a r s p i n r e s e r v o i r s i n Mn(C00CH 3) 2.4H 20 c o o l i n g r e l a t i v e l y q u i c k l y even i n z e r o f i e l d . The t h e r m a l c o u p l i n g between t h e 5 5Mn n u c l e a r magnons and t h e phonon l a t t i c e o f Mn(C00CH 3) 2.4H 20 a t z e r o a p p l i e d f i e l d i s much s t r o n g e r t h a n t h a t o b s e r v e d i n MnCl 2 . 4 H 2 0 . T h i s can be e x p l a i n e d by t h e l a r g e " e l e c t r o n i c magnon" component o f t h e " n u c l e a r magnons" w i t h wave v e c t o r n e a r k=0, and t h e p o s s i b i l i t y o f a s t r o n g " e l e c t r o n i c magnon"-phonon c o u p l i n g due t o t h e low symmetry o f t h e Mn 2* environment. 5 . 2 The M a g n e t i c p r o p e r t i e s o f Manganese A c e t a t e T e t r a h y d r a t e Manganese A c e t a t e T e t r a h y d r a t e has a c r y s t a l i g r a p h i c l a y e r 35 (a-b) p l a n e s t r u c t u r e and i t s m a g n e t i c p r o p e r t i e s have been 3 6 summarized by Okuda e t a l . A space p r o j e c t i o n o f t h e manganese 102 i o n s i n one o f t h e c r y s t a l o g r a p h i c l a y e r s i s shown i n f i g u r e 5. l a . The manganese i o n s o f a l a y e r a r e a r r a n g e d i n groups o f t h r e e i o n s and t h e i o n s i n a group a r e c o u p l e d t o g e t h e r by oxygen and a c e t a t e l i n k a g e s (see f i g u r e 5.1b). Each t r i p l e t o f Mn 2 + i o n s i s c o u p l e d t o f o u r o t h e r t r i p l e t s by a c e t a t e l i n k a g e s and t h e r e a r e no s t r o n g bonds between d i f f e r e n t l a y e r s . The oxygen l i n k a g e s w i t h i n a t r i p l e t p r o v i d e t h e major superexchange pathways and t h e t h r e e s p i n s o f a t r i p l e t a r e bound by a s t r o n g a n t i f e r r o m a g n e t i c exchange c o u p l i n g o f t h e o r d e r o f ( J / k )=45 K. The superexchange c o u p l i n g between t h e t r i p l e t s o f a l a y e r i s v i a t h e a c e t a t e l i n k a g e s and i t i s f e r r o m a g n e t i c and much weaker 37 t h a n t h e i n t r a - t r i p l e t a n t i f e r r o m a g n e t i c exchange . There a r e no s t r o n g superexchange pathways between l a y e r s and t h e i n t e r l a y e r c o u p l i n g i s v e r y weak and a n t i f e r r o m a g n e t i c . The h i g h degree o f ma g n e t i c two d i m e n s i o n a l i t y i s e v i d e n t from t h e r a t i o o f i n t r a - p l a n a r f e r r o m a g n e t i c c o u p l i n g t o i n t e r - p l a n a r a n t i f e r r o m a g n e t i c c o u p l i n g , J f/J a f«10 3. Mn(COOCH ) .4H 0 o r d e r s a t T «3.18 K a l o n g t h e a - a x i s w i t h 3 2 2 n a d j a c e n t p l a n e s a n t i p a r a l l e l . The e f f e c t i v e m a g n e t i c moment o f each t r i p l e t group i s c l o s e t o (5/2)u and t h e a n i s o t r o p y f i e l d s b a r e e s t i m a t e d t o be B c=0.135 T and B*=0.86 T , ( t h e c - a x i s i s A A p e r p e n d i c u l a r t o t h e p l a n e and t h e b - a x i s l i e s i n t h e p l a n e p e r p e n d i c u l a r t o t h e easy a - a x i s (see f i g u r e 5 . 1 a ) ) . F o r f i e l d s a p p l i e d a l o n g t h e easy a x i s t h e samples used i n t h e e x p e r i m e n t s e x h i b i t a metamagnetic phase t r a n s i t i o n a t B a=0.0006 T t o a mixed phase c o n s i s t i n g o f p a r a m a g n e t i c and a n t i f e r r o m a g n e t i c domains (see f i g u r e 5.2). A t TL=0 t h e s a t u r a t i o n o f t h e sample m a g n e t i z a t i o n o c c u r s a t B =0.014 T. The v a l u e s o f a p p l i e d f i e l d 103 F i g u r e 5.1: The Low Temperature S p i n Arrangement i n MnfCOOCH ) .4H O * 3 ' 2 2 a) The low t e m p e r a t u r e s p i n arrangement i n one o f t h e l a y e r s o f Mn(C00CH 3) .4H 20; a t z e r o a p p l i e d f i e l d a d j a c e n t l a y e r s have an a n t i p a r a l l e l s p i n arrangement a t each s i t e , b) A more d e t a i l e d d i a g r a m o f t h e atoms w h i c h p r o v i d e t h e major superexchange pathways between t h e Mn2* i o n s . 104 B a [T] 0. 014 0.0006-As -TT Paramagnetic Tl TT M i x e d Phase TJ, Antiferromagnetic 1 > 0.15 3.18 T L [ K ] F i g u r e 5.2: The Low F i e l d Phase Diagram o f Mn(COOCH 3) 2.4H 20 The r e g i o n s o f t h e phase diagram amenable t o s t u d y by NMRON a r e t h o s e t o t h e l e f t o f t h e dashed l i n e . The shaded r e g i o n i s a mixed phase r e g i o n c o n s i s t i n g o f p a r a m a g n e t i c and a n t i f e r r o m a g n e t i c domains. F o r t h e geometry o f t h e samples used and a t z e r o t e m p e r a t u r e t h e metamagnetic phase t r a n s f o r m a t i o n b e g i n s a t an a p p l i e d f i e l d o f 0.6 mT and t h e s a t u r a t i o n m a g n e t i s a t i o n i s r e a c h e d a t an a p p l i e d f i e l d o f 0.014 T. 105 a t t h e phase boundarys were d e t e r m i n e d by s q u i d magnetometry measurements on samples i d e n t i c a l t o t h o s e used i n t h e e x p e r i m e n t s . The e l e c t r o n i c magnon spectrum o f Mn(COOCH 3) .4H 20 i n t h e a n t i f e r r o m a g n e t i c phase has 12 branches s i n c e t h e r e a r e 12 35 m a g n e t i c atoms i n t h e magnetic u n i t c e l l . The magnon spectrum has 8 h i g h energy branches w h i c h i n v o l v e t h e r e l a t i v e m o t i o n o f s p i n s i n t h e t r i p l e t and 4 low energy branches i n w h i c h each t r i p l e t behaves as a s i n g l e e f f e c t i v e s p i n o f S=(5/2). The d i s p e r s i o n o f t h e low energy branches i s d e t e r m i n e d by t h e i n t r a - p l a n a r f e r r o m a g n e t i c c o u p l i n g , J f , and t h e i n t e r - p l a n a r a n t i f e r r o m a g n e t i c c o u p l i n g , J . A u s e f u l model system f o r t h e m a g n e t i c l a t t i c e o f Mn(COOCH 3) .4HzO i s o b t a i n e d by r e p l a c i n g each t r i p l e t group by a s i n g l e s p i n o r d e r e d i n t h e same d i r e c t i o n as t h e Mn2 e l e c t r o n i c s p i n s and c o u p l e d t o n e i g h b o r i n g s p i n s by t h e same i n t e r a c t i o n s as t h o s e c o u p l i n g t h e t r i p l e t s o f s p i n s i n t h e r e a l system. Each o f t h e s e e f f e c t i v e s p i n s i s c o u p l e d t o t h r e e n u c l e a r s p i n s , (see f i g u r e 5.3), and t h e arrangement o f t h e e f f e c t i v e e l e c t r o n i c s p i n s i n t h e o r d e r e d s t a t e i s shown i n f i g u r e 5.4. There a r e two Mn s i t e s (denoted by Mnl and Mn2 i n f i g u r e 5.3) and two Mn i s o t o p e s , p r o d u c i n g a t o t a l o f 4 s e t s o f NMR l i n e s . The complete CW NMRON resonance spectrum i s shown i n f i g u r e 5.5. The two l o w e r f r e q u e n c y narrow l i n e w i d t h r e s o n a n c e m u l t i p l e t s a r e t h o s e o f 5 4Mn. The f i r s t o f t h e s e o c c u r s a t a f r e q u e n c y o f 435 MHz and c o r r e s p o n d s t o t h e Mnl s i t e . The h i g h e r 5 4Mn re s o n a n c e o c c u r s a t a f r e q u e n c y o f 475 MHz and has t w i c e 106 435 MHz Mn2-i t - M n i - -Mn2 i B 475 MHz 475 MHz F i g u r e 5 . 3 : The S 4Mn N u c l e a r Resonance S i t e s a) Each t r i p l e t o f manganese s p i n s has two n u c l e a r r e s o n a n c e s i t e s and a t z e r o f i e l d t h e two 5 4Mn re s o n a n c e m u l t i p l e t s a r e p o s i t i o n e d a t t h e f r e q u e n c i e s w r i t t e n b e s i d e each e l e c t r o n i c s p i n . There i s a low f r e q u e n c y r e s o n a n c e a t t h e Mnl s i t e and a h i g h f r e q u e n c y r e s o n a n c e o f t w i c e g r e a t e r i n t e n s i t y a t t h e Mn2 s i t e . The s t r u c t u r e o f t h e e f f e c t i v e - s p i n system used t o ap p r o x i m a t e a M n 2 + t r i p l e t i s shown on t h e r i g h t hand s i d e o f t h e f i g u r e . Each e f f e c t i v e s p i n i s c o u p l e d t o t h r e e Manganese n u c l e i and i n t h e diagram t h e s o l i d a r r ow r e p r e s e n t s t h e o r d e r e d e l e c t r o n i c moment w h i l e t h e dashed arrow r e p r e s e n t s t h e n u c l e a r s p i n d i r e c t i o n i n t h e low t e m p e r a t u r e o r d e r e d s t a t e . 107 : /fv : 4-Ta-: /p : A) : 4 . : 4 / U : /f. : B ) C ) F i g u r e 5.4: The Low F i e l d e f f e c t i v e S p i n S t r u c t u r e o f Mn(COOCH ) . 4H 0 * 3 ' 2 2 a) The arrangement o f e f f e c t i v e e l e c t r o n i c moments and n u c l e a r s p i n s w i t h i n a p l a n e , b) The e l e c t r o n i c s p i n arrangement o f t h e p l a n e s o f e f f e c t i v e s p i n s i n z e r o f i e l d , i n t h i s phase t h e r e two e l e c t r o n i c and s i x n u c l e a r s p i n s p e r m a g n e t i c u n i t c e l l , c) The e l e c t r o n i c s p i n arrangement o f t h e p l a n e s o f e f f e c t i v e s p i n s i n f i e l d s above 0.014T, i n t h i s phase t h e r e i s one e l e c t r o n i c and t h r e e n u c l e a r s p i n s p e r magnetic u n i t c e l l . 108 420 460 500 540 580 620 FREQUENCY (MHZ) F i g u r e 5 . 5 : T h e Complete Manganese NMR Spectrum f o r Mn(COOCH ) .4HO a t B=0.4 T * 3 ' 2 2 a The l o w e r f r e q u e n c y s h a r p changes i n a n i s o t r o p y c o r r e s p o n d t o 5 4Mn NMRON r e s o n a n c e s w h i l e t h e t h e upper changes a r e t h e r m a l l y d e t e c t e d S 5Mn resonance l i n e s . 109 t h e a m p l i t u d e o f t h e l o w e r f r e q u e n c y r e s o n a n c e . T h i s r e s o n a n c e i s a t t r i b u t e d t o n u c l e i a t t h e Mn2 s i t e . B o t h o f t h e r e s o n a n c e s c o n s i s t o f a m u l t i p l e t o f 6 r e s o n a n c e l i n e s , b u t i n t h e e x p e r i m e n t shown i n f i g u r e 5.5 most o f t h i s s t r u c t u r e i s unobserved due t o t h e l a r g e f r e q u e n c y s t e p o f 1 MHz used t o o b t a i n t h e d a t a , (see s e c t i o n 5.3). The upper r e s o n a n c e l i n e s a r e t h e r m a l l y d e t e c t e d 5 5Mn resonance l i n e s w i t h t h e f i r s t o f t h e s e b e i n g t h e Mnl s i t e r e s o n a n c e a t 545 MHz and t h e second b e i n g an Mn2 s i t e r e sonance a t 590 MHz. Note t h a t because o f t h e c o n d i t i o n s used i n t h e e x p e r i m e n t t h e r e l a t i v e i n t e n s i t y o f t h e s e l i n e s does n o t r e f l e c t t h e number o f n u c l e i i n v o l v e d i n each r e s o n a n c e , (see s e c t i o n 5.5) A s k e t c h o f t h e low t e m p e r a t u r e e x c i t a t i o n spectrum o f t h e a p p r o x i m a t e s t r u c t u r e i s shown i n f i g u r e 5.6 f o r z e r o a p p l i e d f i e l d , and i n f i g u r e 5.7 f o r a p p l i e d f i e l d s a p p l i e d a l o n g t h e a - a x i s above 0.014 T ( i . e . i n t h e m a g n e t i c a l l y s a t u r a t e d p a r a m a g n e t i c p h a s e ) . Each diagram shows t h e magnon d i s p e r s i o n c u r v e s f o r wave v e c t o r k c o r r e s p o n d i n g t o a d i r e c t i o n p e r p e n d i c u l a r t o t h e f e r r o m a g n e t i c p l a n e s , ( d e f i n e d as k i ) , and t h e spectrum f o r k p a r a l l e l t o t h e p l a n e s , ( d e f i n e d as k / / ) . The f i r s t d e s c r i p t i o n i s f o r magnons w i t h wave v e c t o r a l o n g k i . The band d e s i g n a t e d #1 i n f i g u r e 5.6 r e p r e s e n t s two d e g e n e r a t e bands o f e l e c t r o n i c magnons w i t h a s t r u c t u r e v e r y s i m i l a r t o t h e magnons o f t h e u n i a x i a l a n t i f e r r o m a g n e t i n z e r o a p p l i e d f i e l d . The e l e c t r o n i c s p i n s i n t h e p l a n e p r e c e s s i n phase and t h e d i s p e r s i o n o f t h e bands i s d e t e r m i n e d by t h e weak i n t e r l a y e r c o u p l i n g . The bandwidth i s e q u a l t o gu B , b a f (B *0.6 mT), and t h e energy gap i s gju B , (B «0.2 T) . The a f b A A 110 F i g u r e 5.6: The E x c i t a t i o n Spectrum f o r t h e Model Mn(C00CH 3) 2.4H 20 System a t Zero A p p l i e d F i e l d The upper d i s p e r s i o n c u r v e i s f o r t h e e l e c t r o n i c magnons and t h e l o w e r c u r v e s a r e f o r t h e n u c l e a r magnons. The wave v e c t o r s k// c o r r e s p o n d t o a d i r e c t i o n a l o n g t h e m a g n e t i c p l a n e s and k i t o a d i r e c t i o n p e r p e n d i c u l a r t o t h e p l a n e s . The v e r t i c a l a x i s i s n o t t o s c a l e and t h e r e l e v a n t e n e r g i e s a r e d i s c u s s e d i n t h e t e x t . I l l F i g u r e 5 .7: The E x c i t a t i o n Spectrum f o r t h e Model Mn(C00CH 3) 2.4H 20 System f i e l d s above 0.014 T The upper d i s p e r s i o n c u r v e i s f o r t h e e l e c t r o n i c magnons and t h e lo w e r c u r v e s a r e f o r t h e n u c l e a r magnons. The wave v e c t o r s k// c o r r e s p o n d t o a d i r e c t i o n a l o n g t h e ma g n e t i c p l a n e s and k i t o a d i r e c t i o n p e r p e n d i c u l a r t o t h e p l a n e s . The v e r t i c a l a x i s i s n o t t o s c a l e and t h e r e l e v a n t e n e r g i e s a r e d i s c u s s e d i n t h e t e x t . 112 bands #2 and #3 a r e d o u b l y d e g e n e r a t e n u c l e a r magnon bands and t h e e x c i t a t i o n s o f t h e s e bands i n v o l v e m o t i o n o f t h e Mn2 s i t e s p i n s . The SN i n t e r a c t i o n between t h e l a y e r s i s v e r y weak so t h a t t h e r e i s no d i s p e r s i o n a l o n g t h e k i d i r e c t i o n . N u c l e a r magnon band #4 i s a d o u b l y d e g e n e r a t e band i n v o l v i n g n u c l e i a t t h e Mnl s i t e . The gap i n t h e n u c l e a r magnon bands i s d e t e r m i n e d by t h e s t a t i c h y p e r f i n e i n t e r a c t i o n 5 5 t J and t h e energy s h i f t o f n t h e i n p l a n e k=0 n u c l e a r mode, h ( 5 5 w -n ). n 0 The magnons w i t h i n t h e p l a n e a r e d e s c r i b e d by 8 bands. Curve #5 r e p r e s e n t s a d o u b l y d e g e n e r a t e magnon band and magnons from t h e s e bands i n v o l v e s t h e r e l a t i v e m o t i o n o f s p i n s i n t h e p l a n e . The d i s p e r s i o n o f t h e band i s d e t e r m i n e d by t h e i n t r a - p l a n a r f e r r o m a g n e t i c c o u p l i n g , , t h e bandwidth i s gu f aB f, w i t h B f«2.4 T, and t h e gap i n t h e band i s gu B , w i t h B «0.2 T. E x p r e s s e d i n b A A terms o f f r e q u e n c y t h e gap i s 8*10 9 Hz, and t h e bandwidth i s 1*10 1 1 Hz. T h i s r e l a t i v e l y l a r g e r a t i o o f bandwidth t o band gap i m p l i e s a range o f 4 magnetic l a t t i c e s p a c i n g s f o r t h e i n p l a n e SN i n t e r a c t i o n , (see e q u a t i o n 2.35b),- and t h e r e f o r e n u c l e i w i t h i n t h e p l a n e a r e s t r o n g l y c o u p l e d p r o d u c i n g w e l l d e f i n e d n u c l e a r magnon e x c i t a t i o n s . Band #6 i s a n u c l e a r magnon band w i t h a k=0 mode whi c h i n v o l v e s t h e m o t i o n o f b o t h Mnl s i t e n u c l e i w h i c h a r e 180° o u t o f phase, and s i n c e s t r o n g c o u p l i n g between n u c l e i o c c u r s t h r o u g h t h e k=0 e l e c t r o n i c magnon, t h e r e i s v e r y l i t t l e d i s p e r s i o n i n t h i s band. Band #7 a g a i n i n v o l v e s m o t i o n o f b o t h o f t h e S 5Mn2 s i t e n u c l e i , b u t i n t h e k=0 mode b o t h n u c l e i p r e c e s s i n phase and t h i s mode e x h i b i t s s t r o n g f r e q u e n c y p u l l i n g . Band #8 i n v o l v e s n u c l e i a t t h e Mn2 s i t e and a g a i n t h e d i s p e r s i o n a l o n g t h e k// d i r e c t i o n i s l a r g l y due t o 113 t h e s t r o n g f r e q u e n c y p u l l i n g o f t h e low k n u c l e a r magnons. I n t h e p a r a m a g n e t i c phase ( f i g u r e 5.7) t h e magnon d i s p e r s i o n r e l a t i o n s h i p s a l o n g k// a r e v e r y s i m i l a r t o t h e c o r r e s p o n d i n g c u r v e s i n t h e a n t i f e r r o m a g n e t i c phase. The r e a s o n f o r t h i s i s t h a t t h e m a g n e t i c s t r u c t u r e o f a p l a n e i s i d e n t i c a l i n b o t h phases. The major d i f f e r e n c e s between t h e phases o c c u r a l o n g k i : t h e r e i s a h a l v i n g o f t h e magnetic u n i t c e l l i n t h e p a r a m a g n e t i c phase, and a change o f t h e e l e c t r o n i c d i s p e r s i o n r e l a t i o n s h i p s i m i l a r t o t h a t w h i c h o c c u r s f o r t h e p a r a m a g n e t i c phase magnons of M n C l 2 . 4 H 2 0 ( I n t h e f i e l d o r d e r e d p a r a m a g n e t i c phase o f an a n t i f e r r o m a g n e t t h e l o w e s t energy magnons have a h i g h k wave v e c t o r , see s e c t i o n 4.7 f i g u r e 4.12). To summarise t h e g r o s s f e a t u r e s o f t h e m a g n e t i c e x c i t a t i o n s , t h e e l e c t r o n i c magnon spectrum i s v e r y a n i s o t r o p i c w i t h s t r o n g i n - p l a n e d i s p e r s i o n , t h e r e i s weak d i s p e r s i o n p e r p e n d i c u l a r t o t h e p l a n e and a gap a t k=0. The SN i n t e r a c t i o n i s l o n g ranged i n t h e p l a n e w i t h a range, b Q , e q u a l t o 4 m a g n e t i c l a t t i c e s p a c i n g s and t h e i n p l a n e n u c l e a r magnons a r e w e l l d e f i n e d e x c i t a t i o n s . The i n t e r p l a n a r SN i n t e r a c t i o n i s n e g l i g i b l e i n b o t h t h e a n t i f e r r o m a g n e t i c phase and t h e p a r a m a g n e t i c phase and n u c l e a r magnons w i t h wave v e c t o r a l o n g kj. form a v e r y narrow band. For f i e l d s above 0.014 T t h e gap i n t h e e l e c t r o n i c spectrum i n c r e a s e s by an amount gu B w h i l e t h e magnon bandwidth remains b a unchanged. The gap i n t h e h i g h e r energy n u c l e a r magnon band, n Q,and t h e bandwidth, 5 f i , d e c r e a s e w i t h i n c r e a s i n g f i e l d (see e q u a t i o n 2.40 o f s e c t i o n 2.5 and t h e d i s c u s s i o n f o u n d t h e r e ) . The gap i n t h e lo w e r n u c l e a r magnon band i n c r e a s e s w i t h f i e l d 114 and i t s bandwidth i s narrowed. The 5 4Mn reso n a n c e f r e q u e n c i e s , 5 4 u , a r e s h i f t e d by t h e n e x t e r n a l f i e l d w i t h t h e h i g h e r f r e q u e n c y r e s o n a n c e d e c r e a s i n g and t h e lo w e r f r e q u e n c y resonance i n c r e a s i n g w i t h f i e l d . A t an a p p l i e d f i e l d o f 2.64 T t h e n u c l e a r magnon bands merge and t h e 5 4 M n l and 5 4Mn re s o n a n c e s l e v e l c r o s s (see f i g u r e 5.8). 5.3 The CW NMRON 5 4Mn Resonance spectrum CW NMRON reso n a n c e e x p e r i m e n t s were p e r f o r m e d t o d e t e r m i n e t h e number o f reso n a n c e s i t e s and t h e v a l u e s o f t h e h y p e r f i n e f i e l d f o r each s i t e . A b r i e f d e s c r i p t i o n o f t h e two o b s e r v e d s i t e s has been g i v e n i n s e c t i o n 5.2 and i n t h i s s e c t i o n a more d e t a i l e d d i s c u s s i o n o f t h e e x p e r i m e n t s and o f t h e s t r u c t u r e o f th e h y p e r f i n e m u l t i p l e t s i s p r e s e n t e d . The s p e c t r a were o b t a i n e d u s i n g s t a n d a r d CW NMRON t e c h n i q u e s and an example o f t h e spectrum o f t h e Mn2 s i t e t a k e n a t Ba=0.2 T and T L=57 mK i s shown i n f i g u r e 5.9. T h i s spectrum was measured u s i n g an unmodulated r f f i e l d w h i c h was s t e p p e d t h r o u g h t h e reson a n c e l i n e s i n 100 kHz s t e p s w i t h a d w e l l t i m e o f 1000 s p e r c h a n n e l . There a r e s i x m t o m+1 t r a n s i t i o n s and f i v e o f t h e s e a r e c l e a r l y v i s i b l e i n f i g u r e 5.9. The l o w e s t f r e q u e n c y r e s o n a n c e i s t h e m=-3 t o m=-2 t r a n s i t i o n o f t h e 5 4Mn2 h y p e r f i n e m u l t i p l e t and t h e s u c c e s s i v e r e s o n a n c e s a r e spaced by «1 MHz. The l i n e s p l i t t i n g s a r e due t o t h e magn e t i c pseudoquadrupole i n t e r a c t i o n and t h e e l e c t r i c q u a d r u p o l e i n t e r a c t i o n (see e q u a t i o n s 2.5). A comparison o f t h e o b s e r v e d s i g n a l a m p l i t u d e s under b o t h unmodulated and f r e q u e n c y modulated r f i r r a d i a t i o n showed t h a t t h e reso n a n c e l i n e s a t low f i e l d a r e homogeneously broadened w i t h a l i n e w i d t h o f 400 kHz. The cause 115 480 - i 470-460H 450 440 H 430 x x x >o<> X X o 1 1 1 r 0.5 1 1.5 2 FIELD (T) 2^ n 3 F i g u r e 5.8: 5 4 Mn Resonance The F i e l d Dependence o f t h e F r e q u e n c i e s The h i g h e r f r e q u e n c y m=-3 t o m=-2 t r a n s i t i o n d e c r e a s e s w i t h f i e l d and t h e l o w e r f r e q u e n c y m=3 t o m=2 t r a n s i t i o n i n c r e a s e s w i t h f i e l d , t h e res o n a n c e f r e q u e n c i e s c r o s s a t an e x t e r n a l f i e l d o f B =2.64T. a 116 \Z 0.930 -CO 0.910 I-Q 0.890 L U ~ 0.870 CE cn o 0.850 * i I ! 1 II1 ' i V 1 ! ' » iHllllW ' I 1 1 " i l l / ,1IIIU . l ' 1 ! . . I i i i 472.0 474.0 476.0 478.0 480.0 482.0 FREQUENCY (MHZ) F i g u r e 5 . 9 : The 5 4Mn2 NMRON Resonance i n Mn(COOCH ) . 4 H O f o r B =0.2 T 3 2 2 a T h i s i s an example o f a s h o r t T NMRON re s o n a n c e spectrum. F i v e o f t h e s i x Am±l t r a n s i t i o n s o f t h e 5 4Mn2 s i t e n u c l e i a r e v i s i b l e . The l o w e s t f r e q u e n c y l a r g e s t a m p l i t u d e t r a n s i t i o n i s t h e m=-3 t o m=-2 res o n a n c e , t h e l i n e i s homogeneously broadened and 400KH.Z wide. The l i n e s p l i t t i n g s a r e 1.2MHz and t h e y a r e due t o a c o m b i n a t i o n o f t h e magn e t i c pseudoquadrupole i n t e r a c t i o n and t h e e l e c t r i c q u a d r u p o l e i n t e r a c t i o n . 117 458 471 474 477 480 FREQUENCY (MHZ) F i g u r e 5.10: The 5 4Mn2 NMRON Resonance i n MnfCOOCH ) .4H O f o r B =0.5 T * 3' 2 2 a The v a l u e o f T i s much l o n g e r t h a n t h a t o f t h e p r e v i o u s f i g u r e and t h e second m=-2 t o m=-l t r a n s i t i o n d e c r e a s e s t h e a x i a l a n i s o t r o p y . The l i n e w i d t h and t h e l i n e s p l i t t i n g a r e a l m o s t t h e same as t h e p r e v i o u s f i g u r e . 118 o f t h e l i n e w i d t h i s somewhat o f a my s t e r y . A t t h i s v a l u e o f f i e l d and t e m p e r a t u r e t h e p o p u l a t i o n o f t h e r m a l e l e c t r o n i c magnons i s t o o s m a l l t o cause a b r o a d e n i n g o f t h i s magnitude by 14 Raman T 2 p r o c e s s e s and a n o t h e r e x p l a n a t i o n f o r T g must be sought. The a m p l i t u d e and s i g n o f t h e reso n a n c e depends on t h e r e l a t i v e v a l u e s o f t h e r f f i e l d sweep r a t e and t h e s p i n - l a t t i c e r e l a x a t i o n r a t e . R e d i s t r i b u t i o n o f t h e p o p u l a t i o n s o f a l l l e v e l s o c c u r t h r o u g h s p i n - l a t t i c e r e l a x a t i o n , so t h a t s p e c t r a l p r o f i l e s depend on t h e sweep r a t e . S a t u r a t i n g a g i v e n t r a n s i t i o n a l t e r s t h e p o p u l a t i o n s o f a l l o f t h e energy l e v e l s and t h e r e s u l t i s t h a t each t r a n s i t i o n o f f i g u r e 5.9 causes t h e same s i g n o f a n i s o t r o p y change. T h i s b e h a v i o r i s c l e a r l y d e m o n s t r a t e d by comparing t h e shape o f t h e resonance spectrum i n f i g u r e 5.9, w i t h t h a t o f f i g u r e 5.10 where t h e s p i n l a t t i c e r e l a x a t i o n t i m e i s l o n g . The f i r s t m=-3 t o m=-2 reso n a n c e o f f i g u r e 5.10 i n c r e a s e s t h e magnitude o f t h e a x i a l a n i s o t r o p y as does t h e f i r s t r e s o n a n c e o f f i g u r e 5.9, t h e second m=-2 t o m=-l reso n a n c e d e c r e a s e s t h e a x i a l a n i s o t r o p y w h i l e t h e c o r r e s p o n d i n g r e s o n a n c e i n f i g u r e 5.9 once a g a i n causes an i n c r e a s e i n t h e a x i a l a n i s o t r o p y . The l o w e r f r e q u e n c y 5 4 M n l resonance has a s i m i l a r s t r u c t u r e t o t h e 5 4Mn2 re s o n a n c e , b u t t h e i n t e n s i t y o f t h e 5 4 M n l l i n e s i s one h a l f o f t h a t o f t h e 5 4Mn2 l i n e s . A n o t h e r d i f f e r e n c e between t h e s i t e s i s t h a t t h e s p i n - l a t t i c e r e l a x a t i o n t i m e o f t h e 5 4 M n l s i t e i s «1000 t i m e s l o n g e r t h a n t h a t o f t h e 5 4Mn2 s i t e . The most p r o b a b l e e x p l a n a t i o n f o r t h i s b e h a v i o r i s d i s c u s s e d i n 38 s e c t i o n 5.6. A s t u d y o f t h e f i e l d dependence o f t h e re s o n a n c e 119 f r e q u e n c i e s and l e v e l s p l i t t i n g s , g i v e s t h e v a l u e o f t h e h y p e r f i n e c o u p l i n g c o n s t a n t s as < 5 4AS>/h = -435 MHz f o r t h e Mnl s i t e and < 5 4AS>/h= -477 MHz f o r t h e Mn2 s i t e and t h e r e s u l t s o f t h e a n a l y s i s , ( t a k i n g i n t o a c c o u n t t h e second o r d e r 'pseudoquadrupole' i n t e r a c t i o n ) , a r e c o n s i s t e n t w i t h an e l e c t r i c q u a d r u p o l e c o u p l i n g c o n s t a n t o f P/h*0.1 MHz f o r b o t h s i t e s . F o r a pure i o n i c bond when t h e e f f e c t i v e s p i n v a l u e f o r t h e Mn i o n would be <S z>=(5/2), minus a s m a l l s p i n d e v i a t i o n and c r y s t a l f i e l d e f f e c t , a v a l u e o f < 5 4AS>/h=-500 MHz would be e x p e c t e d . The d e c r e a s e i n < 5 4AS>/h f o r t h e two a c e t a t e s i t e s i s p o s s i b l y 13 . . due t o t h e s t r o n g c o v a l e n t e f f e c t s d e c r e a s i n g t h e e l e c t r o n i c s p i n d e n s i t y a t t h e s i t e o f t h e Mn 2* i o n and a l a r g e z e r o p o i n t s p i n d e v i a t i o n o f t h e Mn 2* s p i n . These e f f e c t s would be c o n s i s t e n t w i t h t h e s t r o n g a n t i f e r r o m a g n e t i c i n t e r - t r i p l e t c o u p l i n g . 5.4 The F i e l d Dependence o f T i The i n i t i a l CW NMRON measurements i n Mn(COOCH ) .4H 0 a t low x 3 ' 2 2 f i e l d r e v e a l e d some v e r y s u r p r i s i n g b e h a v i o r r e g a r d i n g t h e magnitude o f t h e s p i n - l a t t i c e r e l a x a t i o n t i m e s f o r t h e Mnl and Mn2 s i t e s . The r e l a x a t i o n t i m e o f t h e Mn2 s i t e f o r f i e l d s below 0.1T was so s m a l l t h a t i t c o u l d n o t be measured by CW NMRON methods because t h e r f power l e v e l s r e q u i r e d t o o b s e r v e t h e re s o n a n c e caused e x c e s s i v e non-resonant h e a t i n g o f t h e sample. A n o t h e r p u z z l i n g r e s u l t was t h e l a r g e d i f f e r e n c e i n r e l a x a t i o n t i m e s measured f o r t h e s i t e s . The Mnl s i t e c o u l d be o b s e r v e d a t z e r o f i e l d u s i n g CW NMRON w h i l e t h e Mn2 re s o n a n c e c o u l d n o t , and a t a f i e l d o f 0.2 T t h e Mnl r e l a x a t i o n t i m e was 10 3 t i m e s 120 g r e a t e r t h a n t h a t o f t h e Mn2 s i t e . A t z e r o f i e l d t h e gap i n t h e magnon spectrum i s a l m o s t h a l f o f t h e z e r o f i e l d gap i n M nCl 2.4H 20 and one might e x p e c t t h a t t h e r e l a x a t i o n t i m e s measured i n Mn(COOCH ) .4H O s h o u l d be a t 3 ' 2 2 most an o r d e r o f magnitude l e s s t h a n t h o s e measured i n t h e f o r m e r . F u r t h e r m o r e , i f i t i s assumed t h a t t h e dominant modes i n v o l v e d i n t h e r e l a x a t i o n p r o c e s s a r e low f r e q u e n c y f e r r i m a g n e t i c modes t h e n t h e r e l a x a t i o n t i m e s o f b o t h s i t e s s h o u l d d i f f e r by no more t h a n t h e r a t i o o f t h e s q u a r e o f t h e h y p e r f i n e c o u p l i n g c o n s t a n t s a t each s i t e , i . e . a maximum d i f f e r e n c e o f 20% ( The a m p l i t u d e o f t h e f e r r i m a g n e t i c mode e l e c t r o n i c s p i n f l u c t u a t i o n s i s a l m o s t i d e n t i c a l a t each s i t e ) . A s e r i e s o f measurements p r e s e n t e d i n t h i s and t h e n e x t s e c t i o n were c a r r i e d o ut i n an a t t e m p t t o e l u c i d a t e t h e mechanism o f s p i n - l a t t i c e r e l a x a t i o n and d i s c o v e r why t h e r e l a x a t i o n t i m e s o f t h e s i t e s d i f f e r e d by such a l a r g e amount. The e x p e r i m e n t s a l s o p r o v i d e d an e x c e l l e n t i l l u s t r a t i o n o f t h e e f f i c a c y o f p u l s e d NMRON f o r m e a s u r i n g v e r y s h o r t r e l a x a t i o n t i m e s . The f i e l d dependence o f T was measured f o r v a l u e s o f a p p l i e d f i e l d i n t h e range 0 T t o 3 T a t a l a t t i c e t e m p e r a t u r e o f 40 mK. The p u l s e d T measurements where p e r f o r m e d by a p p l y i n g a 180° p u l s e a t t h e m=-3 t o m=-2 t r a n s i t i o n f r e q u e n c y and t h e r e s u l t s o f t h e measurements f o r f i e l d s between B =0 T and a B a=0.25 T a r e shown i n F i g u r e 5.11. Many measurements were pe r f o r m e d i n t h e v e r y low f i e l d r e g i o n t o l o o k f o r any e f f e c t o f t h e metamagnetic mixed phase s t a t e on no such i n f l u e n c e was seen, t h e r e l a x a t i o n t i m e r e m a i n i n g c o n s t a n t a t a v a l u e 121 -1.5 0 0.05 0.1 0.15 0.2 0.25 F IELD [T] F i g u r e 5 . 1 1 : The F i e l d Dependence o f T i n Mn(COOCH ) .4H 0 f o r B =0 T t o 0.25 T 3 ' 2 2 a A t B a = 0 . 1 5 T t h e magnon bandwidth i s t o o narrow t o a l l o w a t h r e e n u c l e a r magnon r e l a x a t i o n p r o c e s s and a h i g h e r o r d e r p r o c e s s becomes t h e d o m i n a t i n g r e l a x a t i o n mechanism. 122 4000 3000 eg T - 2000 1000 0 o o o o o o 2.4 2.5 2.6 2.7 2.8 2.9 FIELD CD F i g u r e 5 . 1 2 : The F i e l d Dependence o f T i n Mn(COOCH ) .4H O f o r B = 2 . 3 T t o 3 T •3 & 2 Ok The f i e l d dependence o f T i n t h e r e l a x a t i o n t i m e minimum, a t B a = 2 . 6 4 T t h e re s o n a n c e f r e q u e n c i e s o f t h e two manganese s i t e s l e v e l c r o s s and T shows an a b r u p t i n c r e a s e . 123 c l o s e t o 100 ms up t o B =0.15 T. T h i s b e h a v i o r can be e x p l a i n e d a by t h e modes c o n t r i b u t i n g t o t h e 5 4 Mn r e l a x a t i o n b e i n g s i m i l a r i n t h e p a r a m a g n e t i c and a n t i f e r r o m a g n e t i c domains. A t Ba«0.015 T t h e s l o p e o f t h e f i e l d dependence o f T undergoes a d r a m a t i c i n c r e a s e w i t h T e v e n t u a l l y r e a c h i n g 10 6 s a t B a=0.6 T. When B=1.8 T t h e r e l a x a t i o n t i m e b e g i n s t o d e c r e a s e and i t f a l l s t o a v a l u e o f t h e o r d e r o f 200 s a t B =2.5 T. The r e l a x a t i o n t i m e a t h e n e x h i b i t s a v e r y p e c u l i a r b e h a v i o r ; i t r e a c h e s a l o c a l maximum a t B=2.64 T, (T i s o f t h e o r d e r o f 3500 s) , deceases a 1 t o a n o t h e r minimum a t 2.8 T and t h e n b e g i n s a s t e e p monotoriic r i s e as t h e a p p l i e d f i e l d i s f u r t h e r i n c r e a s e d (see f i g u r e 5.12). The jump i n T whi c h o c c u r s a t 2.64 T i s q u i t e d r a m a t i c , T i n c r e a s e s by a f a c t o r o f 30 as t h e a p p l i e d f i e l d i s i n c r e a s e d from 2.5 T t o 2.64 T. The s h a r p i n c r e a s e i n T i n d i c a t e s t h a t a change must be o c c u r r i n g i n one o f t h e t h e r m a l b a t h s i n v o l v e d i n t h e r e l a x a t i o n p r o c e s s . B e f o r e a t t e m p t i n g an e x p l a n a t i o n o f t h e ob s e r v e d r e l a x a t i o n b e h a v i o r i t i s i n s t r u c t i v e t o d e s c r i b e t h e t h e r m a l NMR e x p e r i m e n t s on t h e u n i f o r m mode r e s o n a n c e s . 5 . 5 The F i e l d dependence o f t h e Thermal NMR Resonances The u n i f o r m resonance modes o f t h e n u c l e a r magnon branches d e s c r i b e d i n s e c t i o n 5.2 were i n v e s t i g a t e d u s i n g t h e r m a l NMR because i t was s u s p e c t e d t h a t t h e s e modes c o u l d be p l a y i n g an e s s e n t i a l r o l e i n t h e r e l a x a t i o n phenomena d i s c u s s e d i n s e c t i o n 5.4. The r e s u l t s o f t h r e e t h e r m a l NMR r u n s a r e shown i n f i g u r e s 5.13, 5.14, 5.15. I n t h e measurement a t z e r o a p p l i e d f i e l d t h e r e a r e two t h e r m a l r e s o n a n c e s w h i c h appear t o be o f e q u a l a m p l i t u d e 124 (see f i g u r e 5.13). The resonance l i n e s were measured u s i n g a 200 s d w e l l t i m e and s t e p p i n g t h e f r e q u e n c y by 1 MHz t h r o u g h each c h a n n e l . No f r e q u e n c y m o d u l a t i o n was n e c e s s a r y because t h e reson a n c e l i n e s a r e homogeneously broadened. The l o w e r f r e q u e n c y r e s o n a n c e i s t h a t o f t h e u n i f o r m mode o f t h e Mnl s i t e n u c l e a r magnons. The a b s o r p t i o n o f r f power b e g i n s a t 510 MHz and c o n t i n u e s f o r t h e f o l l o w i n g 30 MHz o f t h e f r e q u e n c y sweep. The second h i g h e r f r e q u e n c y resonance i s t h a t o f t h e Mnl u n i f o r m mode. I t b e g i n s a t 560 MHz and c o v e r s a s i m i l a r f r e q u e n c y r a n g e . A t h e r m a l NMR measurement w i t h B a=0.004 T i s shown i n f i g u r e 5.14. I n t h i s r u n t h e r f f i e l d a m p l i t u d e was r e d u c e d and t h e magnitude o f t h e res o n a n c e s i s more r e p r e s e n t a t i v e o f t h e numbers o f n u c l e a r s p i n s i n v o l v e d i n each mode. The Mn2 mode s p i n s a r e t w i c e as dense as t h e Mnl mode s p i n s and t h e a m p l i t u d e o f t h e Mn2 t h e r m a l NMR s i g n a l i s c o r r e s p o n d i n g l y t w i c e as l a r g e t h e Mnl s i g n a l . The d i p j u s t b e f o r e t h e f i r s t r e s o n a n c e i s an e x p e r i m e n t a l a r t i f a c t and t h e Mnl l i n e a b s o r p t i o n s t a r t s a t a s l i g h t l y l o w e r f r e q u e n c y t h a n appears i n t h e f i g u r e s . The a r t i f a c t i s due t o an unplanned f r e q u e n c y dependent c o u p l i n g o f t h e t e m p e r a t u r e c o n t r o l l e r t o t h e f r e q u e n c y s y n t h e s i s e r . The shape o f t h e resonance l i n e s shown i n f i g u r e s 5.12 and 5.13 can be e x p l a i n e d by t e m p e r a t u r e dependent f r e q u e n c y p u l l i n g . From e q u a t i o n 2.39b t h e f r e q u e n c y p u l l i n g o f t h e u n i f o r m Mnl mode i s c a l c u l a t e d t o be 47 MHz a t T L=0, and t h e p o s i t i o n o f t h e u n p u l l e d resonance c a l c u l a t e d from t h e 5 4 M n l res o n a n c e i s 543 MHz. The a b s o r p t i o n s h o u l d b e g i n a t about 500 MHz, b u t , as mentioned above, t h e r e i s a sudden d i p i n t h e 125 r f power i n p u t i n t h e v i c i n i t y o f t h i s f r e q u e n c y . The s t a r t i n g f r e q u e n c y o f t h e o b s e r v e d resonance i s , however, c l o s e t o t h e c a l c u l a t e d v a l u e . The f r e q u e n c y o f t h e u n i f o r m mode i n c r e a s e s w i t h t e m p e r a t u r e , and, as t h e f r e q u e n c y sweep p r o c e e d s t h e sample t e m p e r a t u r e r i s e s due t o t h e energy d e p o s i t e d i n t h e 5 5Mn s p i n system and t h e u n i f o r m mode reso n a n c e f r e q u e n c y f o l l o w s t h e f r e q u e n c y o f t h e a p p l i e d r f f i e l d . A t 535 MHz t h e c o o l i n g r a t e from t h e sample t o t h e c o l d f i n g e r exceeds t h e power i n p u t from t h e r f f i e l d and t h e sample has r e a c h e d t h e maximum t e m p e r a t u r e c o n s i s t e n t w i t h t h i s i n p u t power. The reso n a n c e f r e q u e n c y o f t h e u n i f o r m mode has a l s o r e a c h e d a maximum v a l u e and can no l o n g e r f o l l o w t h e i n c r e a s i n g f r e q u e n c y o f t h e a p p l i e d r f f i e l d , t h i s c a uses t h e s h a r p peak i n t h e o b s e r v e d t h e r m a l r e s o n a n c e l i n e . A s i m i l a r e x p l a n a t i o n a p p l i e s t o t h e upper t h e r m a l r e s o n a n c e l i n e The t h e r m a l r e s o n a n c e s were a l s o p e r f o r m e d w i t h a r e v e r s e d f r e q u e n c y sweep d i r e c t i o n , s t a r t i n g a t h i g h f r e q u e n c y and sweeping t h e a p p l i e d r f f r e q u e n c y down. The e s t i m a t e d u n i f o r m mode l i n e w i d t h measured by comparing t h e s t a r t f r e q u e n c i e s o f t h e f o r w a r d and r e v e r s e f r e q u e n c y sweeps i s 10 MHz. The t h e r m a l NMR spectrum was measured a t t h e Mnl-Mn2 l e v e l c r o s s i n g f i e l d o f 2.64 T. A t t h i s f i e l d t h e n u c l e a r magnon branches c r o s s and a s i n g l e narrow t h e r m a l NMR l i n e i s o b s e r v e d see f i g u r e 5.15. 126 CO LU 0.90 0.86 S 0.82 0.78 cr cc o 0.74 «' i II i i i i it i> •II i i HI ii «i« ' ••lH* V 510 530 550 570 590 FREQUENCY (MHZ) F i g u r e 5.13: 5 5Mn Thermal NMR a t Z e r o A p p l i e d F i e l d . T h e r m a l l y d e t e c t e d u n i f o r m n u c l e a r magnon modes, f o r a d i s c u s s i o n o f t h e l i n e s h a p e see s e c t i o n 5.5. 127 >- 0.92 CO LU Q LU K l O 0.88 0.84 0.80 0.76 ll, II. ' i ih 1 480 510 540 570 600 FREQUENCY (MHZ) F i g u r e 5.14: 5 5Mn Thermal NMR a t B A = 0 . 0 0 4 T. I n t h i s e x p e r i m e n t t h e s t r e n g t h o f t h e a p p l i e d r f was r e d u c e d from t h a t used i n f i g u r e 5.13. A r e d u c e d i r r a d i a t i o n power l e v e l s t h e r e l a t i v e i n t e n s i t i e s o f t h e t h e r m a l NMR l i n e s i n t h i s f i g u r e i s r e p r e s e n t a t i v e o f t h e number o f s p i n s i n v o l v e d i n each mode. 128 >-r — I CO LU Q LU CX CC O 1.82 1.78 1.74 1.70 1.66 I I ' I (iiiiiiJ/ntyiiiii'iii11! 'iii'iyi'inimiiiiiiiiiiiiii I J 500 530 560 590 FREQUENCY (MHZ) F i g u r e 5.15: 5 5Mn Thermal NMR a t B = 2 . 6 4 T a A t t h i s v a l u e o f a p p l i e d f i e l d t h e u n i f o r m modes o f t h e r e s p e c t i v e s i t e s have t h e same f r e q u e n c y and t h e t h e r m a l NMR spectrum c o n s i s t s o f a s i n g l e narrow l i n e . 129 5.6 5 4Mn S p i n - L a t t i c e R e l a x a t i o n i n Mn(C00CH 3) .4H 20 I n t h i s s e c t i o n t h e r e s u l t s o f t h e s p i n - l a t t i c e r e l a x a t i o n t i m e measurements p r e s e n t e d i n s e c t i o n 5.4 a r e d i s c u s s e d . The low f i e l d r e l a x a t i o n mechanism f o r b o t h 5 4 M n l and 5 4Mn2 n u c l e i i s most p r o b a b l y d i r e c t r e l a x a t i o n t o t h e S 5 M n l n u c l e a r magnons v i a m u l t i - n u c l e a r magnon s c a t t e r i n g p r o c e s s e s . Other p o s s i b l e mechanisms i n c l u d e r e l a x a t i o n t o t h e e l e c t r o n i c magnons o r d i r e c t r e l a x a t i o n t o t h e l a t t i c e phonons v i a a v i r t u a l i n t e r m e d i a t e m a g n e t i c e x c i t a t i o n . The l a t t e r two r e l a x a t i o n mechanisms a r e d i s c o u n t e d s i n c e t h e y a r e weak and do n o t produce t h e l a r g e d i f f e r e n c e i n t h e r e l a x a t i o n t i m e s o f t h e d i f f e r e n t s i t e s o r t h e sh a r p f i e l d dependent i n c r e a s e i n T o b s e r v e d a t low f i e l d s (see f i g u r e 5.11). The H a m i l t o n i a n f o r a s i n g l e 5 4Mn c o u p l e d t o t h e n u c l e a r magnon system i s H = 5 5 H + H (54,55)+ h 5 4 C J I * (5.1a) t S N n 5 4 5 5 H = - h 5 5 w N 1 / 2 I 2 - l / 2 ( h 5 5 t o 5 5 A ) Y (ho ) _ 1 I * I " (5.1b) n 0 / x n ' ^ x k' k k v ' k H(54,55) = N " 1 / 2 I I U ( e x p ( - i k . r ) I * I " k j ' + e x p ( + i k o r j J I k I * 4 ) (5.1c) I n t h i s e q u a t i o n 5 5H i s t h e H a m i l t o n i a n f o r t h e n u c l e a r magnon system, (see e q u a t i o n 2.37), H (54,55) i s t h e SN i n t e r a c t i o n SN between t h e 5 4Mn and 5 5Mn n u c l e i ( I 5 4 a r e 5 4Mn s p i n o p e r a t o r s and t h e o p e r a t o r s I a r e t h e n u c l e a r magnon o p e r a t o r s d e f i n e d i n 130 e q u a t i o n 2.36) and t h e f i n a l t e r m i s t h e Mn s t a t i c h y p e r f i n e i n t e r a c t i o n . An e x p a n s i o n o f t h e t i m e e v o l u t i o n o p e r a t o r f o r a s p i n system governed by H t c o n t a i n s o p e r a t o r p r o d u c t s such as t h o s e w r i t t e n above t h e dia g r a m m a t i c r e p r e s e n t a t i o n s o f t h e 3 and 5 n u c l e a r magnon r e l a x a t i o n p r o c e s s e s shown i n f i g u r e 5.16. The c o e f f i c i e n t s e and K a r e n o r m a l i z e d t r a n s i t i o n a m p l i t u d e s and t h e y can be c a l c u l a t e d from t h e e x p a n s i o n o f t h e e v o l u t i o n o p e r a t o r . 0 and K depend on t h e wave v e c t o r s o f t h e n u c l e a r magnons i n v o l v e d i n t h e p r o c e s s and t h e magnitude o f t h e t r a n s i t i o n a m p l i t u d e s f o r a g i v e n p r o c e s s d e c r e a s e s r a p i d l y as t h e number o f magnons i n v o l v e d i n t h e p r o c e s s i n c r e a s e s . The S 5 M n l n u c l e a r magnon bandwidth i s 50 MHz and spans t h e range o f f r e q u e n c i e s from 510 MHz t o 560 MHz (see f i g u r e 5.13). The S 4Mn2 reso n a n c e l i n e i s p o s i t i o n e d a t 475 MHz and a p r o c e s s i n v o l v i n g 3 n u c l e a r magnons i s c a p a b l e o f r e l a x i n g t h e n u c l e i as • . 5 4 t h e n u c l e a r magnon bandwidth, S f i , i s g r e a t e r t h a n ( tj^—nQ) , (see f i g u r e 5.16A). The 5 4 M n l re s o n a n c e f r e q u e n c y i s 435 MHz and t h e r e l a x a t i o n p r o c e s s must i n v o l v e a t l e a s t 5 n u c l e a r magnons (see f i g u r e 5.16C). The l a r g e d i f f e r e n c e i n r e l a x a t i o n t i m e s o f t h e two s i t e s i s e x p l a i n e d by t h e l a r g e r number o f n u c l e a r magnons r e q u i r e d f o r t h e 5 4Mn r e l a x a t i o n p r o c e s s . I n c r e a s i n g t h e a p p l i e d f i e l d i n c r e a s e s t h e e l e c t r o n i c magnon gap and t h i s c a u s e s a weakening o f t h e SN i n t e r a c t i o n and a n a r r o w i n g o f t h e n u c l e a r magnon bandwidth. These t r e n d s combined w i t h t h e i n c r e a s i n g s e p a r a t i o n o f t h e S 4Mn2 and 5 5Mnl-magnon e n e r g i e s g i v e a r e l a x a t i o n t i m e w h i c h shows a monotonic i n c r e a s e w i t h a p p l i e d f i e l d . The f i e l d dependence o f t h e 5 4Mn2 r e l a x a t i o n 131 F i g u r e 5.16: H i g h Order N u c l e a r Magnon R e l a x a t i o n P r o c e s s e s A) A t h r e e n u c l e a r magnon r e l a x a t i o n p r o c e s s i n w h i c h a 5 4Mn n u c l e a r s p i n f l i p s i n c r e a s i n g i t s ' energy by a b s o r b i n g a t h e r m a l n u c l e a r magnon, t h e o u t g o i n g n u c l e a r magnon c a r r i e s away t h e energy d i f f e r e n c e between t h e 5 4Mn s p i n f l i p and t h e absorbed n u c l e a r magnon. B) The h e r m i t i a n c o n j u g a t e v e r s i o n o f A) . C) A f i v e n u c l e a r magnon r e l a x a t i o n p r o c e s s i n w h i c h one o f t h r e e i n coming t h e r m a l n u c l e a r magnons i s abs o r b e d by t h e 5 4Mn n u c l e u s and t h e energy d i f f e r e n c e appears i n t h e two o u t g o i n g magnons, k ' " and k'"'. D) The h e r m i t i a n c o n j u g a t e f i v e magnon p r o c e s s . 132 t i m e f o r f i e l d s between 0 T and 0.25 T i s shown i n f i g u r e 5.11. F o r f i e l d s above 13^=0.17 T t h e n u c l e a r magnon bandwidth i s t o o narrow t o a l l o w an energy c o n s e r v i n g 3 magnon p r o c e s s and t h e s l o p e o f t h e r e l a x a t i o n c u r v e i n c r e a s e s . T h i s i n c r e a s i n g s l o p e i s an i n d i c a t i o n t h a t f o r B a>0.17 T a h i g h e r o r d e r p r o c e s s , such as t h e 5 magnon p r o c e s s o f f i g u r e 5.16C, has t a k e n o v e r from t h e 3 magnon r e l a x a t i o n p r o c e s s as t h e dominant r e l a x a t i o n mechanism. The r e l a x a t i o n t i m e c o n t i n u e s t o i n c r e a s e w i t h f i e l d up t o Ba=1.8 T, and f o r h i g h e r a p p l i e d f i e l d s t h e r e l a x a t i o n t i m e d e c r e a s e s r e a c h i n g a minimum a t 2.64 T (see f i g u r e 5.12). T h i s minimum i s a s c r i b e d t o a combined 5 4Mn2, p r o t o n and 5 5Mn n u c l e a r magnon l e v e l c r o s s i n g e vent analogous t o t h a t d e s c r i b e d i n s e c t i o n 4.6 f o r MnCl .4H0. 2 2 One way t o c a l c u l a t e t h e r e l a x a t i o n r a t e f o r t h i s p r o c e s s i s f i r s t t o do a p e r t u r b a t i o n c a l c u l a t i o n o f t h e e i g e n s t a t e s o f t h e 5 4Mn - 1H system and t h e n t r e a t t h e r e l a x a t i o n p r o c e s s as b e i n g a d i r e c t p r o c e s s between t h e 5 4Mn- 1H e i g e n s t a t e s i n d u c e d by t h e SN i n t e r a c t i o n . The H a m i l t o n i a n f o r t h e combined 5 4 M n - p r o t o n - n u c l e a r magnon system i s H ! = Hz + H n ^ V + V + H + HSN< 5 4' 5 5> (5.2) where H = h( (j I z n z 1 z. - Id I ) 54 0 1 ' (5.3) and 133 H d - ^ s i V h U d ( ( I 5 4 i : ( l - 3 c o s 2 c ) + 1/4 ( l - 3 c o s 2 c ) ( i ; 4 r +I; 4 I + ) - 3 / 2 s i n ( c ) c o s ( e ) (I* 4 I 2 + I * 4 I * ) - 3 / 2 s i n ( e ) c o s ( e ) (I~ 4I Z + 1 * ^ ) - 3 / 4 s i n 2 ( e ) ( i ; 4 i ; ) - 3 / 4 s i n 2 ( c ) ( i ; 4 i ; ) ) ( 5 > 4 ) H i s t h e sum o f t h e 5 4Mn h y p e r f i n e i n t e r a c t i o n and t h e 5 4Mn and z H Zeeman i n t e r a c t i o n s . H ( I I ) 3 9 i s t h e 5 4Mn- 1H d i p o l e - d i p o l e 1 dd 54 1 H a m i l t o n i a n ( t h e o p e r a t o r s I and I i a r e r e s p e c t i v e l y t h e 5 4Mn and p r o t o n n u c l e a r s p i n o p e r a t o r s ) , and e i s t h e a n g l e between t h e 5 4Mn- 1H i n t e r n u c l e a r v e c t o r and t h e s p i n q u a n t i s a t i o n a x i s . H ( I I t ) i s t h e p r o t o n homonuclear d i p o l e - d i p o l e i n t e r a c t i o n and i t d e s c r i b e s t h e c o u p l i n g o f t h e p r o t o n o f i n t e r e s t t o t h e o t h e r p r o t o n s i n t h e sample. I n t h e f o l l o w i n g d e r i v a t i o n o f t h e d i r e c t p r o c e s s r e l a x a t i o n r a t e t h e r e l a x a t i o n p r o c e s s i s t r e a t e d as a s i n g l e n u c l e a r magnon s c a t t e r i n g o f f a 5 4Mn n u c l e u s c o u p l e d t o an i s o l a t e d p r o t o n . F o r a s i m p l e d i s c u s s i o n o f t h e r e l a x a t i o n p r o c e s s H ( I I ) w i l l be i g n o r e d ) . H ( I I ) i s dd 1 1 dd 1 1 i m p o r t a n t f o r t h e r e l a x a t i o n p r o c e s s and t h e e f f e c t s o f d i p o l e c o u p l i n g w i t h i n t h e p r o t o n b a t h w i l l be d i s c u s s e d l a t e r . When B =2.64 T t h e d i p o l e i n t e r a c t i o n s t r e n g t h hto i s v e r y a d much s m a l l e r t h a n e i t h e r t e rm o f H and good z e r o o r d e r z e i g e n s t a t e s a r e |ms4>|mi>, t h e quantum numbers m g 4 and m b e i n g t h e z - p r o j e c t i o n o f a n g u l a r momentum f o r 5 4Mn and 1H. The e i g e n v a l u e s f o r t h e s t a t e s Im >|m > a r e E =h(m 5 4 ( j + m 1to ) 1 9 1 54 1 1 0 v 54 n 1 0' and t h e energy l e v e l s a s s o c i a t e d w i t h t h e l o w e s t two s t a t e s o f t h e S=-5/2 5 4Mn h y p e r f i n e m u l t i p l e t a r e shown i n f i g u r e 5.17. The a d m i x t u r e c o e f f i c i e n t £ i s due t o t h e t h i r d and f o u r t h terms 134 o f e q u a t i o n 5.4 and t h e y a l l o w a weak SN i n d u c e d t r a n s i t i o n between t h e z e r o o r d e r s t a t e s | a> and |d>, i f t h e c o n d i t i o n hn = E i s s a t i s f i e d . The t r a n s i t i o n r a t e , Q , f o r t h e d i r e c t k 0 . • a d ' p r o c e s s r e l a x a t i o n o f t h e s t a t e |a> t o t h e s t a t e |d> i s Q a d= 27ih"1I |<d|<T,k| H s j T > | a > | 2 S ( h ( n k - ( 5 4w n+ 1a> 0))) (5.5) Tk Here | T > i s an i n i t i a l s t a t e o f t h e n u c l e a r magnon b a t h , H g N i s t h e SN i n t e r a c t i o n and | T,k> i s t h e i n i t i a l s t a t e p l u s t h e e x t r a magnon |k> r e s u l t i n g from t h e r e l a x a t i o n p r o c e s s . The e x p r e s s i o n f o r H g N i n terms o f s i t e dependent s p i n o p e r a t o r s i s g i v e n by H = U V ( I * I " + I " I * ) ' (5.6) SN J J j , 54 J * 54 J * ' v ' Here j r e f e r s t o t h e 5 4Mn s i t e and j ' r e f e r s t o t h e 5 5 Mn s i t e s . A f t e r t r a n s f o r m i n g t o n u c l e a r s p i n wave o p e r a t o r s d e f i n e d by 2.10b t h e f o l l o w i n g e x p r e s s i o n i s o b t a i n e d f o r < d | H s N | a > < d I H I a > = < d I I" N " 1 / 2 £ £ U ,exp ( - ikor ,) I + I a > ' SN ' ' 5 4 z - ^ j j . r v j > ' k 1 k J ' = CN"1/2E E U exp ( - i k o r ) I* (5.7) k j ' 3 3 F o r d i r e c t p r o c e s s r e l a x a t i o n i n d u c e d by t h e SN i n t e r a c t i o n t h e e f f e c t s o f d y n a m i c a l c o r r e l a t i o n s w i t h i n t h e 5 5Mn s p i n b a t h a r e made e x p l i c i t t h r o u g h t h e wave v e c t o r dependent p a r t o f t h e r e l a x a t i o n a m p l i t u d e d e f i n e d by 135 G(k) = £ U j r e x p ( - i k o r r ) (5.8) Q u a l i t a t i v e l y , r e l a x a t i o n t o n u c l e a r magnons w i t h wave v e c t o r l e s s t h a n t h e i n v e r s e range o f t h e SN i n t e r a c t i o n , b" 1, i s enhanced w h i l e t h e r e l a x a t i o n r a t e t o modes w i t h k>b~* i s de c r e a s e d and may even go t o z e r o . E q u a t i o n 5.5 can be w r i t t e n as a sum o f s i n g l e n u c l e a r magnon r e l a x a t i o n p r o c e s s e s as Q a d= 2TTC2 (hN ) _ 1 I | <T,k| G(k)I*|T>| 25(h ( n k - ( " u ^ ' u j ) ) (5.9) a Tk F o r h i g h n u c l e a r s p i n p o l a r i z a t i o n s e x c i t a t i o n s c r e a t e d by t h e o p e r a t o r I * can be t r e a t e d as bosons because < [1*1", ] > R S S k k > and e q u a t i o n 5.9 becomes Q a d= 2TTC2(hN)-1£ G ( k ) * G ( k ) ( l +<I*I^>) « (h(Vk~(54u^u>q) ) ) (5.10a) 3 k <I*I~> = (1-exp (0 n kh)) _ 1 (5.10b) I f G(k)*G(k) i s s e t e q u a l t o U 2 f o r a l l k, and i f en kh<l, t h e n e q u a t i o n 5.10a becomes Q a d= 2TrC2/h U 2 ( l + (0 s sw h)' 1) N _ 1 E 6(h (n k - ( 5 4 a) n + 1 cJ o ) ) ) (5.11) k I n t h i s e x p r e s s i o n n has been s e t e q u a l t o 5 5co because k n 5fi « n « S 5 C J f o r a l l k. k n The r e l a x a t i o n r a t e depends on t h e p r e c i s e form o f t h e 136 f r e q u e n c y o v e r l a p o f t h e n u c l e a r magnon band and t h e p r o t o n r e s o n a n c e l i n e . The d e n s i t y o f n u c l e a r magnon s t a t e s , N ( k ) , i n t h e r e g i o n o f o v e r l a p i s t h e most i m p o r t a n t f a c t o r . A s i m p l e e s t i m a t e o f t h e r e l a x a t i o n r a t e can be found by s e t t i n g t h e d e n s i t y o f n u c l e a r magnon modes a c t i v e i n d i r e c t p r o c e s s r e l a x a t i o n t o Here 80, i s t h e n u c l e a r magnon bandwidth g i v e n by e q u a t i o n 2.13b and N i s t h e t o t a l number o f n u c l e a r magnon modes. Upon making t h i s a p p r o x i m a t i o n a p p r o x i m a t i o n 5.11 r e d u c e s t o T h i s n a i v e t h e o r y over e s t i m a t e s t h e v a l u e o f t h e r e l a x a t i o n r a t e by a f a c t o r o f 10, b u t t h i s i s n o t t o s u r p r i s i n g c o n s i d e r i n g t h e d r a s t i c a p p r o x i m a t i o n s made i n t h e d e r i v a t i o n o f 5.13 and t h e c o m p l e x i t y o f t h e p r o t o n and n u c l e a r magnon b a t h s i n t h e r e a l system. A more a c c u r a t e t h e o r y would use many body e i g e n s t a t e s o f t h e complete p r o t o n H a m i l t o n i a n , i . e . e i g e n s t a t e s o f H + H f l I ) , t o d e s c r i b e t h e p r o t o n b a t h . H ( I I ) has two Z da 1 1 dd 1 1 major e f f e c t s on t h e r e l a x a t i o n p r o c e s s , i t d e c r e a s e s C as p r o t o n - p r o t o n s p i n f l i p s compete w i t h t h e p r o t o n - d i p o l e c o u p l i n g t o t h e S 4Mn, and i t i s i m p o r t a n t i n t h e r e l a x a t i o n o f t h e s t a t e |b> (see f i g u r e 5.17). The r e l a x a t i o n mechanism f o r t h e |b> s t a t e i n v o l v e s a t r a n s i t i o n from t h e s t a t e |b> t o t h e s t a t e |a> N(k) = N / (hSn) (5.12) Q = (2TrC 2/fi ) U 2 ( 1 + (j3 5 S ( J h ) " 1 ) (hSfl) ad n - 1 (5.13) 137 | a > = | - 2 > | + l / 2 > + 2 C | - 2 > | - l / 2 > 1 (J 1 |b>=|-2>|"l/2> 5 4 Cd |C>=|-3>|+l/2> Cd |d>=|-3>|-l/2>+3C|-3>|+l/2> F i g u r e 5.17: D i r e c t P r o c e s s N u c l e a r Magnon R e l a x a t i o n The energy l e v e l s and wave f u n c t i o n s i n v o l v e d i n d i r e c t p r o c e s s n u c l e a r magnon r e l a x a t i o n f o r t h e l o w e s t two l e v e l s o f t h e h y p e r f i n e m u l t i p l e t . 1w j i s t h e p r o t o n Zeeman f r e q u e n c y , 5 4 t d n i s t h e f r e q u e n c y o f t h e m=-3 t o m=-2 h y p e r f i n e t r a n s i t i o n and fi^ i s t h e f r e q u e n c y o f t h e n u c l e a r magnon i n v o l v e d i n t h e d i r e c t p r o c e s s r e l a x a t i o n . 138 i n d u c e d by H ( I I ) . A n o t h e r c o m p l i c a t i o n i s t h e e s t i m a t i o n dd 1 1 o f C because t h e e s t i m a t i o n s h o u l d i n c l u d e t h e e l e c t r o n i c component o f t h e 5 4Mn n u c l e a r s p i n wave f u n c t i o n s . T h i s e l e c t r o n i c c o n t r i b u t i o n t o t h e n u c l e a r d i p o l e moment i s d i s t r i b u t e d o v e r many magnetic u n i t c e l l s and i t s magnitude i s d i f f i c u l t t o e s t i m a t e . A lo w e r bound f o r C i s p r o v i d e d by t h e u s u a l "unenhanced" n u c l e a r m agnetic d i p o l e i n t e r a c t i o n , b u t even t h i s may n o t be c o r r e c t as H ( I I ) can d e c r e a s e t h e v a l u e o f dd 1 1 c. The a s s u m p t i o n s made i n t h e d e r i v a t i o n o f e q u a t i o n 5.11 a r e n a i v e , b u t t h e d e r i v a t i o n i l l u s t r a t e s t h a t t h a t t h e l e v e l c r o s s i n g r e l a x a t i o n p r o c e s s can o c c u r w i t h t h e s p i n c o u p l i n g s w h i c h a r e p r e s e n t i n t h e sample and g i v e s an e x p l i c i t example o f how d y n a m i c a l c o r r e l a t i o n o f t h e 5 5Mn n u c l e a r s p i n s can a f f e c t t h e r e l a x a t i o n r a t e ( e q u a t i o n 5.6). The e x p l a n a t i o n o f t h e peak i n t h e r e l a x a t i o n t i m e o b s e r v e d a t t h e l e v e l c r o s s i n g ( f i g u r e 5.12) i s complex and has many c o n t r i b u t i n g f a c t o r s , and i t i s n e c e s s a r y f i r s t t o g i v e a d i s c u s s i o n o f t h e n u c l e a r s p i n c o u p l i n g s w i t h i n a t r i p l e t . I f t h e system were a x i a l l y symmetric t h e SN c o u p l i n g between t h e Mnl s i t e and Mn2 s i t e n u c l e a r s p i n s would be s t r o n g l y s u p p r e s s e d s i n c e t h e s p i n s a t t h e r e s p e c t i v e s i t e s p r e c e s s i n o p p o s i t e d i r e c t i o n s (The h y p e r f i n e i n t e r a c t i o n i s n e g a t i v e f o r b o t h n u c l e a r s p i n s and t h e y p o i n t i n o p p o s i t e d i r e c t i o n s ) . I f t h e e l e c t r o n i c and n u c l e a r system were a x i a l l y s ymmetric t h e n u c l e a r magnon bands a r i s i n g from each s i t e would be u n c o u p l e d and t h e 5 5 M n l ( 5 5Mn2) n u c l e a r magnons c o u l d o n l y c o n t r i b u t e t o 5 4 M n l ( 5 4Mn2) r e l a x a t i o n . I n f a c t t h e system i s 139 f a r from b e i n g a x i a l l y symmetric, and t h e l a r g e r a t i o o f B° t o B a, (see s e c t i o n 5.1), l e a d s t o a c o n s i d e r a b l e degree o f A e l l i p t i c a l p o l a r i z a t i o n o f t h e e l e c t r o n i c and n u c l e a r modes. N o n - c o n s e r v a t i o n o f t h e z-component o f a n g u l a r momentum i n t h e SN i n t e r a c t i o n a l l o w s a r e s o n a n t c o u p l i n g between t h e Mnl and Mn2 s i t e s when B =2.64T. W i t h i n a g i v e n t r i p l e t t h e Mn2 s p i n s a a r e s t r o n g l y c o u p l e d by t h e SN i n t e r a c t i o n w h i l e t h e Mnl-Mn2 c o u p l i n g i s weaker, b u t s t i l l p e r m i t s a c o n s i d e r a b l e Mnl (Mn2) n u c l e a r magnon c o n t r i b u t i o n t o 5 4Mn2 ( 5 4 M n l ) r e l a x a t i o n • • . 5 4 • The p l o t o f T ^ s B g shown i n f i g u r e 5.12 i s f o r Mn2 s p i n s a f t e r t h e m=-3 t o m=-2 t r a n s i t i o n i s e x c i t e d . A t B =2.64 T t h e a 5 4Mn2 and 5 4 M n l l i n e s o v e r l a p so t h a t a t t h i s f i e l d r e s o n a n c e o f t h e 5 4 M n l s p i n s a l s o o c c u r s . T h i s means t h a t t h e measured 5 4Mn2 r e l a x a t i o n r a t e has a c o n t r i b u t i o n from t h e 5 4 M n l s p i n s , w h i c h r e l a x more s l o w l y because Mnl n u c l e a r magnons a r e fewer i n number and t h e Mnl h y p e r f i n e f i e l d s a r e s m a l l e r . U n f o r t u n a t e l y i t i s d i f f i c u l t t o s e p a r a t e o u t t h e d i f f e r e n t c o n t r i b u t i o n s i n t h e o b s e r v e d s i g n a l because t h e r e l a x a t i o n r a t e s a r e n o t t o o d i f f e r e n t and t h e y a r e m u l t i e x p o n e n t i a l i n n a t u r e . The d r a m a t i c i n c r e a s e i n T a t t h e l e v e l c r o s s i n g i s l i k e l y due t o t h e c o u p l i n g o f n u c l e a r magnons from each s i t e and t h e r e s u l t i n g change i n t h e s t r u c t u r e o f t h e modes. F o r example, m o t i o n s o f t h e two s e t s o f magnons c o u l d be c o r r e l a t e d i n such a way t o be 180° o u t o f phase. An a l t e r n a t i v e , and s i m p l e r , e x p l a n a t i o n i s t h a t t h e d e n s i t y o f n u c l e a r magnon s t a t e s i n t h e r e g i o n o f k space a p p r o p r i a t e f o r 5 4Mn2 r e l a x a t i o n f o r some r e a s o n i s s h a r p l y d e c r e a s e d a t B a=2.64 T. The r e l a x a t i o n peak a t 2.64T i s most l i k e l y due t o t h e 140 r e s o n a n t c o u p l i n g o f t h e n u c l e a r magnons o f t h e d i f f e r e n t s i t e s , b u t t h e r e l a x a t i o n p r o c e s s i s v e r y i n t r i c a t e and c a l c u l a t i n g t h e r e l a x a t i o n r a t e s i s a f o r m i d a b l e t a s k . 5.7 S p i n Echoes i n Mn(COOCH ) .4H 0 r ' 3 ' 2 2 I n t h i s s e c t i o n t h e r e s u l t s o f a s e l e c t i v e ( s i n g l e quantum) Hahn s p i n echo s t u d y o f t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn a r e pr e s e n t e d . A s e l e c t i v e Hahn s p i n echo sequence can o n l y r e f o c u s an inhomogeneously broadened r e s o n a n c e l i n e . The b r o a d e n i n g mechanisms can r e s u l t from v a r i a t i o n s i n t h e s t a t i c h y p e r f i n e o r qua d r u p o l e i n t e r a c t i o n s from i m p u r i t i e s o r be due t o d i p o l e i n t e r a c t i o n s w i t h a non-resonant s p i n s p e c i e s such as t h e p r o t o n s i n t h e sample. The e f f e c t s o f t h e homogeneous SN i n t e r a c t i o n between n e i g h b o r i n g 5 4Mn n u c l e i a r e n o t r e f o c u s e d by a Hahn echo and t h e s p i n - e c h o a m p l i t u d e w i l l show o s c i l l a t i o n s as a f u n c t i o n o f p u l s e s p a c i n g used i n t h e echo sequence i f t h e SN i n t e r a c t i o n i s t h e dominant s p i n - s p i n i n t e r a c t i o n . The f r e q u e n c y o f t h e o s c i l l a t i o n s w i l l be r e p r e s e n t a t i v e o f t h e s t r e n g t h o f t h e SN i n t e r a c t i o n . I n f i g u r e 5.18 t h e Hahn s p i n echo a m p l i t u d e i s shown as a f u n c t i o n o f t h e p u l s e s p a c i n g used i n t h e echo sequence. The ex p e r i m e n t was performed on t h e m=-3 t o m=-2 t r a n s i t i o n o f 5 4Mn a t Ba=0.3 T u s i n g a 350 ns 90° p u l s e and a 700 ns 180° p u l s e . The echo a m p l i t u d e shows an o s c i l l a t i o n o f a p p r o x i m a t e l y 1 MHz i n d i c a t i n g t h a t t h e s p i n i s s u b j e c t t o an i n t e r a c t i o n w h i c h i s no t r e f o c u s e d by a Hahn echo. A s i m i l a r measurement a t B =0.4 T J a i s shown i n f i g u r e 5.19 and f o r t h i s v a l u e o f B t h e o s c i l l a t i o n f r e q u e n c y has d e c r e a s e d t o 500 kHz. O s c i l l a t i o n s o f t h e a p p r o p r i a t e f r e q u e n c y were a l s o o b s e r v e d i n t h e FIDs measured a t b o t h f i e l d s . The 5 4Mn s p i n system i s randomly d i s t r i b u t e d t h r o u g h o u t t h e sample and a l l v a l u e s o f i n t e r - s p i n s e p a r a t i o n o c c u r . The average s e p a r a t i o n depends upon t h e c o n c e n t r a t i o n o f t h e r a d i o a c t i v e n u c l e i and i n t h e sample used f o r t h e e x p e r i m e n t s t h e average s e p a r a t i o n i s 50 magnetic l a t t i c e u n i t s . The mean SN i n t e r a c t i o n f o r t h i s s p a c i n g i s e s t i m a t e d t o be 1.2*10 2 Hz w h i c h i s f a r t o o s m a l l t o accou n t f o r t h e o b s e r v e d o s c i l l a t i o n s . I f two 5 4Mn n u c l e i happen t o be i n t h e same t r i p l e t t h e n t h e i n t e r a c t i o n between them i s o f t h e o r d e r o f 1MHz, b u t such an 5 4 o c c u r r e n c e i s v e r y r a r e and, a l t h o u g h t h e spectrum o f t h e Mn s p i n - s p i n c o u p l i n g s does have h i g h f r e q u e n c y components t h e i n t e n s i t y o f t h e s e components i s t o o s m a l l t o g i v e t h e ob s e r v e d echo a m p l i t u d e o s c i l l a t i o n s . One p o s s i b l e e x p l a n a t i o n f o r t h e o s c i l l a t i o n s i s t h a t t h e r e q u i r e m e n t s o f s e l e c t i v e e x c i t a t i o n o f t h e m=-3 t o m=-2 t r a n s i t i o n have n o t been e x a c t l y met and t h a t t h e o s c i l l a t i o n s a r e due t o t h e pseudoquadrupole i n t e r a c t i o n . I n t h i s c a s e t h e l o w e s t t h r e e l e v e l s o f t h e 5 4Mn h y p e r f i n e m u l t i p l e t would be e x c i t e d and as t h e Hahn echo sequence does n o t r e f o c u s t h e pseudoquadrupole i n t e r a c t i o n and o s c i l l a t i o n s i n t h e echo a m p l i t u d e would o c c u r . The bandwidth o f t h e 90° p u l s e s i s o f t h e o r d e r o f 3 MHz and s i n c e t h e psuedoquadrupole s p l i t t i n g i s o n l y 1.2 MHz t h i s m ight e x p l a i n t h e r e s u l t o b t a i n e d a t B a=0.3 T. On t h e o t h e r hand, t h e r e was no change o b s e r v e d i n t h e e q u a t o r i a l a n i s o t r o p y , i n d i c a t i n g t h a t t h e m=-l l e v e l was n o t p o p u l a t e d a t 142 t h e end o f t h e p u l s e sequence. A l s o t h e o s c i l l a t i o n f r e q u e n c y a t Ba=0.4 T i s o n l y 500 kHz w h i c h i s h a l f o f t h e pseudoquadrupole s p l i t t i n g . The f r e q u e n c y o f t h e r f p u l s e s was r e d u c e d by 500 khz i n an e f f o r t t o see i f any change o c c u r r e d i n t h e s i g n a l . No such change o c c u r r e d and o s c i l l a t i o n s o f t h e same f r e q u e n c y were o b s e r v e d i n d i c a t i n g t h e e f f e c t d i d n o t a r i s e from a g e n e r a t i o n o f d o u b l e quantum coherence because, i n t h i s c a s e , t h e o s c i l l a t i o n f r e q u e n c y would be e x p e c t e d t o change w i t h t h e f r e q u e n c y o f t h e a p p l i e d p u l s e s . The l a c k o f change o f t h e e q u a t o r i a l a n i s o t r o p y , t h e i n v a r i a n c e o f t h e s i g n a l t o a change of t h e i r r a d i a t i o n f r e q u e n c y and t h e f r e q u e n c y o f t h e o s c i l l a t i o n when B=0.4 T r u l e o u t t h e p o s s i b i l i t y t h a t t h e o s c i l l a t i o n s a r e due t o more t h a n two l e v e l s b e i n g e x c i t e d . These r e s u l t s a r e p r e l i m i n a r y : t h e e x p e r i m e n t a l o b s e r v a t i o n s m ight be i n d i c a t i n g an i n t e r e s t i n g and u n e x p l a i n e d phenomenon r e s u l t i n g from t h e p u l s e d e x c i t a t i o n o f t h e u n i f o r m mode o f a mag n e t i s e d n u c l e a r system w i t h a random l o n g - r a n g e d s p i n i n t e r a c t i o n , o r t h e y may be an a r t i f a c t w h i c h can o f t e n o c c u r i n p u l s e d NMRON s p i n echo s t u d i e s . To s e t t l e t h i s q u e s t i o n more e x p e r i m e n t s a r e r e q u i r e d . 143 >-r— i — i CO LU 0.84 0.80 LU ^ 0.76 o 0.72 I I I I I1 HI ill,/ 1" I 1 N H ' « "I1 1 i i | i i i l i i i i l i i i l l n i i \ i h i / i i , i i | i l , , i h^ i , i i , i i | , , i i i , i 0 2000 4000 6000 8000 TIME (NS) Figure 5.18: The Amplitude of the Hahn Spin Echo at Ba=0.3T The peak of the Hahn spin echo i s recorded as a function of pulse spacing t . The baseline i s the thermal equilibrium anisotropy and the o s c i l l a t i o n i n the echo amplitude has a frequency of about 1 MHz. 144 >-CO LU 0.84 0.80 Q LU rvj 0.76 cr QI O 0.72 I1 l| | MMl I' JI>/I'V I |IV |I"I, | |II | |IIIIII | 'II , | | | |I,II | , I 'I ,I III'I,I I | | I 0 3000 6000 9000 12000 T IME (NS) F i g u r e 5.19: The A m p l i t u d e o f t h e Hahn S p i n Echo a t B a=0.4 T The peak o f t h e Hahn s p i n echo i s r e c o r d e d as a f u n c t i o n o f p u l s e s p a c i n g t . The b a s e l i n e i s t h e t h e r m a l e q u i l i b r i u m a n i s o t r o p y and t h e o s c i l l a t i o n i n t h e echo a m p l i t u d e has a fr e q u e n c y o f about 500 KHz. 145 Chapter 6 Summary and Concluding Remarks The results presented in the thesis demonstrate the successful application of selective excitation pulsed NMRON methods to the study of low temperature 54Mn nuclear spin-lattice relaxation mechanisms in magnetic insulators. Thermal NMR and CW NMRON has been used to complement the pulsed measurements and these methods have provided some valuable information used for the elucidation of spin-lattice relaxation mechanisms. Selective single and double quantum excitation sequences have been used for the f i r s t time in NMRON to obtain single and double quantum rotation patterns, FID, Hahn spin echoes and pulsed T measurements. Pulsed excitation methods are well suited to the study of systems with very short relaxation times and i t has been demonstrated that spin-lattice relaxation down to the order of 100 ms can easily be measured. The application of selective pulsed excitation techniques in searching for NMRON resonances with short relaxation times has also been demonstrated. The 54Mn-MnCl2.4H20 system has been studied. The temperature dependence of the spin-lattice relaxation time at zero f i e l d was measured between 35 mk and 90 mk and i t was found that the dominant process between 65 mk and 90 mk is an electronic magnon Raman process and below 65 mk a direct relaxation process 146 dominates. The e x a c t n a t u r e o f t h e l i m i t i n g low t e m p e r a t u r e r e l a x a t i o n p r o c e s s was n o t e s t a b l i s h e d , b u t a s i m i l a r measurement o f t h e l i m i t i n g r e l a x a t i o n t i m e p e r f o r m e d a t 4 T i n t h e p a r a m a g n e t i c phase y i e l d e d a much l a r g e r v a l u e f o r T . Because t h e measured l i m i t i n g r e l a x a t i o n t i m e depends on t h e mag n e t i c s t r u c t u r e o f MnCl 2.4H 20 i t has been c o n c l u d e d t h a t t h e o b s e r v e d d i r e c t p r o c e s s i n v o l v e s m a g n e t i c e x c i t a t i o n s . Measurements o f FID and Hahn s p i n echoes have been used t o d e t e r m i n e t h e magnitude and n a t u r e o f t h e s p i n - s p i n r e l a x a t i o n , 5 4 , , , , mechanism f o r Mn o r i e n t e d i n MnCl 2.4H 20 a t z e r o a p p l i e d f i e l d . Measurements o f t h e s i n g l e quantum FID have shown t h a t t h e s i n g l e quantum l i n e w i d t h i s 35 kHz and from s i n g l e quantum Hahn s p i n echo measurements a v a l u e o f 17 kHz has been o b t a i n e d f o r t h e r e - f o c u s s e d l i n e w i d t h . The d o u b l e quantum FID and echo measurements produced d o u b l e quantum l i n e w i d t h s t w i c e t h a t o b s e r v e d f o r t h e s i n g l e quantum e x p e r i m e n t s and i t has been * , 5 4 , , , , c o n c l u d e d t h a t t h e major Mn s p i n - s p i n r e l a x a t i o n mechanism i s of m a g n e t i c o r i g i n . The s t r e n g t h o f t h e i n t e r a c t i o n i s c o n s i s t e n t w i t h t h a t due t o t h e h e t e r o n u c l e a r d i p o l e - d i p o l e c o u p l i n g t o t h e p r o t o n b a t h . NMRON was o b s e r v e d f o r t h e f i r s t t i m e i n t h e p a r a m a g n e t i c phase o f MnCl .4H 0. The resonance l i n e s a r e 300 KHz wide and 2 2 inhomogeneously broadened. The b r o a d e n i n g mechanism i s c o n s i s t e n t w i t h t h a t due t o t h e v a r i a t i o n o f t h e l o c a l e l e c t r o n i c d i p o l e f i e l d s . An a n a l y s i s o f t h e f i e l d dependence o f t h e r e s o n a n c e f r e q u e n c i e s has a l l o w e d us t o o b t a i n a v a l u e o f < 5 4AS>/h=513.6 (1) MHz f o r t h e p a r a m a g n e t i c phase h y p e r f i n e 147 f i e l d . A comparison of that value with one obtained from s i m i l a r measurements i n the antiferromagnetic phase has shown the antiferromagnetic phase zero point spin deviation i s S=0.01. The small value of the antiferromagnetic spin deviation i s consistent with the magnetic properties of MnCl 2.4H 20. 5 4 The f i e l d and temperature dependence of the Mn T has been measured f o r values of f i e l d above the spin f l o p paramagnetic phase t r a n s i t i o n . A f i e l d dependent T minimum was discovered at Ba=2.64 T and from the measurement of the temperature dependence of T i t was determined that the relaxation mechanism operative over the range of f i e l d corresponding to the minimum involves excitations with energies s i m i l a r to the hyperfine s p l i t t i n g s . A mechanism involving the proton bath and the 55Mn nuclear magnons was postulated and t h i s mechanism explained both the width of the minimum and the order of magnitude of the observed relaxation times. The 54Mn-Mn(COOCH3) 2.4H20 system has also been investigated. The CW NMRON spectrum has been measured and the value of the hyperfine coupling constants f o r the two s i t e s has been determined. For the 5 4Mnl s i t e <54AS>/h=-435(1) MHz and for the 54Mn2 s i t e <54AS>/h=-478(1) MHz. The f i e l d dependence of the low f i e l d s p i n - l a t t i c e relaxation time has also been studied. I t was found that the Mn2 s i t e relaxation time i s very short at low f i e l d s and that the Mnl s i t e relaxation time i s 3 orders of magnitude greater than that observed f o r the Mn2 s i t e . I t i s suggested that the most l i k e l y relaxation mechanism i s d i r e c t relaxation to the nuclear magnons. Further evidence for the 148 nuclear magnons contributing to relaxation was provided by the thermal NMR measurements, which showed that the nuclear magnon excitation spectrum was consistent with the postulated multi-nuclear magnon relaxation processes. The high f i e l d spin-lattice relaxation behavior has also been measured and a T minimum at B =2.74 T analogous to that 1 a observed in MnCl .4H 0 was discovered. The width of the minimum 2 2 i s consistent with that determined from the f i e l d dependent overlap of the proton and 55Mn nuclear resonance spectra and a simplified theory of the relaxation mechanism was derived. A sharp anomaly was observed in the relaxation time at the f i e l d corresponding to the level crossing of the resonance lines from the two Mn sites. The exact reason for the anomalous behavior of T has not been determined, but some possible mechanisms related to the resonant coupling of nuclear magnons from the two sites are discussed. A Hahn echo study of the low f i e l d single quantum spin-spin relaxation processes was performed. It was found that that the echo amplitude oscillated with pulse spacing but whether this is a real effect or an experimental artifact must be decided by future experiments. In summary, the work presented in the thesis shows the successful application of multiple quantum selective excitation methods to pulsed NMRON in ordered magnetic insulators. The pulsed methods developed complement well established NMRON techniques and provide a powerful tool for the measurement of low temperature nuclear spin relaxation phenomena. NMRON studies 149 o f magnet ic i n s u l a t o r s a r e r e l a t i v e l y few i n number and many n o v e l and i n t e r e s t i n g systems awai t s tudy by NMRON methods. F o r example NMRON r e l a x a t i o n measurements c o u l d be used t o s t u d y e l e c t r o n i c sp in-wave s c a t t e r i n g phenomena i n i n s u l a t i n g s p i n 40 g l a s s e s such as t h e (CH ) NHCo Mn C l .2H O system o r o t h e r 3 1 3 ' 3 1 - x x 3 2 J d i s o r d e r e d magnet ic i n s u l a t o r s . Another use o f r a d i o a c t i v e i m p u r i t y probes such as 5 4 M n 2 + i s i n t h e s t u d y o f magnet i c f i e l d dependent e x c i t a t i o n gaps such as t h a t found i n t h e d i s o r d e r e d g r o u n d s t a t e 1 - d i m e n s i o n a l a n t i f e r r o m a g n e t N i ( C H N ) NO (CIO) 2 8 2 2 2 4 (NENP) 4 . 1 The o b s e r v a t i o n o f v e r y s h o r t low t e m p e r a t u r e n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t imes i n magnet ic i n s u l a t o r s i n d i c a t e s t h a t t h e s e m a t e r i a l s may be s u i t a b l e h o s t s f o r NO n u c l e a r s t r u c t u r e s t u d i e s o f s h o r t l i v e d r a d i o a c t i v e i s o t o p e s ( i n so c a l l e d "On L i n e " NO e x p e r i m e n t s ) . Up t o now t h e s e s t u d i e s have been r e s t r i c t e d t o meta l h o s t s as i t was g e n e r a l l y b e l i e v e d t h a t r e l a x a t i o n t imes i n i n s u l a t o r s were t o o l o n g . The h i g h heat c a p a c i t i e s and s h o r t r e l a x a t i o n t imes observed i n t h i s work suggest t h a t the s e a r c h f o r an i n s u l a t i n g NO h o s t m a t e r i a l i s v e r y w o r t h w h i l e . 150 B i b l i o g r a p h y 1 2 3 4 6 7 8 N. Bloembergen and G.M. Temmer. Phys. Rev., 89:883, 1953 Low-Temperature N u c l e a r O r i e n t a t i o n . E d i t e d by N. J . Stone and H. Potsma. ( N o r t h H o l l a n d ) , 1986. E . M a t t h i a s and R.J. H o l l i d a y . Phys. Rev. L e t t . , 17:897, 1966, H. R. F o s t e r , P'. Cooke, P. H. C h a p l i n , P. Lynam, D. E. Swan G. V. H. W i l s o n . Phys. Rev. L e t t . 38:1546, 1977. H. R. F o s t e r , P. Cooke, P. H. C h a p l i n , P. Lynam and G. V. H. W i l s o n . Hyp. I n t e r a c t n . 4:357, 1978. A. K o t l i c k i and B. G. T u r r e l l . Hyp. I n t e r a c t n . 11:197, 1981. A. K o t l i c k i and B. G. T u r r e l l . Phys. Rev. L e t t . , 56:7, 1986. A. L. A l l s o p , M. de A r a u j o , G. J . Bowden, R.G. C l a r k e and N. J . Stone. J . PhysC 17:415, 1984. L. N i e s e n and W.J Huiskamp. P h y s i c a . 50:259, 1970. U. Fano. Mod. Phys. 29:74, 1957. S. Vega and A. P i n e s . J . Chem. Phys., 66:5624, 1977. E. T. J a n e s . Phys. Rev. 98:1099, 1955. A. K o t l i c k i , B. A. Mcleod, M. Shot and B. G. T u r r e l l . Phys. 14 V. J a c c a r i n o . Magnetism 2A. E d i t t e d by G. T. Rado and H. S u h l . (Academic P r e s s , New York) 15 . . E. A. Turov and M. P. P e t r o v , N u c l e a r - M a g n e t i c Resonance i n F e r r o and A n t i f e r r o m a g n e t s . H a l s t e d P r e s s , 1972. 1 6 F. K e f f e r . E n c y c l o p e d i a o f P h y s i c s , V o l . 1 8 . E d i t e d by H. P. J . W i j n (New York, S p r i n g e r V e r l a g ) . 2:109, 1966. 1 7 T. H o l s t i e n and H. P r i m a k o f f . Phys. Rev.., 58:1098, 1940. i ft H. S u h l . Phys. Rev., 109:606, 1958. 19 A. Nakamura. P r o g r . Theor. Phys., 20:542, 1958. 151 2 0 P. R i c h a r d s . Phys. Rev. 173:581, 1968. 2 1 D. Beeman and P. P i n c u s . Phys. Rev. 166,2:359, 1968. 2 2 P. P i n c u s and J . W i n t e r . Phys. Rev. L e t t . , 7,7:270, 1961. 23 M. Le G r o s , A. K o t l i c k i and B. G. T u r r e l l . Hyp. I n t e r a c t n . 51:1111, 1989. 24 D. P, Weitekamp. Time Domain M u l t i p l e Quantum NMR. Advances i n M a g n e t i c Resonance V o l 3 : 3 . 25 M. Le Gros, A. K o t l i c k i and B. G. T u r r e l l . Hyp. I n t e r a c t n . 36:161, 1987. 2 6 A. Z a l k i n , J . D. F o r r e s t e r and D. H. Templeton I n o r g . Chem. 3:529, 1964. 27 Z. M. E l S a f f a r and G. M. Brown. A c t a . C r y s t a l l o g r . S e c t . B 27:66, 1971. 2 8 R. D. Spence and v. N a g a r a j a n . Phys. Rev. 149:191, 1966. 29 R. F. Altmam, S. Spooner, D. P. Landau and J . E. R i v e s . Phys. Rev. B. 11:458, 1975. 30 R. L. A. G o r l i n g , B. G. T u r r e l l and P. W. M a r t i n . Can. J . Phys. 55:1526, 1977. 31 J . F eder and E. P y t t e . Phys. Rev. 168,2:640, 1968. 3 2 J . E. R i v e s and V. B e n e d i c t Phys. Rev. 12,5:1908, 1975. 3 3 P. W. Anderson. Phys. Rev. 86,5:694. (1952) 34 . A. R Miedema, R. F. W i e l i n g a , and W. J . Huiskamp. P h y s i c a 31:835, (1965). 35 P. B u r l e t , P. B u r l e t and E. F. B e r t a u t . S o l i d S t a t e Commun. 14:665, 1974. 3 6 P. B e a u v i l l a n and J . P. Renard. P h y s i c a 86:667, 1971. 37 Y. Okuda, M. Matsuura and T. Haseda. J . Phys. Soc. J a p . 44:371, 1978. 39 . M. LeGros, B. G. T u r r e l l , and A. K o t l i c k i . J a p . J o u r n . A p p l . Phys. 26:865, (1987). 152 A. Abragam. The P r i n c i p l e s o f N u c l e a r M a g n e t i s i m . O x f o r d U n i v e r s i t y P r e s s London, New York. A. Cheikhrouhou, C. Dupas, J . P. Itenard and P. V e i l l e t . J o u r n . o f Magnetism and Mag. M a t e r i a l s 49:201, (1985) J . P. Renard, M. V e r d a g u e r and J - P. R e g n a u l t . E u r o p h y s i c s L e t t . 3:945, (1987). 153 APPENDIX A A . l D e t a i l s o f t h e NMRON Probe and Sample P r e p a r a t i o n . A d e t a i l e d diagram o f t h e sample, c o l d f i n g e r and t h e NMRON probe i s shown i n f i g u r e A . l . The sample, ( 1 ) , i s a t t a c h e d t o a c o l d f i n g e r e x t e n s i o n , ( 2 ) , by a l a y e r o f m y l a r f o i l u s i n g s i l i c o n g r e a s e as a c o n t a c t agent. The c o l d f i n g e r e x t e n s i o n i s clamped t o t h e c o l d f i n g e r o f t h e d i l u t i o n r e f r i g e r a t o r , ( 3 ) , by a clamp, (4) , d e s i g n e d t o a l l o w r e m o v a l o f t h e c o l d f i n g e r e x t e n s i o n from t h e NMRON a p p a r a t u s w i t h o u t t h e NMRON probe. The NMRON probe c o n s i s t s o f a t h r e e t u r n NMR c o i l m a n u f a c t u r e d from a 3mm wide s t r i p o f 0.1mm b r a s s f o i l , ( 5 ) . The ends o f t h e NMR c o i l a r e s o l d e r e d t o two 2mm t h i c k b r a s s l u g s , (6) , w h i c h a r e screwed i n t o n y l o n s u p p o r t r o d s , (7) . The f i x e d p l a t e o f t h e t u n i n g c a p a c i t o r , ( 8 ) , i s a t t a c h e d t o one o f t h e b r a s s l u g s w h i l e t h e a d j u s t a b l e " grounded" c a p a c i t o r p l a t e , ( 9 ) , i s a t t a c h e d t o a t h i n s t a i n l e s s s t e e l r o d , ( 1 0 ) , w h i c h can be r o t a t e d from o u t s i d e t h e c r y o s t a t (see f i g u r e A . 2 ) . The mat c h i n g c i r c u i t , L l and C l o f f i g u r e 3.1 page 52, i s mounted between t h e b r a s s l u g o f one o f t h e n y l o n s u p p o r t r o d s and t h e body, (11}, o f t h e probe. The RF power i s s u p p l i e d t o t h e probe t h r o u g h RGU-174 50 ohm c o a x i a l c a b l e , ( 1 2 ) . A s c h e m a t i c o f t h e probe mounted i n t h e IK h e a t s h i e l d o f t h e d i l u t i o n r e f r i g e r a t o r i s shown i n f i g u r e A.2. Movement o f t h e t u n i n g p l a t e o f t h e t u n i n g c a p a c i t o r i s a c h i e v e d by an arrangement o f p u l l e y s and d e n t a l f l o s s c o r d s w h i c h l i n k t h e r o t a t i o n o f t h e e x t e r n a l t u n i n g c o n t r o l w i t h t h e s t a i n l e s s s t e e l r o d ( 1 0 ) . 154 155 F i g u r e A.2: NMRON Probe Mounted i n t h e IK Heat S h i e l d A) The IK h e a t s h i e l d o f t h e d i l u t i o n r e f r i g e r a t o r . B) D e n t a l F l o s s t u n i n g l i n e . C) P u l l e y s . D) T u n i n g mechanism. As d e s c r i b e d p r e v i o u s l y t h e samples were grown from seed c r y s t a l s by s l o w e v a p o r a t i o n o f a wat e r s o l u t i o n f o r M n C l 2 . 4 H 2 0 and s l o w c o o l i n g o f a s u p e r s a t u r a t e d s o l u t i o n f o r Mn(COOCH 3) ,4H 20. I n t h e former method a seed c r y s t a l o f MnCl 2«4H 20 was p l a c e d i n a s h a l l o w r e c t a n g u l a r s l o t m i l l e d i n t o a p e r s p e x p l a t e . A few drops o f r a d i o a c t i v e M n C l 2 . 4 H 2 0 s o l u t i o n was t h e n p l a c e d i n t h e t r o u g h c o v e r i n g t h e seed c r y s t a l and a m i c r o s c o p e c o v e r s l i p was s e a l e d t o t h e t r o u g h w i t h s i l i c o n g r e a s e . As t h e wat e r e v a p o r a t e d from t h e s o l u t i o n t h e seed c r y s t a l grew i n t o a f l a t r e c t a n g u l a r p l a t e w i t h d i m e n s i o n s d e t e r m i n e d by t h o s e o f t h e m i l l e d s l o t (see f i g u r e A . 3a). The Mn(COOCH 3) .4H 20 samples were grown by p l a c i n g a s m a l l seed c r y s t a l a drop o f s a t u r a t e d s o l u t i o n c o n t a i n e d i n a p r o p e r l y shaped c o n t a i n e r and c o v e r e d by m i n e r a l o i l (see f i g u r e A.3b). The t e m p e r a t u r e o f t h e m i n e r a l o i l was s l o w l y r e d u c e d and t h e seed c r y s t a l formed i n t o a sample w i t h a shape d e t e r m i n e d by t h e c o n t a i n e r . 157 F i g u r e A.3: Sample Growth P r o c e d u r e s a) Growth o f MnCl .4H0 samples. (R) Seed c r y s t a l immersed i n r a d i o a c t i v e s o l u t i o n . (S) M i c r o s c o p e c o v e r s l i p . (T) P e r s p e x p l a t e , b) Growth o f Mn(C00CH 3) .4H 20. (U) Seed c r y s t a l immersed i n r a d i o a c t i v e s o l u t i o n . (V) M i n e r a l o i l . (W) P e r s p e x b e a k e r . (X) Temperature r e g u l a t e d e n c l o s u r e . 158 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0084990/manifest

Comment

Related Items