@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Koster, Evert"@en ; dcterms:issued "2011-03-22T18:58:14Z"@en, "1972"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The pulsed N.M.R. technique has been used to study the ferromagnets Ni, Fe₂P and Fe₃P. The dependence of the N.M.R. free induction decay on the strength of the applied r.f. field and on pulse length has been studied in nickel powder. The results indicate that the applied r.f. field is enhanced and that there is a distribution of enhancement factors. The distribution can be explained in the light of a model in which the domain walls vibrate like pinned membranes. The maximum enhancement factor is estimated to be 4700. The N.M.R. of ³¹P and ⁵⁷Fe has been observed in Fe₂P. Zero field resonances have been observed at the frequencies 17.5 MHz, 20.5 MHz, 77.5 MHz and 86.6 MHz at 1.5 K. These results allowed the deduction of the hyperfine fields at the various atomic sites. These are H[sub n] (FeI)=148 koe., H[sub n] (FeII)= 123 koe., H[sub n] (PI)=50.2 koe. and H[sub n] (PII)=45.0 koe.. From the shift of the N.M.R. frequency on application of an external magnetic field the sign of the phosphorous hyperfine fields is shown to be positive. The temperature dependence of the ³¹P N.M.R. frequency has also been studied and the data is well 2 fxtted by a T² law. Domain wall enhancement of the applied r.f. field was studied in the light of the pinned membrane model. Studies of the nuclear relaxation times indicate that thermal fluctuations of the domain walls provide the dominant relaxation mechanism. In Fe₃P a rather complicated N.M.R; spectrum was observed. Resonances occur at 41.7 MHz, 37.2 MHz, 34.5 MHz, 27.5 MHz and 24.8 MHz. These are all attributed to iron sites and correspond to hyperfine fields of 304 koe., 271 koe., 200 koe., and 180. koe. . Domain wall enhancements were also studied in the light of the pinned membrane model. Nuclear relaxation times were also determined and the results indicate that thermal fluctuations of the domain walls provide the dominant relaxation mechanism."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/32726?expand=metadata"@en ; skos:note "Z 2 4 A PULSED N.M.R. STUDY OF THE FERROMAGNETS N i , F e 2 P and F e 3 P - by EVERT KOSTER .Sc., The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department o f P h y s i c s We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March, 1972 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and s tudy . I f u r t h e r agree t h a t permiss ion fo r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copy ing o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed wi thout my w r i t t e n p e r m i s s i o n . Department of fHySiCS The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada R e s e a r c h S u p e r v i s o r B.G. T u r r e l l * i i ABSTRACT c The p u l s e d N.M.R. t e c h n i q u e has been used t o st u d y t h e fer r o m a g n e t s N i , F e 2 P and F e 3 P . The dependence o f th e N.M.R. f r e e i n d u c t i o n decay on 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 . f i e l d and on p u l s e l e n g t h has been s t u d i e d i n n i c k e l powder. The r e s u l t s i n d i c a t e t h a t t h e a p p l i e d r . f . f i e l d i s enhanced and t h a t t h e r e i s a d i s t r i b u t i o n o f enhancement f a c t o r s . The d i s t r i -b u t i o n can be e x p l a i n e d i n t h e l i g h t o f a model i n w h i c h t h e domain w a l l s v i b r a t e l i k e p i n n e d membranes. The maximum enhancement f a c t o r i s e s t i m a t e d t o be 4700. 31 57 The N.M.R. o f P and Fe has been o b s e r v e d i n F e 2 P . Zero f i e l d r e s o n a n c e s have been o b s e r v e d a t t h e f r e q u e n c i e s 17.5 MHz, 20.5 MHz, 77.5 MHz and 86.6 MHz a t 1.5 K. These r e s u l t s a l l o w e d t h e d e d u c t i o n o f t h e h y p e r f i n e f i e l d s a t t h e v a r i o u s a t o m i c s i t e s . These a r e H n ( F e I ) = 1 4 8 koe., H n ( F e I I ) = 123 koe., H n(PI)=50.2 koe. and H n ( P I I ) = 4 5 . 0 koe.. From t h e s h i f t o f t h e N.M.R. f r e q u e n c y on a p p l i c a t i o n o f an e x t e r n a l m a g n e t i c f i e l d t h e s i g n o f t h e phosphorous h y p e r f i n e f i e l d s i s shown t o be p o s i t i v e . The t e m p e r a t u r e dependence o f t h e 31 P N.M.R. f r e q u e n c y has a l s o been s t u d i e d and t h e d a t a i s w e l l 2 f x t t e d by a T law. Domain w a l l enhancement o f t h e a p p l i e d r . f . f i e l d was s t u d i e d i n t h e l i g h t o f th e p i n n e d membrane model. r S t u d i e s o f t h e n u c l e a r r e l a x a t i o n t i m e s i n d i c a t e t h a t t h e r m a l f l u c t u a t i o n s o f t h e domain w a l l s p r o v i d e t h e dominant r e l a x -a t i o n mechanism. XXX I n Fe^P a r a t h e r c o m p l i c a t e d N.M.R; sp e c t r u m was o b s e r v e d . Resonances o c c u r a t 41.7 MHz, 37.2 MHz, 34.5 MHz, 27.5 MHz and 24.8 MHz. These a r e a l l a t t r i b u t e d t o i r o n s i t e s and c o r r e s -pond t o h y p e r f i n e f i e l d s o f 304 koe., 271 k o e . , 200 koe., and 180. koe. . Domain w a l l enhancements were a l s o s t u d i e d i n t h e l i g h t o f t h e p i n n e d membrane model. N u c l e a r r e l a x a t i o n t i m e s were a l s o d e t e r m i n e d and t h e r e s u l t s i n d i c a t e t h a t t h e r m a l f l u c t u a t i o n s o f t h e domain w a l l s p r o v i d e t h e dominant r e l a x a t i o n mechanism. i v TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i i LIST OF ILLUSTRATIONS . v i i i ACKNOWLEDGEMENTS X CHAPTER I INTRODUCTION 1 I I N.M.R. IN FERROMAGNETIC MATERIALS 10 ( i ) F e r r o m a g n e t i s m 10 ( i i ) Temperature Dependence o f t h e M a g n e t i z a t i o n 11 ( i i i ) H y p e r f i n e F i e l d s i n Ferromagnets 15 ( i v ) R.F. Enhancement i n Ferromagnets 21 (v) N u c l e a r M a g n e t i c R e l a x a t i o n i n Ferromagnets 25 I I I APPARATUS AND EXPERIMENTAL PROCEDURE 2 9 A p p a r a t u s ( i ) P u l s e d O s c i l l a t o r s . . . . 29 ( i i ) Dewar System 34 ( i i i ) Sample C o i l 34 ( i v ) The R e c e i v i n g System.... 35 (v) T i m i n g A p p a r a t u s 38 E x p e r i m e n t a l T echnique ( i ) S e a r c h f o r Zero F i e l d N.M.R. L i n e s 41 ( i i ) Measurement o f t h e Enhancement F a c t o r 42 ( i i i ) Measurement o f R e l a x a t i o n Times 43 V Page CHAPTER IV NICKEL . 46 (a) E x p e r i m e n t a l R e s u l t s 46 (b) D i s c u s s i o n 48 V F e 2 P 56 (a) I n t r o d u c t i o n 56 (b) E x p e r i m e n t a l R e s u l t s 60 ( i ) Zero F i e l d S p e c t r a 60 ( i i ) Temperature and F i e l d Dependence o f t h e P ( I I ) Resonant Freq u e n c y 63 ( i i i ) Enhancement F a c t o r s 65 ( i v ) N u c l e a r S p i n R e l a x a t i o n 65 ( i ) Z ero F i e l d S p e c t r a 75 ( i i ) Temperature and F i e l d Dependence o f t h e P ( I I ) Resonant Frequency 79 ( i i i ) Enhancement F a c t o r s 82 ( i v ) N u c l e a r S p i n R e l a x a t i o n 84 VI F e 3 P 88 (a) I n t r o d u c t i o n 88 (b) E x p e r i m e n t a l R e s u l t s 90 ( i ) Zero F i e l d Resonances 90 ( i i ) Enhancement F a c t o r s 94 ( i i i ) N u c l e a r R e l a x a t i o n Times 94 v i Page (c) D i s c u s s i o n o f E x p e r i m e n t a l R e s u l t s 98 ( i ) Zero F i e l d Resonances 98 ( i i ) Enhancement F a c t o r s 100 ( i i i ) N u c l e a r S p i n R e l a x a t i o n 101 CHAPTER V I I CONCLUSIONS 103 v i i LIST OF TABLES T a b l e Page 31 I . V c U ' - i n t i o n o f P N.M.R. f r e q u e n c y w i t h t e m p e r a t u r e 63 I I . N u c l e a r s p i n l o n g i t u d i n a l and t r a n s v e r s e r e l a x a t i o n t imes 71 I I I N.M.R. d a t a f o r F e 9 P a t h e l i u m t e m p e r a t u r e s 76 v i i i L IST OF ILLUSTRATIONS F i g u r e Page 3- 1 B l o c k d i a g r a m o f p u l s e d o s c i l l a t o r 30 2 Low power p u l s e d o s c i l l a t o r 32 3 P u l s e f o r m i n g c i r c u i t 33 4 Sample c o i l c i r c u i t 36 5 P r e a m p l i f i e r 37b 6 Cascode i n p u t s t a g e and f i r s t g a i n c o n t r o l l e d s t a g e 39 7 Second g a i n c o n t r o l l e d , o u t p u t and d e t e c t o r s t a g e s 40 4- 1 FID a m p l i t u d e v e r s u s r . f . f i e l d s t r e n g t h . 47 2 F r e q u e n c y dependence o f t h e FID a m p l i t u d e 49 3 dependence o f t h e FID a m p l i t u d e : r i g i d p l a n e model 51 5- 1 • Diagram o f F e 2 P c r y s t a l s t r u c t u r e 58 2 N e a r e s t n e i g h b o u r c o n f i g u r a t i o n s i n F e 2 P . 59 3 Zero f i e l d f r e q u e n c y dependence o f t h e s p i n -echo a m p l i t u d e i n F e 2 P a t 1.5 K 61 4 Zero f i e l d f r e q u e n c y dependence o f t h e s p i n -echo a m p l i t u d e i n F e 2 P a t 1. 5 K . .. 62 31 5 Change i n P r e s o n a n c e f r e q u e n c y w i t h a p p l i e d f i e l d 64 6 S p i n - e c h o a m p l i t u d e v e r s u s r . f . f i e l d s t r e n g t h : P ( I I ) 1.5 K 66 7 S p i n - e c h o a m p l i t u d e v e r s u s r . f . f i e l d s t r e n g t h : • P(I) 1.5 K 67 i x F i gure Page 31 5- 8 L o n g i t u d i n a l r e l a x a t i o n of P(I) i n Fe 2P at 1.5 K ... 68 31 9 L o n g i t u d i n a l r e l a x a t i o n of P ( I I ) i n Fe 2P at 1.5 K 69 57 10 L o n g i t u d i n a l r e l a x a t i o n of Fe(I) i n Fe 2P at 1.5 K 70 31 11 Transverse r e l a x a t i o n of P(I) i n Fe 2P at 1.5 K 72 31 12 Transverse r e l a x a t i o n of P ( I I ) i n Fe 2P at 1.5 K and 77 K 73 57 13 Transverse r e l a x a t i o n of Fe(I) i n Fe 2P at 1.5 K 74 31 14 Temperature dependence of the P ( I I ) N.M.R. frequency 80 6- 1 The s t r u c t u r e of Fe^P p r o j e c t e d onto the b a s a l plane 89 2 Zero f i e l d spin-echo spectrum of Fe^P at 1.5 K 91 3 Zero f i e l d spin-echo spectrum of Fe.jP at 1.5 K 92 4 Zero f i e l d spin-echo spectrum of Fe^P at 1,5 K 93 57 5 dependence o f the Fe(I) spin-echo amplitude i n Fe 3P at 1.5 K -95 57 6 L o n g i t u d i n a l r e l a x a t i o n of Fe(I) i n Fe^P at 1.5 K 96 57 7 Transverse r e l a x a t i o n of Fe(I) i n Fe^P at 1.5 K 97 X ACKNOWLEDGEMENTS I w i s h t o e x p r e s s my s i n c e r e g r a t i t u d e t o Dr. B.G. T u r r e l l f o r s u g g e s t i n g t h e work, and f o r h i s g u i d a n c e t h r o u g h -out t h e work. I would l i k e t o thank Dr. John Noble f o r t h e h e l p f u l d i s c u s s i o n s on t h e equipment used i n t h i s work. I would l i k e t o thank Mr. J . L e e s , g l a s s b l o w e r , f o r making t h e h e l i u m dewars used i n t h i s work, and f o r making and s e a l i n g t h e g l a s s sample h o l d e r s . I w i s h t o e x p r e s s my g r a t i t u d e t o Dr. D. L l . W i l l i a m s f o r h i s a s s i s t a n c e d u r i n g Dr. T u r r e l l ' s l e a v e o f absence. I am q r a t e f u l t o Mr. R.G. B u t t e r s o f t h e m e t a l l u r g y department f o r h i s a s s i s t a n c e i n t h e p r e p a r a t i o n o f t h e samples employed i n t h i s work. F i n a n c i a l a s s i s t a n c e p r o v i d e d by a N a t i o n a l R e s e a r c h C o u n c i l S t u d e n t s h i p i s a l s o g r a t e f u l l y acknowledged. 1 CHAPTER I INTRODUCTION The N u c l e a r M a g n e t i c Resonance (N.M.R.) t e c h n i q u e has been e s t a b l i s h e d as a p o w e r f u l t o o l f o r t h e s t u d y o f h y p e r f i n e i n t e r -a c t i o n s i n a wide v a r i e t y o f m a t e r i a l s . I n p a r t i c u l a r , i s has p r o v e d t o be e x t r e m e l y u s e f u l i n t h e s t u d y o f h y p e r f i n e f i e l d s i n f e r r o m a g n e t i c a l l y o r d e r e d systems ( P o r t i s and L i n d q u i s t , 1 9 6 5 ) . N u c l e a r r e s o n a n c e s t u d i e s o f t h e s e systems c a n e l u c i d a t e t h e s t a t i c and dynamic n u c l e a r h y p e r f i n e c o u p l i n g . The magnitude and d i r e c t i o n o f t h e n u c l e a r h y p e r f i n e f i e l d , i t s t e m p e r a t u r e dependence, and t h e f i e l d d i s t r i b u t i o n s r e s u l t i n g from i m p u r i t y s u b s t i t u t i o n a r e examples o f t h e s t a t i c m a g n e t i c i n f o r m a t i o n g a i n e d from r e s o n a n c e s t u d i e s . Measurements o f t h e c h a r a c t e r -i s t i c r e l a x a t i o n t i m e s f o r s p i n - s p i n and s p i n - l a t t i c e c o u p l i n g , and enhancements o f t h e a p p l i e d r . f . f i e l d due t o domain w a l l s p r o v i d e i n f o r m a t i o n c o n c e r n i n g t h e dynamic i n t e r a c t i o n s o f t h e n u c l e a r s p i n system. The N.M.Rl r e s u l t s t a k e n t o g e t h e r w i t h measurements o f m a g n e t i c moments (e.g. n e u t r o n s c a t t e r i n g e x p e r -iments) can l e a d t o a f a i r l y c omplete u n d e r s t a n d i n g o f t h e h y p e r f i n e f i e l d and i t s s o u r c e s . The e x p e r i m e n t a l methods used i n N.M.R. work may be d i v i d e d i n t o s t e a d y s t a t e and p u l s e t e c h n i q u e s . I n t h e s t e a d y s t a t e t e c h n i q u e t h e a b s o r p t i o n o f power by t h e n u c l e a r s p i n s i s d e t e c t e d by t h e c o n v e n t i o n a l r e s o n a n c e t e c h n i q u e o f m o d u l a t i n g t h e o s c i l l a t o r f r e q u e n c y and a m p l i f y i n g t h e m o d u l a t i o n e n v e l o p e 2 v i a l o c k - i n d e t e c t o r t o p r e s e n t t h e f i r s t d e r i v a t i v e o f t h e reson a n c e l i n e . S i n c e t h e f i r s t d e r i v a t i v e d e c r e a s e s w i t h l i n e -w i d t h , t h e use o f t h e s t e a d y s t a t e t e c h n i q u e i s u s u a l l y l i m i t e d t o n a r r o w - l i n e r esonance and l i n e s h a p e s t u d i e s . The p u l s e t e c h n i q u e i s e s p e c i a l l y u s e f u l f o r t h e o b s e r v a t i o n o f t h e b r o a d -l i n e r e s o n a n c e s o f t e n found i n f e r r o m a g n e t i c systems as i t p r o v i d e s b e t t e r d i s c r i m i n a t i o n a g a i n s t background r e s o n a n c e s t h a n do t h e c o n v e n t i o n a l s t e a d y s t a t e t e c h n i q u e s (Dean e t . a l . , 1967). I t a l s o e n a b l e s d i r e c t o b s e r v a t i o n o f n u c l e a r r e l a x a t i o n . The work d e s c r i b e d i n t h i s t h e s i s r e p r e s e n t s an a p p l i c a t i o n o f t h e p u l s e d N.M.R. t e c h n i q u e t o a s t u d y o f t h e f e r r o m a g n e t s N i , F e 2 P and Fe^P. The e x p e r i m e n t on n i c k e l was d e s i g n e d t o s t u d y domain w a l l dynamics i n t h e m e t a l . The e x p e r i m e n t s on F e 2 P and Fe^P a l l o w e d t h e measurement of h y p e r f i n e f i e l d s a t v a r i o u s s i t e s , t h e t e m p e r a t u r e dependence o f t h e h y p e r f i n e f i e l d , r e l a x a t i o n t i m e s and domain w a l l c h a r a c t e r i s t i c s . . A n u c l e u s w i t h t o t a l a n g u l a r momentum 1ft, has a s s o c i a t e d w i t h i t a m a g n e t i c d i p o l e moment jd=g>ljuilI, where g^ i s t h e n u c l e a r g f a c t o r and jx^the n u c l e a r magneton. The Zeeman i n t e r a c t i o n o f t h e m a g n e t i c d i p o l e moment,fd, w i t h a m a g n e t i c f i e l d H, i s g i v e n by K = \" /f-H (1.1) The energy e i g e n v a l u e s c o r r e s p o n d i n g t o t h e e i g e n s t a t e s |m> o f t h i s H a m i l t o n i a n a r e g i v e n by E = g U mH (1.2) m ^ m = I , I - l , . . . , - I 3 where m den o t e s t h e e i g e n v a l u e o f I , and z i s t h e d i r e c t i o n z o f t h e a p p l i e d f i e l d H. I n t h e r m a l e q u i l i b r i u m t h e n u c l e a r s p i n system can be d e s c r i b e d by t h e p o p u l a t i o n d e n s i t i e s o f t h e energy l e v e l s E^, g i v e n by t h e B o l t z m a n d i s t r i b u t i o n f u n c t i o n -E /kT P = f m (1.3) ' V -E /kT where T den o t e s t h e l a t t i c e t e m p e r a t u r e , t h e l a t t i c e b e i n g t h e en v i r o n m e n t i n w h i c h t h e n u c l e a r s p i n s a r e l o c a t e d . The n e t m a g n e t i z a t i o n o f a b u l k sample c o n t a i n i n g N s p i n s i s t h e n g i v e n by i i M = NT.P^X (M)-= NV.P„q.. M.m - Ng?>U?I(I+l)H ( 1 4 ) 3kT kT K ' ' The e q u a t i o n o f m o t i o n o f t h e m a g n e t i z a t i o n , M, i n t h e p r e s e n c e o f a f i e l d H, n e g l e c t i n g t h e i n t e r a c t i o n of t h e s p i n s w i t h t h e i r s u r r o u n d i n g s , i s dM d t : = t r [ H ^ ] d . 5 ) where X i s t h e Zeeman h a m i l t o n i a n ( e q u a t i o n 1.1). Upon a p p l y i n g t h e commutation r e l a t i o n s h i p s f o r t h e components o f a n g u l a r momentum t h i s becomes | = ^ ( M x H ) = tfrt (M x H) { l m 6 ) 4 The m o t i o n c o r r e s p o n d s t o an undamped p r e c e s s i o n o f t h e magne-t i z a t i o n about t h e d i r e c t i o n o f t h e a p p l i e d f i e l d w i t h an a n g u l a r v e l o c i t y <£H. V» i s t h e n u c l e a r g y r o m a g n e t i c r a t i o . I f t h e a p p l i e d f i e l d c o n s i s t s o n l y o f a s t a t i c f i e l d H Q i n t h e z d i r e c t i o n t h e n i t i s e v i d e n t t h a t M z i s t i m e i n d e p e n d e n t w h i l e t h e components M x and v a r y s i n u s o i d a l l y w i t h t i m e w i t h a f r e q u e n c y ^=/NHO. uj, i s c a l l e d t h e Larmor f r e q u e n c y . I n o r d e r t o s o l v e (1.6) i t i s c o n v e n i e n t t o t r a n s f o r m t o a frame o f r e f e r e n c e r o t a t i n g w i t h a n g u l a r v e l o c i t y c*> w i t h r e s p e c t t o t h e l a b o r a t o r y frame. I n t h i s r o t a t i n g frame t h e e q u a t i o n o f m o t i o n f o r M becomes SM dM L u s i n g (1.6) t h i s becomes |f = M x [H + ] U . 8 ) I f H i s j u s t t h e s t a t i c f i e l d a l o n g t h e z d i r e c t i o n , and i f we choose ^\"V* k, where k i s a u n i t v e c t o r a l o n g t h e z d i r e c t i o n , t h e n t h e m a g n e t i z a t i o n i s s t a t i o n a r y i n t h e r o t a t i n g frame. I n t h e l a b o r a t o r y frame i t p r e c e s s e s about t h e f i e l d H Q a t t h e Larmor f r e q u e n c y . Suppose now t h a t t h e t o t a l f i e l d H i s t h e sum o f a c o n s t a n t f i e l d and a f i e l d p e r p e n d i c u l a r t o and r o t a t i n g about 5 i t w i t h an angular v e l o c i t y OJ . can \"be w r i t t e n -1 = H1 ( i c o s o / t + isinwt) (1.9) where i_ and j_ denote u n i t v e c t o r s along the x and y axes r e s p e c t i v e l y , o f the l a b o r a t o r y frame. Tak i n g t o l i e along the u n i t v e c t o r i ' i n the r o t a t i n g frame, e q u a t i o n (1.7) becomes •|| = y„M x [k(H Q+ u>//„ ) + i , H 1 ] (1.10) = VI * H e f f where ^ e f f = ^ (V\" -/* } + i ' H l In the r o t a t i n g frame, t h e r e f o r e t h e m a g n e t i z a t i o n p r e o e s R e s about an e f f e c t i v e f i e l d w i t h an ang u l a r v e l o c i t y {[H *H+w] + ( JfMH1) } . When \\&£>> M the e f f e c t of the r . f . f i e l d i s n e g l i g i b l e . The e f f e c t o f the r . f . f i e l d becomes a p p r e c i -a b l e when uJS-^H^. When cj =-V HH Q, M p r e c e s s e s about the d i r e c t i o n i _ ' w i t h an angular v e l o c i t y w,= c^H^. T h i s i s the phenomenon of n u c l e a r magnetic resonance. I f the f i e l d i s a p p l i e d f o r a time T , then the m a g n e t i z a t i o n would p r e c e s s through an angle iv/r*'/ and the s o l u t i o n s o f e q u a t i o n (1.6) can be w r i t t e n M (T) = M cos (w,T) z o M. (T) = M sin(w,f ) exp ( i u r ) (1.11) + O 1 . 0 M L = M +iM + x y 6 A f t e r t h e r . f . p u l s e i s c u t o f f , t h e p r e c e s s i n g m a g n e t i z a t i o n i s g i v e n by M (t) = M cos (u,r ) Z O M.(t) = M s i n ( u , T ) e x p ( i H t ) (1.12) T O A '90 degre.e. p u l s e ' , f o r w h i c h uf= t j ^ o r odd m u l t i p l e s t h e r e o f , p roduces t h e g r e a t e s t a m p l i t u d e o f p r e c e s s i n g magnet-i z a t i o n . The a m p l i t u d e v a n i s h e s f o l l o w i n g an * 180 degree p u l s e \" , t h a t i s , when u;,T='ff. ' I n p r a c t i c e , t h e sample i s p l a c e d i n s i d e a c o i l w h i c h i s p a r t o f an L-C c i r c u i t t u n e d t o t h e r e s o n a n c e f r e q u e n c y . R.F. v o l t a g e i s a p p l i e d t o t h e c o i l p r o d u c i n g a l i n e a r l y p o l a -r i z e d s i n u s o i d a l f i e l d p e r p e n d i c u l a r t o t h e s t a t i c f i e l d . T h i s o s c i l l a t i n g f i e l d can be decomposed i n t o two c o u n t e r - r o -t a t i n g components, one w i t h f r e q u e n c y u> , and t h e o t h e r w i t h f r e q u e n c y - UJ . When t h e res o n a n c e c o n d i t i o n i s s a t i s f i e d f o r one component t h e o t h e r i s 2 W o f f r e s o n a n c e and i t s e f f e c t can be n e g l e c t e d (see e.g. Abragam,1961). The r e s o n a n t compo-nent t u r n s t h e m a g n e t i z a t i o n i n t o t h e x,y p l a n e . F o l l o w i n g t h e p u l s e t h e components o f t h e m a g n e t i z a t i o n i n t h e x,y p l a n e p r e c e s s about w i t h a f r e q u e n c y u>„, and i n d u c e a v o l t a g e i n t h e p i c k - u p c o i l . T h i s ' f r e e i n d u c t i o n ' , s i g n a l i s a m p l i f i e d and d e t e c t e d by t h e r e c e i v e r . I t has been assumed u n t i l now t h a t t h e a p p l i e d f i e l d i s u n i f o r m . T h i s i s n o t t h e case i n p r a c t i s e as t h e r e i s 7 always some i n h o m o g e n e i t y a s s o c i a t e d w i t h any a p p l i e d f i e l d . The i n h o m o g e n e i t y r e s u l t s i n a s c a t t e r o f Larmor f r e q u e n c i e s . T h i s s c a t t e r can be d e s c r i b e d by a shape f u n c t i o n f(H). I f we now w i s h t o f i n d t h e p r e c e s s i n g m a g n e t i z a t i o n f o l l o w i n g t h e a p p l i c a t i o n o f an r . f . p u l s e a t t h e c e n t r a l Larmor f r e q u e n c y , t h e n we have t o t a k e i n t o a c c o u n t t h e s p r e a d i n Larmor f r e q u e n c i e s . The p r e c e s s i n g m a g n e t i z a t i o n i s now g i v e n by M + ( t ) = M Q r°sin(w,r ) e x p ( i uJ0 t ) f (CJ) d (1.13) - CO I f we assume t h a t C J , i s much s m a l l e r t h a n t h e w i d t h o f t h e shape f u n c t i o n and t h a t t h e d u r a t i o n o f t h e p u l s e i s t h e o r d e r o f l / u > i . t h e n t h e n r e c e s s i n a m a a n f t - . i ? . a t i n n w i l l b e M + ( t ) = M Q s i n (u»,r ) exp ( i w / t ) / f ( O J > U ) exp ( i u t ) du (1.14) As t approaches i n f i n i t y , because o f t h e d e s t r u c t i v e i n t e r -f e r e n c e among t h e c o n t r i b u t i o n s o f d i f f e r e n t p a r t s o f t h e sample t o t h e t r a n s v e r s e m a g n e t i z a t i o n , M ( t ) goes t o z e r o . I f f o r example, t h e shape f u n c t i o n i s a L o r e n t z i a n c u r v e f (u0°+u) = [ l / ( b 2 + u 2 ) ] b / i r , Then M ( t ) = M Q s i n ( w , r ) e x p ( - b t ) = M Q s i n ( u , r ) e x p ( - t / T * ) (1.15) The decay t i m e i s t h e n i n v e r s e l y p r o p o r t i o n a l t o t h e l i n e w i d t h , b. 8 As t h e t r a n s v e r s e m a g n e t i z a t i o n decays so w i l l t h e v o l t a g e i n d u c e d i n t h e p i c k - u p c o i l . I t i s p o s s i b l e t o r e s t o r e t h e p r e c e s s i n g m a g n e t i z a t i o n t o i t s o r i g i n a l v a l u e by t h e a p p l i -c a t i o n o f an '180 degree p u l s e ' . T h i s i s t h e s p i n - e c h o t e c h -n i q u e (Hahn,1950). I n t h e s p i n - e c h o e x p e r i m e n t , t h e 180 degree p u l s e a p p l i e d a t a ti m e t a f t e r a 90 deg r e e p u l s e , t u r n s t h e p r e c e s s i n g m a g n e t i z a t i o n t h r o u g h 180 degrees about t h e x a x i s o f t h e r o t a t i n g frame. A t a f u r t h e r t i m e 2 t , t h e n u c l e a r s p i n s r e p h a s e and a s i g n a l maximum r e s u l t s . T h i s s i g -n a l maximum i s c a l l e d a s p i n - e c h o . When m e t a l l i c samples a r e us e d , t h e s k i n d e p t h e f f e c t i n t r o d u c e s i n h o m o g e n e i t i e s i n t h e r . f . f i e l d w h i c h make i t i m p o s s i b l e t o s a t i s f y t h e 90,180 degre c o n d i t i o n s f o r a l l t h e n u c l e i . T h i s l i m i t s t h e a n m l i t u d e o f th e echo. F o r m e t a l s we t a k e t h e terms 90 and 180 degree p u l s e s t o mean p u l s e s whose w i d t h s a r e such t h a t t h e f r e e i n d u e t i o n decays f o l l o w i n g t h e p u l s e s have maximum and minimum a m p l i t u d e s r e s p e c t i v e l y . I n t h e p r e c e e d i n g d i s c u s s i o n r e l a x a t i o n e f f e c t s have been i g n o r e d . I n any r e a l system t h e r e a r e i n t e r a c t i o n s c a p a b l e o f t r a n s f e r r i n g energy from t h e e x c i t e d s p i n systems t o t h e l a t t i c e . The r a t e a t w h i c h t h e s p i n system r e - e s t a b l i s h e d e q u i l i b r i u m w i t h t h e l a t t i c e i s c h a r a c t e r i z e d by a 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^. 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 i s d e t e r mined e s s e n t i a l l y by t h e t r a n s v e r s e components o f t h e l o c a l f l u c t u a t i n g f i e l d s a t t h e Larmor f r e q u e n c y ( S l i c h t e r , 1 9 6 3 ) . 9 A l s o p r e s e n t are i n t e r a c t i o n s which tend t o m a i n t a i n thermal e q u i l i b r i u m w i t h i n the s p i n system. The r a t e a t which these i n t e r a c t i o n s e s t a b l i s h e q u i l i b r i u m w i t h i n the s p i n system i s c h a r a c t e r i z e d by a t r a n s v e r s e r e l a x a t i o n time T 2 . In terms o f the c o r r e l a t i o n f u n c t i o n s of the l o c a l f l u c -t u a t i n g f i e l d s , T^ and T 2 are g i v e n by, y 2 r 6 0 (1 16) 1/ T l= J < H + ( t ) H _ ( 0 ) > e x p ( - i H t ) d t -oft 2 «*> 1/T 2= ^ + fdt (1.17) 1 - C o In many cases the approach t o e q u i l i b r i u m can be d e s c r i b e d by the phenomenological equations proposed by B l o c h (194 6) , g = *M x H + (M xi-M i ) / T 2 + (M o-M z)k/ T l The second and t h i r d terms r e p r e s e n t r e l a x a t i o n e f f e c t s . In the absence o f the r . f . f i e l d the s o l u t i o n s t o t h i s e q u a t i o n i n the r o t a t i n g r e f e r e n c e frame may be w r i t t e n M x ( t ) = M x ( 0 ) e x p [ - t / T 2 ] M y(t) = M (0) e x p [ - t / T 2 ] M z ( t ) = MQ+ (M z(0) + M Q ) e x p [ - t / T 1 ] (1.19) T^ and T 2 can be determined e x p e r i m e n t a l l y by o b s e r v i n g the time dependence o f H , H and M , ^ x' y z 10 CHAPTER I I N.M.R. i n F e r r o m a g n e t i c M a t e r i a l s ( i ) F e r r o m a g n e t i s m I n f e r r o m a g n e t i c m a t e r i a l s t h e r e e x i s t s a s t r o n g i n t e r a c t i o n w h i c h t e n d s t o a l i g n t h e a t o m i c d i p o l e s . As a r e s u l t a spontaneous m a g n e t i z a t i o n , M, e x i s t s ; even i n t h e absence o f a m a g n e t i c f i e l d t h e r e i s a m a g n e t i c moment. Above a c r i t i c a l t e m p e r a t u r e , T , c a l l e d t h e C u r i e t e m p e r a t u r e , t h e spontaneous m a g n e t i z a t i o n v a n i s h e s . The s t r o n g i n t e r a c t i o n w h i c h t e n d s t o a l i g n t h e a t o m i c d i p o l e s may be c o n s i d e r e d as e q u i v a l e n t t o some i n t e r n a l m a g n e t i c f i e l d H__. Thermal a g i -t a t i o n o f t h e atoms opposes t h e o r i e n t i n g e f f e c t o f t h e f i e l d . Thusc t h e C u r i e t e m p e r a t u r e must be t h e t e m p e r a t u r e a t w h i c h t h e t h e r m a l a g i t a t i o n i s s u f f i c i e n t t o d e s t r o y t h e spontaneous m a g n e t i z a t i o n . T h i s p e r m i t s an e s t i m a t e o f H m t o be made. F o r atoms w i t h a d i p o l e moment o f one Bohr magneton, we have X H = kT y r m c F o r T = 1000 K, a v a l u e c l o s e t o t h a t o b s e r v e d f o r i r o n , t h i s * 7 i m p l i e s t h a t H i s a p p r o x i m a t e l y 10 Oe.. H e i s e n b e r g (1928), has shown t h a t t h i s f i e l d i s due t o th e quantum m e c h a n i c a l exchange i n t e r a c t i o n . I n t h e s i m p l e s t case t h e H a m i l t o n i a n d e s c r i b i n g t h i s s t r o n g exchange i n t e r -a c t i o n between t h e e l e c t r o n s p i n s may be w r i t t e n (2.1) 11 E i t h e r a p a r a l l e l o r a n t i - p a r a l l e l o r d e r i n g may r e s u l t d e p e nding on t h e s i g n o f t h e exchange i n t e g r a l J . I n f e r r o -m a g n e t i c m a t e r i a l s t h e exchange i n t e g r a l i s p o s i t i v e and a p a r a l l e l o r d e r i n g i s f a v o r e d . I n f e r r o m a g n e t i c m a t e r i a l s such as i r o n , t h e f erromagne-t i s m may be a t t r i b u t e d t o t h e e l e c t r o n s i n t h e p a r t i a l l y f i l l e d band c o r r e s p o n d i n g t o t h e d e l e c t r o n s t a t e s i n t h e f r e e atom. The exchange i n t e r a c t i o n i s s u c h t h a t a t low\" t e m p e r a t u r e s , i n s t e a d o f e l e c t r o n s o c c u p y i n g t h e l o w e s t s t a t e s i n b a l a n c e d p a i r s , t h e r e i s an e x c e s s o f e l e c t r o n s w i t h s p i n s p o i n t i n g one d i r e c t i o n , g i v i n g r i s e t o a spontaneous m a g n e t i z a t i o n . The energy due t o t h e exchange i n t e r a c t i o n d e c r e a s e s as t h e number o f e x c e s s p a r a l l e l s p i n s i n c r e a s e s . T h i s d e c r e a s e i n energy i s accompanied by an i n c r e a s e i n energy due t o t h e e l e c -t r o n s moving t o s t a t e s o f h i g h e r energy i n t h e d band. The e q u i l i b r i u m m a g n e t i z a t i o n depends on t h e number o f e l e c t r o n s , t h e form o f t h e band, t h e magnitude o f t h e exchange i n t e r a c t i o n and t h e t e m p e r a t u r e ( i i ) Temperature Dependence o f t h e M a g n e t i z a t i o n (a) C o l l e c t i v e E l e c t r o n Theory T h i s t h e o r y i s a band model t h e o r y o f f e r r o m a g n e t i s m . / I t was f i r s t t r e a t e d om d e t a i l by S t o n e r (1938) . The t h e o r y i s based on t h e f o l l o w i n g t h r e e a s s u m p t i o n s ; 1. The 3d band i s p a r a b o l i c i n t h e n e i g h b o r h o o d o f t h e F e r m i s u r f a c e , t h a t i s , t h e d e n s i t y o f s t a t e s has t h e form 12 2. The exchange i n t e r a c t i o n between t h e e l e c t r o n s may be r e p r e s e n t e d by a m o l e c u l a r f i e l d . 3. The e l e c t r o n s o r h o l e s obey F e r m i - D i r a c s t a t i s t i c s . A c c o r d i n g t o t h e c o l l e c t i v e e l e c t r o n t h e o r y , t h e m a g n e t i z a t i o n v a r i e s w i t h t e m p e r a t u r e because o f r e d i s t r i b u t i o n o f e l e c t r o n s among t h e o n e - e l e c t r o n s t a t e s , t h a t i s , t h e t r a n s f e r o f e l e c -t r o n s between t h e u p - s p i n and t h e down-spin bands. The t h e o r y d i s t i n g u i s h e s between two i m p o r t a n t c a s e s . 1. A l l s p i n - u p s t a t e s l i e a t l e a s t E i n energy below t h e F e r m i l e v e l . T h i s g i v e s f o r T much l e s s t h a n T 3 c M o _ M ( T ) (2 2) — = A ( T ) e x P [ - E/kT] M o A(T) i s a s l o w l y v a r y i n g f u n c t i o n o f T. 2. U n f i l l e d s t a t e s o c c u r i n b o t h up and down-spin bands a t T=0 K. F o r t h i s case we have M -M(T) 0 — = ST^ (2.3) - M o The c o e f f i c i e n t S depends upon t h e shape o f t h e band, (b) S p i n Wave Theory C o n s i d e r a f e r r o m a g n e t i c specimen a t a b s o l u t e z e r o . The t h i r d law o f thermodynamics r e q u i r e s t h a t t h e s p i n system be c o m p l e t e l y o r d e r e d . S i n c e t h e system must a l s o be i n i t s ground s t a t e , i t f o l l o w s t h a t t h e s p i n quantum number of each atom 13 w i l l have i t s maximum v a l u e . Now assume t h a t t h e t e m p e r a t u r e i s r a i s e d s l i g h t l y c a u s i n g one s p i n t o be r e v e r s e d . The exchange f o r c e s w i l l t e n d t o i n v e r t t h e r e v e r s e d s p i n . A r e v e r -s a l o f t h e s p i n would r e t u r n t h e system t o i t s ground s t a t e . T h i s i s u n l i k e l y s i n c e t h e t e m p e r a t u r e has been r a i s e d . I t t u r n s o u t t h a t t h e r e v e r s e d s p i n t r a v e l s from one atom t o a n o t h e r , t h e exchange always o c c u r r i n g between n e i g h b o r i n g atoms. T h i s p r o p a g a t i o n o f t h e r e v e r s e d s p i n t h r o u g h a c r y s -t a l i s c a l l e d a s p i n wave. As t h e t e m p e r a t u r e i s i n c r e a s e d t h e number o f s p i n waves i n c r e a s e s and i n t e r a c t i o n s can t a k e p l a c e among t h e s p i n waves. A c c o r d i n g t o Dyson (1956), who t r e a t e d t h e c a s e of a H e i s e n -b e r g f e r r o m a g n e t , t h e e r r o r i n the c a l c u l a t i o n o f t h e m a g n e t i -z a t i o n when s p i n wave i n t e r a c t i o n s a r e n e g l e c t e d i s s m a l l f o r T < 0.5T c. To compute t h e d e c r e a s e i n t h e m a g n e t i z a t i o n a t a temper-a t u r e T, i t i s o n l y n e c e s s a r y t o know t h e number o f s p i n waves t h a t have been e x c i t e d , i . e . , M - M(T) a n - 2 - — £ <«k> (2 -4) M M k - o o where gy3 i s t h e moment a s s o c i a t e d w i t h a u n i t o f s p i n e x c i -t a t i o n , M Q i s t h e m a g n e t i z a t i o n a t a b s o l u t e z e r o , andZX'tk) i s t h e sum o v e r a l l k v a l u e s o f t h e t h e r m a l l y e x c i t e d s p i n wave numbers. I f one now u t i l i z e s t h e f a c t t h a t s p i n waves obey Bose s t a t i s t i c s , and one knows t h e energy s p e c t r u m o f t h e s p i n 14 waves, t h e n a c c o r d i n g t o Dyson one o b t a i n s t h e f o l l o w i n g r e s u l t f o r t h e t e m p e r a t u r e dependence o f t h e m a g n e t i z a t i o n M - M(T) r/0 — = Cl' / + VT ' + (2.5) M o F o r a more d e t a i l e d c o n s i d e r a t i o n o f s p i n waves i n f e r r o m a g n e t s t h e r e a d e r i s r e f e r r e d t o t h e comprehensive r e v i e w a r t i c l e by K e f f e r (1966). E x p e r i m e n t a l measurements o f t h e t e m p e r a t u r e dependence o f t h e s a t u r a t i o n m a g n e t i z a t i o n i n n i c k e l (Pugh and A r g y l e , 1962) and o f n e u t r o n d i f f r a c t i o n i n i r o n (Lowde and Umakantha, 1960), as w e l l as o t h e r e x p e r i m e n t s , have d e m o n s t r a t e d c l e a r l y t h e e x i s t e n c e o f s p i n waves o f l o n g w a v e l e n g t h i n m e t a l l i c sub-s t a n c e s . C o n c l u s i o n s have been drawn from t h i s t h a t t h e model o f a H e i s e n b e r g f e r r o m a g n e t and t h e t h e o r y o f s p i n waves i s g e n e r a l l y a p p l i c a b l e . S t u d i e s by Thompson e t . a l . ( 1 9 6 4 ) have i n d i c a t e d t h a t b o t h s p i n wave and s i n g l e p a r t i c l e t y p e e x c i t a t i o n s can be e x p e c t e d t o c o n t r i b u t e t o t h e t e m p e r a t u r e dependence o f t h e s a t u r a t i o n m a g n e t i z a t i o n i n f e r r o m a g n e t s . Any m e a n i n g f u l a n a l y s i s o f t h e d a t a w i l l i n v o l v e a s e p a r a t i o n i n t o s p i n wave and s i n g l e p a r -t i c l e c o n t r i b u t i o n s . T h i s r e q u i r e s t h a t s m a l l changes i n t h e m a g n e t i z a t i o n be known w i t h g r e a t a c c u r a c y ( W o h l f a r t h , 1 9 7 0 ) . 15 ( i i i ) H y p e r f i n e F i e l d s i n Ferromagnets I t has been found t h a t i n many magnetic m a t e r i a l s t h e r e i s , i n the absence of an a p p l i e d magnetic f i e l d , a v e r y l a r g e e f f e c t i v e h y p e r f i n e f i e l d a t the nuc l e u s . The o r i g i n o f these f i e l d s i n fe r r o m a g n e t i c metals was f i r s t d i s c u s s e d by Ma r s h a l l ( 1 9 5 8 ) . The most a u t h o r i t a t i v e d i s c u s s i o n o f the sub-j e c t i s by Watson and Freeman(1961,1965). P r t i s and L i n d q u i s t a l s o d i s c u s s N.M.R. and h y p e r f i n e f i e l d s i n ferromagnets. The p u l s e d N.M.R. technique was f i r s t demonstrated to be e s p e c i a l l y u s e f u l i n the study o f the b r o a d l i n e s p e c t r a f r e q u e n t l y encoun-t e r e d i n ferromagnets by Asayama e t a l . ( 1 9 6 3 ) . More r e c e n t l y the a p p l i c a t i o n o f the p u l s e d N.M.R. technique t o the study o f h y p e r f i n e f i e l d d i s t r i b u t i o n s i n ferromagnets i s d i s c u s s e d by Budnick and S k a l s k i ( 1 9 6 7 ) . Atomic h y p e r f i n e f i e l d s a r i s e from the i n t e r a c t i o n o f the magnetic moment o f the nucleus w i t h the e l e c t r o n i c s p i n and o r b i -t a l moments. F o l l o w i n g Fermi(1930) and Fermi and Segre(1933), the H a m i l t o n i a n d e s c r i b i n g t h i s i n t e r a c t i o n f o r a s i n g l e atom may be w r i t t e n X = -gw-nr S^'I + 3 — + 5 1 ( 2 , 6 ) r r Here L,S, and I r e p r e s e n t r e s p e c t i v e l y , e l e c t r o n o r b i t a l , e l e c -t r o n s p i n and n u c l e a r s p i n angular momentum o p e r a t o r s . are the Bohr and n u c l e a r magnetons, and g and are the e l e c -t r o n i c and n u c l e a r s p e c t r o s c o p i c s p l i t t i n g f a c t o r s . The d e l t a f u n c t i o n term i s c a l l e d the Fermi c o n t a c t term, and i s non-zero o n l y f o r those e l e c t r o n s which have a non- v a n i s h i n g p r o b a b i l i t y of b e i n g found a t the nucl e u s , i . e . the s e l e c t r o n s . * 16 E q u a t i o n (2.6) may be r e w r i t t e n i n the form M=-JJ;Hn (2.7) where i s the n u c l e a r magnetic moment and H n i s the t o t a l magnetic f i e l d a t the nucleus a r i s i n g from the r e s t o f the atom. The c o n t r i b u t i o n to H a r i s i n g through the Fermi c o n t a c t term n may be w r i t t e n Sc- % A S | f ( 0 ) | 2 (2.8) where \\Y(0)l i s the e l e c t r o n d e n s i t y a t th© n u c l e u s . The Hamil-t o n i a n o f the h y p e r f i n e i n t e r a c t i o n f o r a f r e e aton g i v e n i n equ a t i o n 2.6 can a l s o be u s e f u l f o r d i f f e r e n t i a t i n g the v a r i o u s c o n t r i b u t i o n s t o the h y p e r f i n e f i e l d i n many e l e c t r o n systems i f the 3d e l e c t r o n s are assumed t o be l o c a l i z e d a t the atomic s i t e s . For a f e r r o m a g n e t i c metal the h y p e r f i n e f i e l d may be w r i t t e n as H = H + H + H,+ H, (2.9) —n —s — —d — l o c where H_s i s the f i e l d due t o the s e l e c t r o n s , H L i s the f i e l d due t o the o r b i t a l a n g u l a r momentum o f the 3-d e l e c t r o n s , H^ i s the d i p o l a r f i e l d and H_ l o c i s the l o c a l f i e l d a t the n u c l e u s . The 1-s, 2-s, 3-s and 4-s e l e c t r o n s i n t e r a c t w i t h the nucleus through the Fermi c o n t a c t term. I t i s con v e n i e n t t o c o n s i d e r s e p a r a t e l y the core s e l e c t r o n s and the 4-s e l e c t r o n s . (a) In the u n r e s t r i c t e d Hartree-Fock p i c t u r e , the core s e l e c t r o n s ' wavefunctions are d i s t o r t e d by the exchange poten- :. t i a l a s s o c i a t e d w i t h t h e i r i n t e r a c t i o n w i t h the up - s p i n 3-d e l e c t r o n s . T h i s i n t e r a c t i o n i s spin-dependent and tends t o p u l l out the u p - s p i n e l e c t r o n wavefunctions. T h i s l e a v e s a net down-spin s e l e c t r o n d e n s i t y at the nucleus -17 T h i s g i v e s a n e g a t i v e c o n t r i b u t i o n t o t h e h y p e r f i n e f i e l d v i a th e F e r m i c o n t a c t term. I n i r o n t h i s c o n t r i b u t i o n has been e s t i m a t e d by Watson and Freeman(1961) t o be between -300 and -500 k i l o g a u s s . (b) The exchange i n t e r a c t i o n o f t h e 3-d e l e c t r o n s w i t h t h e 4-s e l e c t r o n s i s s i m i l a r t o t h e c o r e 3-d exchange i n t e r -a c t i o n b u t i n t h i s c a s e t h e u p - s p i n w a v e f u n c t i o n s a r e p u l l e d i n . There i s t h e n a n e t u p - s p i n s e l e c t r o n d e n s i t y a t t h e n u c l e u s due t o t h e 4-s e l e c t r o n s w h i c h g i v e s a p o s i t i v e c o n t r i -b u t i o n . Any a d m i x t u r e o f t h e d band e l e c t r o n w a v e f u n c t i o n s and t h e 4-s band a l s o g i v e s a p o s i t i v e c o n t r i b u t i o n . A nderson and C l o g s t o n ( 1 9 6 1 ) , however, have s u g g e s t e d t h a t any c o v a l e n t m i x i n g o f t h e 4-s e l e c t r o n w a v e f u n c t i o n s i n t o t h e u n f i l l e d down-s p i n 3-d 'band would g i v e a n e g a t i v e c o n t r i b u t i o n w h i c h c o u l d p o s s i b l y c a n c e l t h e a d m i x t u r e c o n t r i b u t i o n t o t h e h y p e r f i n e f i e l d . The n e t c o n d u c t i o n e l e c t r o n c o n t r i b u t i o n t o t h e h y p e r -f i n e f i e l d i s u n c e r t a i n b u t i s p r o b a b l y about 100 k i l o g a u s s . The o r b i t a l c o n t r i b u t i o n , H L, a r i s e s f r o m t h e r e s i d u a l o r b i t a l moments a s s o c i a t e d w i t h t h e 3-d e l e c t r o n s . F o r most o f t h e 3-d f e r r o m a g n e t i c m e t a l s t h e a n g u l a r momentum i s a l m o s t c o m p l e t e l y quenched. However, some o r b i t a l a n g u l a r momentum i s unquenched by t h e s p i n - o r b i t i n t e r a c t i o n r e s u l t i n g i n a p o s i -t i v e c o n t r i b u t i o n t o t h e f i e l d a t t h e n u c l e u s g i v e n by H = 2 / U 2 - g ( 2 . 1 0 ) r 4 F o r i r o n t h i s c o n t r i b u t i o n i s about 3x10 g a u s s . I n r a r e e a r t h f e r r o m a g n e t s t h e r e i s v e r y l i t t l e q u e n c h i n g 18 o f t h e o r b i t a l a n g u l a r momentum and t h i s c o n t r i b u t i o n i s dominant. The d i p o l a r f i e l d , H^, r e s u l t s from t h e d i p o l a r i n t e r -a c t i o n o f t h e m a g n e t i c moments a s s o c i a t e d w i t h t h e n u c l e u s and th e e l e c t r o n s . The H a m i l t o n i a n d e s c r i b i n g t h i s i n t e r a c t i o n i s H * £ \" (2.11) r r Here /iH and yu e a r e t h e n u c l e a r and e l e c t r o n i c d i p o l e moments r e s p e c t i v e l y . M a r s h a l l ( 1 9 5 8 ) has e s t i m a t e d t h e d i p o l a r c o n t r i -b u t i o n i n h e x a g o n a l c o b a l t t o be +8 0 k i l o g a u s s . The l o c a l m a g n e t i c f i e l d a t th e n u c l e u s i s g i v e n by TI — Vt — TN1WJ J. M / O \"I T \\ - l o c ^ ' -— ' - ^ j -where H^ i s t h e e x t e r n a l f i e l d , -DM, i s t h e d e m a g n e t i z i n g f i e l d and (4^/3)14 i s t h e u s u a l L o r e n t z f i e l d . A l t h o u g h s m a l l , t h i s c o n t r i b u t i o n i s i m p o r t a n t f o r d e t e r m i n i n g t h e s i g n o f t h e hyper-f i n e f i e l d . T h i s can be d e t e r m i n e d by o b s e r v i n g t h e s h i f t i n reson a n c e f r e q u e n c y when an e x t e r n a l f i e l d i s a p p l i e d . S i n c e i n a f e r r o m a g n e t i c m a t e r i a l t h e e l e c t r o n i c s p i n s a r e o r d e r e d i t i s seen from e q u a t i o n (2.6) t h a t t h e e f f e c t i v e h y p e r f i n e f i e l d has. a w e l l d e f i n e d d i r e c t i o n , t h a t i s , i t i s p r o p o r t i o n a l t o t h e average v a l u e o f t h e e l e c t r o n i c s p i n . T h i s o r d e r i n g o f t h e s p i n s t h e n , p e r m i t s one t o p e r f o r m t h e N.M.R. ex p e r i m e n t w i t h o u t t h e use o f e x t e r n a l l y a p p l i e d f i e l d s as i s n e c e s s a r y i n c o n v e n t i o n a l N.M.R.. The m a g n e t i z a t i o n , M, i s d i r e c t l y p r o p o r t i o n a l t o t h e 19 average v a l u e o f t h e e l e c t r o n i c s p i n s . I t f o l l o w s t h e n t h a t t h e h y p e r f i n e f i e l d i s p r o p o r t i o n a l t o t h e m a g n e t i z a t i o n , i f t h e mechanisms r e s p o n s i b l e f o r H n a r e n o t t e m p e r a t u r e dependent. Thus t h e measurement o f H n as a f u n c t i o n o f t h e t e m p e r a t u r e can g i v e a d i r e c t measurement o f t h e v a r i a t i o n o f t h e magnet-i z a t i o n w i t h t e m p e r a t u r e . H y p e r f i n e f i e l d s have a l s o been o b s e r v e d a t t h e . n u c l e i o f nonmagnetic i o n s i n d i l u t e s o l u t i o n i n f e r r o m a g n e t i c m e t a l s and a t t h e n u c l e i o f nonmagnetic i o n s i n f e r r o m a g n e t i c compounds such as F e 2 B , F e ^ A l and F e ^ S i . Campbell(1969) has a n a l y z e d t h e e x p e r i m e n t a l d a t a f o r h y p e r f i n e f i e l d s on a wide range o f i m p u r i t i e s i n f e r r o m a g n e t i c m e t a l s u s i n g a model based on t h a t o f D a n i e l and F r i e d e l (1963) . I n t h i s model t h e d moment, Mt, , o f t h e h o s t m e t a l i s assumed t o a c t as an e f f e c t i v e f i e l d on a f r e e e l e c t r o n - l i k e c o n d u c t i o n band, g i v i n g a ' u n i f o r m >: c o n d u c t i o n e l e c t r o n p o l a r i z a t i o n p r o p o r t i o n a l t o /-*K e x c e p t a t t h e i m p u r i t y s i t e . T h e r e , l o c a l s q u are w e l l p o t e n t i a l s and Vj. a c t on t h e s p i n * and s p i n * c o n d u c t i o n e l e c t r o n s r e s p e c -t i v e l y . These l o c a l p o t e n t i a l s produce phase s h i f t s i n t h e c o n d u c t i o n e l e c t r o n w a v e f u n c t i o n s . The phase s h i f t s , w h i c h a r e s p i n dependent, and t h e r e s u l t i n g c o n d u c t i o n e l e c t r o n p o l a -r i z a t i o n depends on t h e s t r e n g t h o f t h e i m p u r i t y p o t e n t i a l . F o r s-p i m p u r i t i e s i n i r o n t h e model p r e d i c t s a c o n d u c t i o n e l e c t r o n p o l a r i z a t i o n a t t h e nonmagnetic i m p u r i t y s i t e w h i c h depends on t h e i m p u r i t y c h a r g e , Z^, t o be s c r e e n e d . On t h e b a s i s o f t h i s model Campbell p r e d i c t s t h a t f o r i m p u r i t i e s w i t h Z^ l e s s t h a n about 2, t h e c o n d u c t i o n e l e c t r o n p o l a r i z a t i o n 20 r e s u l t s i n a n e g a t i v e h y p e r f i n e f i e l d . F o r i m p u r i t i e s w i t h g r e a t e r t h a n 2 a p o s i t i v e h y p e r f i n e f i e l d i s p r e d i c t e d . T h i s b e h a v i o u r has been o b s e r v e d f b r t h e s-p s e r i e s Ag t o Xe as i m p u r i t i e s i n Fe ( C a m p b e l l , 1 9 6 9 , f i g 5 ) . S t u d i e s by B u d n i c k and S k a l s k i ( 1 9 6 7 ) o f t h e A l and S i h y p e r f i n e f i e l d s i n F e 3 A l and F e ^ S i s u g g e s t t h a t t h e s e t r a n s -f e r r e d h y p e r f i n e f i e l d s a r e due p r i m a r i l y t o t h e F e r m i c o n t a c t i n t e r a c t i o n o f t h e s e l e c t r o n s a t t h e nonmagnetic i o n s i t e , w h i c h have been p o l a r i z e d by t h e l o c a l moments o f t h e m a g n e t i c i o n s . The problem o f t r a n s f e r r e d h y p e r f i n e f i e l d s i n m a g n e t i c compounds has been t r e a t e d i n some d e t a i l by Watson and Freeman (1967). A l t h o u g h t h e y d e a l w i t h n o n - m e t a l l i c systems t h e y s u g g e s t t h a t t h e r e s u l t s o f t h e i r i n v e s t i g a t i o n s may be a p p l i -c a b l e t o m e t a l l i c systems. They f i n d t h a t u n p a i r i n g o f t h e c l o s e d s s h e l l s i n t h e nonmagnetic i o n s i t e ; e.g. F i n MnF 2 , o c c u r s when t h e 3-d w a v e f u n c t i o n s o f t h e m a g n e t i c i o n and t h e s w a v e f u n c t i o n s o f t h e nonmagnetic i o n a r e o r t h o g o n a l i z e d . Any c o v a l e n t a d m i x t u r e o f t h e 3-d w a v e f u n c t i o n s w i t h t h e non-m a g n e t i c i o n ' s w a v e f u n c t i o n s conveys a s p i n d e n s i t y o n t o t h e nonmagnetic i o n s i t e w h i c h i s p a r a l l e l t o t h a t o f t h e l o c a l moment. The s p i n d e n s i t y t h u s conveyed c a n l e a d t o some v . .-u n p a i r i n g o f t h e c l o s e d s h e l l s e l e c t r o n s v i a t h e exchange i n t e r a c t i o n . Any u n p a i r i n g o f t h e c l o s e d s h e l l s e l e c t r o n s w i l l r e s u l t i n a h y p e r f i n e f i e l d a t t h e n u c l e u s o f t h e non-m a g n e t i c i o n . However, t h e r e s u l t a n t f i e l d s due t o t h e s e e f f e c t s a r e d i f f i c u l t t o e s t i m a t e . 21 ( i v ) R.F. Enhancement i n Ferromagnets I n f e r r o m a g n e t i c N.M.R. t h e n u c l e a r r e s o n a n c e i s d r i v e n i n d i r e c t l y v i a t h e n u c l e a r - e l e c t r o n i c h y p e r f i n e c o u p l i n g . T h i s i n d i r e c t c o u p l i n g produces an enhanced r . f . f i e l d , H ^, at t h e n u c l e a r s i t e w h i c h i s much l a r g e r t h a n t h e a p p l i e d r . f . f i e l d , H^. One can show t h a t t h e enhancement f a c t o r , H n ^ / H 2 . f i s d i r e c t l y p r o p o r t i o n a l t o t h e a n g l e t h r o u g h w h i c h i s t u r n e d by t h e a p p l i e d r . f . f i e l d . S i n c e t h e h y p e r f i n e f i e l d i s d i r e c t l y p r o p o r t i o n a l t o , t h e enhancement i s s t r o n g l y i n f l u e n c e d by t h e d e t a i l e d p r o p e r t i e s o f t h e exchange c o u p l e d e l e c t r o n s p i n system. I n p a r t ( i ) o f t h i s c h a p t e r i t was p o i n t e d out t h a t t h e o r d e r i n g o f t h e s p i n s g i v e s r i s e t o a spon-t.aneoii« magnetisation, Tn a b u l k sample i t i s found t h a t t h e r e a r e domains o f u n i f o r m m a g n e t i z a t i o n w h i c h a r r a n g e t h e m s e l v e s so as t o m i n i m i z e t h e t o t a l f r e e energy o f t h e b u l k sample. Between domains o f o p p o s i t e m a g n e t i z a t i o n t h e r e e x i s t domain w a l l s t h r o u g h w h i c h t h e o r i e n t a t i o n o f t h e e l e c t r o n i c m a g n e t i c moments changes p r o g r e s s i v e l y t h r o u g h 180 d e g r e e s . I n m u l t i -domain p a r t i c l e s t h e r e a r e two s o u r c e s o f enhancement, c o h e r e n t domain r o t a t i o n and domain w a l l movement. We f i r s t c o n s i d e r t h e enhancement due t o c o h e r e n t domain r o t a t i o n . The r o t a t i o n due t o an a p p l i e d r . f . f i e l d , H^, i s l i m i t e d by an i n c r e a s e i n t h e a n i s o t r o p y e n ergy. T h i s energy a c t s i n such a way t h a t t h e m a g n e t i z a t i o n t e n d s t o be d i r e c t e d a l o n g c e r t a i n d e f i n i t e c r y s t a l l o g r a p h i c d i r e c t i o n s , w h i c h a c c o r -d i n g l y a r e c a l l e d d i r e c t i o n s o f easy m a g n e t i z a t i o n . T h i s e f f e c t 22 may be th o u g h t o f as a r i s i n g from an a n i s o t r o p y f i e l d , H , a w h i c h l i e s i n t h e d i r e c t i o n o f easy m a g n e t i z a t i o n . C o n s i d e r a s i n g l e domain w h i c h has an e l e c t r o n i c m a g n e t i -z a t i o n , M, a l i g n e d a l o n g t h e a n i s o t r o p y f i e l d . A p p l i c a t i o n o f a weak t r a n s v e r s e f i e l d , H^, produces an a n g u l a r d i s p l a c e -ment o f t h e h y p e r f i n e f i e l d g i v e n by H a H a H,«H. j- . .a The r e s u l t i n g t r a n s v e r s e h y p e r f i n e f i e l d , H ^ f a n ^ t n e t o t a l t r a n s v e r s e d r i v i n g f i e l d , H t^, a r e g i v e n by H l H , = H s i n e - H ~ (2.14) n l n n H a H t l= H x+ H n l= H 1 ( l +a ) (2.15) T y p i c a l l y f o r a s p h e r i c a l sample o f n i c k e l H = 135 Oe. a H - 75 koe. n f\\ - 600 The enhancement o f t h e a p p l i e d r . f . f i e l d due t o domain w a l l m o t i o n w i l l now be c o n s i d e r e d . F o l l o w i n g K i t t e l and G a i t (1956) , t h e e q u a t i o n o f m o t i o n f o r a domain w a l l s u b j e c t t o an r . f . f i e l d , H^, i s f o r s m a l l d i s p l a c e m e n t s , x, ( i . e . d i s p l a c e -ments s m a l l compared t o t h e w a l l t h i c k n e s s ) , w r i t t e n as f o l l o w s 2 , „dx , d x „ (2.16) ctx + /3-rr- + in - r - — = 2M H. 1 ' d t ^ t 2 s 1 23 where ex. i s a c o n s t a n t d e s c r i b i n g t h e s t i f n e s s o f t h e w a l l , (i i s a damping c o n s t a n t and m i s an e f f e c t i v e mass o f t h e w domain w a l l . M i s t h e s a t u r a t i o n m a g n e t i z a t i o n . F o r a p e r i o d i c d r i v i n g f i e l d o f f r e q u e n c y u>m , t h e maximum d i s p l a c e m e n t i s g i v e n by 2 M s H l X ° &mW[.(A2- u ) m 2 ) 2 + < 0 / V 2 4 . V / 2 ( 2 ' 1 7 ) i where A = C^iJ2 i s t h e n a t u r a l f r e q u e n c y o f t h e domain w a l l . As a r e s u l t o f t h e d i s p l a c e m e n t x, t h e e l e c t r o n i c s p i n s w i l l r o t a t e t h r o u g h an a n g l e W , and hence t h e r e s u l t i n g t r a n s v e r s e h y p e r f i n e f i e l d a t t h e n u c l e a r s i t e w i l l , f o r s m a l l V , be g i v e n by H,_.,- YH,.=x(^)H._ (2.18) f o r a 180 degree w a l l dV „ 1 . ,x{ _ _ _ s e c h ( r ) From e q u a t i o n s (2.17) and (2.18) t h e enhancement f a c t o r i s found t o be „ M H sech(£) (2.19) Zmr\\(A2+0>Z)2+ (0/m ) 2 c J m 2 ] 1 / 2 U n f o r t u n a t e l y t h i s e x p r e s s i o n does n o t l e n d i t s e l f t o a s i m p l e e s t i m a t e o f t h e enhancement f a c t o r as t h e r e q u i r e d p a r a m e t e r s a r e n o t always r e a d i l y a v a i l a b l e . F o r t h e purpose o f o b t a i n i n g a s i m p l e e s t i m a t e o f t h e domain enhancement f a c t o r i t i s u s e f u l t o c o n s i d e r t h e case oa s p h e r i c a l p a r t i c l e o f d i a m e t e r , d, s p l i t by a s i n g l e domain 24 w a l l i n w h i c h t h e m a g n e t i z a t i o n t u r n s t h r o u g h 180 degrees i n a d i s t a n c e h as i n d i c a t e d i n t h e f o l l o w i n g d i a g r a m . - = (2.22) 21TM d s The component o f t h e i n t e r n a l f i e l d p e r p e n d i c u l a r t o t h e s t a t i c 27 f i e l d i s H ,= H Tfx/s , where S i s t h e domain w a l l t h i c k n e s s , n l n Thus 9 0 H kT s Assuming a L o r e n t z i a n c o r r e l a t i o n s p ectrum P(W) = 2 r< 0 9 ^ ( 1 + c / r T ) where i s t h e c o r r e l a t i o n t i m e , t h e r e l a x a t i o n r a t e caused by t h e s e f l u c t u a t i o n s i s , a c c o r d i n g t o Bloembergen e t . a l . ( 1 9 4 8 ) g i v e n by 1 _ ( tfrtHii) 2 2 kT r c ,„ T l \" * * d 3M 1 + A 2 s Weger found t h a t t h i s mechanism gave r e s u l t s i n r e a s o n a b l e a c c o r d w i t h t h e o b s e r v e d v a l u e s o f T^ f o r F e , N i and Co. The r e l a x a t i o n t i m e a t room t e m p e r a t u r e i s t y p i c a l l y a few hundred m i c r o s e c o n d s . W i n t e r ( 1 9 6 1 ) has c o n s i d e r e d t h i s model i n d e t a i l f o r t h e c a s e o f a u n i a x i a l a n i s o t r o p y and found t h a t f o r a 180 degree w a l l t h e r e l a x a t i o n r a t e a t a t e m p e r a t u r e T i s g i v e n by =• = sech ( r) — (•=•) t a n (—^—— T ) (2.25) where J and K a r e t h e exchange and c r y s t a l l i n e a n i s t r o p y c o n -s t a n t s r e s p e c t i v e l y . P i s a damping c o n s t a n t a s s o c i a t e d w i t h domain w a l l m o t i o n . S p i n - s p i n r e l a x a t i o n t i m e s t u d i e s i n t h e i r o n group m e t a l s have shown t h a t t h e r e i s an u n u s u a l l y s t r o n g c o u p l i n g between 28 t h e n u c l e a r s p i n s (see e.g. Weger e t . a l . , 1 9 6 1 ) . I t has been p o i n t e d o u t by Suhl(1958) and Nakamura(1958) t h a t such a s t r o n g c o u p l i n g a r i s e s because t h e n u c l e i t h r o u g h t h e i r h y p e r -f i n e i n t e r a c t i o n w i l l v i r t u a l l y e x c i t e e l e c t r o n i c s p i n waves. These s p i n waves may be r e - a b s o r b e d by o t h e r n u c l e i r e s u l t i n g i n a s t a t i c c o u p l i n g between t h e n u c l e a r s p i n s . S t e a r n s ( 1 9 6 9 ) has e s t i m a t e d t h a t i n i r o n t h i s e f f e c t g i v e s a c o n t r i b u t i o n o f 2.5 sec t o t h e r a t e o f t r a n s v e r s e r e l a x a t i o n , l / T ^ • The s p i n - l a t t i c e i n t e r a c t i o n a l s o c o n t r i b u t e s t o T 2 (see e q u a t i o n (1.17)) and can produce n o n - e x p o n e n t i a l r e l a x a t i o n w i t h q u a l i t a t i v e l y the same c h a r a c t e r as T,. 29 CHAPTER I I I A p p a r a t u s and E x p e r i m e n t a l P r o c e d u r e A p p a r a t u s E s s e n t i a l l y t h e s p e c t r o m e t e r was a broadband u n i t c a p a b l e o f d e l e v e r i n g r . f . p u l s e s o v e r t h e f r e q u e n c y range 10-200 MHz. The r e c e i v i n g system was c h a r a c t e r i z e d by good r e c o v e r y c h a r a c t e r i s t i c s and h i g h s e n s i t i v i t y , f e a t u r e s w h i c h a r e n e c e s s a r y f o r t h e o b s e r v a t i o n o f the weak s i g n a l s t h a t a r i s e from t h e b r o a d l i n e s e n c o u n t e r e d i n f e r r o m a g n e t i c m a t e r i a l s . I t c o u l d be used i n e i t h e r a swept o r f i x e d f r e q u e n c y mode. The swept f r e q u e n c y mode was used i n t h e s e a r c h f o r z e r o f i e l d r e s o n a n c e s . Measurements o f r e l a x a t i o n ' t i m e s and enhancement f a c t o r s were p e r f o r m e d a t f i x e d f r e q u e n c i e s . A b l o c k d i a g r a m of t h e s p e c t r o m e t e r i s shown i n f i g u r e 3-1. ( i ) P u l s e d O s c i l l a t o r s Two p u l s e d o s c i l l a t o r s were employed; one was used p r i m a r i l y f o r a p p l i c a t i o n s r e q u i r i n g a r e l a t i v e l y h i g h power l e v e l , about 300 v o l t s peak t o peak i n t o 100 ohms, and t h e o t h e r was a low power p u l s e d o s c i l l a t o r w h i c h c o u l d be o p e r a t e d w i t h about 10 v o l t s a c r o s s i t s t a n k c i r c u i t . Frequency c o u l d be swept i n b o t h o s c i l l a t o r s by means o f an e x t e r n a l motor d r i v e . The h i g h power p u l s e d o s c i l l a t o r was an A r e n b e r g model PG-650-c w i t h t h e m o d i f i c a t i o n s f o r e x t r a f a s t , .2 m i c r o s e c o n d s , r i s e and f a l l t i m e s . The o s c i l l a t o r c o n s i s t s o f a 6907 tube w h i c h i s c r o s s - c o n n e c t e d t o form a p u s h - p u l l C o l p i t t s o s c i l -P u l s e d O s c i l l a t o r Tek. 7 T /-•v. 163 Pu] be GeTielaUriis rr Timing U n i t Start) Input Stop 7 Input Sample C o i l Assembly Time I n t e r v a l Unit Preamp. f Scope D i g i t a l Recorder Wide-band A m p l i f i e r Boxcar I n t e g r a t o r S t r i p Chart P o r n r r l p i F i g . 3-1 Block Diagram o f P u l s e d Spectrometer 31 l a t o r . The p l a t e c u r r e n t i n t h e tube i s n o r m a l l y c u t - o f f and i n o r d e r t o cause o s c i l l a t i o n s a l a r g e p o s i t i v e p u l s e i s ap a p p l i e d t o t h e s c r e e n and g r i d o f t h e t u b e . T h i s p u l s e i s s u p p l i e d by a p u l s e a m p l i f i c a t i o n and s h a p i n g network t h a t i s d r i v e n by an e x t e r n a l 10 v o l t g a t e . A f r e q u e n c y range o f 2 MHz t o 130 MHz i s o b t a i n e d t h r o u g h t h e use o f a s e t o f i n t e r -c h a n g eable t a n k c o i l s . The r . f . o u t p u t i s t a k e n from t h e se c o n -d a r y w i n d i n g s o f t h e s e c o i l s . A more d e t a i l e d d e s c r i p t i o n o f t h i s o s c i l l a t o r can be found e l s e w h e r e , K o s t e r ( 1 9 6 8 ) . As t h e a p p l i e d r . f . f i e l d i s enhanced, a r e l a t i v e l y low r . f . f i e l d i s r e q u i r e d when s e a r c h i n g f o r z e r o f i e l d r e s o n a n c e s . The A r e n b e r g o s c i l l a t o r d i d not f u n c t i o n w e l l a t low power l e v e l s . F o r t h i s r e a s o n t h e low power p u l s e d o s c i l l a t o r was c o n s t r u c t e d . A s c h e m a t i c d i a g r a m o f t h i s o s c i l l a t o r i s shown i n f i g u r e 3-2. The o s c i l l a t o r c o n s i s t s o f a 6939 tube w h i c h i s c r o s s - c o n n e c t e d t o form a p u s h - p u l l C o l p i t t s o s c i l l a t o r . A l t h o u g h t h e anode v o l t a g e i s c o n t i n u o u s l y s u p p l i e d , t h e p l a t e c u r r e n t i s n o r m a l l y c u t o f f because t h e s c r e e n and g r i d v o l t a g e s a r e n e g a t i v e l y b i a s e d . I n o r d e r t o cause o s c i l l a t i o n s a l a r g e p o s i t i v e p u l s e o f about 150 v o l t s i s a p p l i e d t o t h e s c r e e n and g r i d l e a k r e s i s t o r s . T h i s p u l s e was produce d by t h e p u l s e f o r m i n g c i r c u i t shown i n f i g u r e 3-3. T h i s c i r c u i t r e q u i r e s about 10 v o l t s i n p u t f o r f u l l o u t p u t . The f r e q u e n c y o f t h e p u l s e d o s c i l l a t o r c o u l d be changed o v e r t h e range 15 - 220 MHz w i t h t h e use o f i n t e r c h a n g e a b l e t a n k c o i l s . Fig...3-2 Low Power Pu l s e d O s c i l l a t o r F i g . 3-3 P u l s e Forming C i r c u i t 34 ( i i ) Dewar System The cryostat consisted of an exposed t i p helium dewar and a s u i t a b l e nitrogen dewar constructed by J . Lees, glass, blower. The t i p of the helium dewar was l e f t unsilvered to allow penetration of the r . f . f i e l d . In the experiments the dewar t i p holding the sample was placed inside the sample c o i l . Cooling of the exposed t i p was achieved by allowing l i q u i d nitrogen to d r i p over i t . ( i i i ) Sample C o i l The search for zero f i e l d N.M.R. l i n e s was made with the sample situated d i r e c t l y i n the tank c o i l of the o s c i l -l a t o r- The s i T P a 1 w?.? takep c i t • H V O - O I I T H +-.hf cpnondsrv ^•P th45* tank c o i l . For fixed frequency work an external c o i l system was employed. In the i d e a l receiving system a l l the noise originates as thermal noise i n the sample c o i l . I f t h i s i s the case then the signal-to-noise r a t i o depends on the c o i l parameters as follows S/N oc KV*Q2 where K i s the f i l l i n g f actor, V i s the volume of the c o i l and Q i s the q u a l i t y factor of the c o i l . For fa s t recovery of the receiver following the r . f . pulse i t i s necessary that the r e s u l t i n g transient i n sample c o i l c i r c u i t be damped out quickly ( i . e . i n a time much less than the recovery time of the amplifiers i n the receiving c i r c u i t ) . This condition requires the sample c o i l c i r c u i t to have a low Q during and j u s t after the a p p l i c a t i o n of the pulse. Thus 35 f o r good s i g n a l t o n o i s e r a t i o s and f a s t r e c o v e r y o f t h e r e c e i v e r i t i s n e c e s s a r y t o have a low Q c i r c u i t d u r i n g and a h i g h Q c i r c u i t a f t e r t h e p u l s e . The low Q-high Q r e q u i r e -ments f o r t h e sample c o i l c i r c u i t a r e met by t h e c i r c u i t shown i n f i g u r e 3-4. T h i s c i r c u i t i s p a s s i v e l y s w i t c h e d between a h i g h Q and a low Q c o n f i g u r a t i o n . When t h e r . f . p u l s e i s a p p l i e d t h e d i o d e s conduct h e a v i l y and t h e d i o d e g a t e behaves l i k e a s h o r t c i r c u i t . The t u n e d c i r c u i t i s t h e n e f f e c t i v e l y s h u n t e d by t h e 50 ohm r e s i s t o r . T h i s e f f e c t s a low Q c i r c u i t and p r o v i d e s p r o p e r m a t c h i n g t o t h e p u l s e d o s c i l l a t o r . When t h e t r a n s i e n t f o l l o w i n g t h e p u l s e has decayed t o l e s s t h a n about 0.5 v o l t s , t h e d i o d e s a r e no l o n g e r i n t h e c o n d u c t i n g s t a t e and t h e g a t e behaves l i k e an open c i r c u i t . T h i s e f f e c t s -a - r e l a t i v e l y h i g h Q c i r c u i t w h i c h i s used t o o b s e r v e t h e n u c l e a r s i g n a l . The n u c l e a r s i g n a l was t a p p e d f r o m t h e tu n e d c i r c u i t t h r o u g h a 12 p f c a p a c i t o r . T h i s v a l u e was a r r i v e d a t by a t r i a l and e r r o r method w h i c h was used t o maximize t h e s i g n a l t o n o i s e r a t i o . The e n t i r e c o i l assembly was mounted i n s i d e a m i n i - b o x f o r s h i e l d i n g , a h o l e b e i n g p r o v i d e d t h r o u g h w h i c h t h e t i p o f t h e h e l i u m dewar p e n e t r a t e d . ( i v ) The R e c e i v i n g System The r e c e i v i n g system v a r i e d a c c o r d i n g t o t h e p a r t i c u l a r a p p l i c a t i o n . F o r work a t f i x e d f r e q u e n c i e s t h e system c o n s i s t e d o f a narrow-banded p r e a m p l i f i e r f o l l o w e d by a wideband a m p l i -f i e r and d e t e c t o r . F o r s t u d i e s a t f r e q u e n c i e s l e s s t h a n 40 MHz an A r e n b e r g model W-600D wideband a m p l i f i e r was used. R.F. Input from Pulse i Osci[(at or F O H 6fe6 50 ( 12 pf Output -o t o Preamp. 7-S O p-f. CA) O N F i g . 3-4 Sample C e i l C i r c u i t 37 A custom b u i l t a m p l i f i e r was used f o r f r e q u e n c i e s i n t h e range 40 MHz t o 110 MHz. The p r e a m p l i f i e r s e r v e d t o s u p p l y enough g a i n t o o v e r i d e t h e n o i s e o f t h e f o l l o w i n g wideband a m p l i f i e r and t o narrow t h e b a ndwidth o f t h e r e c e i v e r , t h u s i m p r o v i n g t h e a t t a i n a b l e s i g n a l t o n o i s e r a t i o . The c i r c u i t shown i n f i g u r e 3-5, c o n s i s t s o f two pentode c o n n e c t e d 77 88 t u b e s i n a c a s c a d e d a m p l i f i e r c o n f i g u r a t i o n f o l l o w e d by a 6CW4 ca t h o d e f o l l o w e r o u t p u t s t a g e . The bandpass c h a r a c t e r i s t i c s o f each s t a g e c o u l d be changed i n d i v i d u a l l y t o o b t a i n t h e d e s i r e d o v e r a l l bandpass c h a r a c t e r i s t i c s . The maximum b a n d w i d t h employed w i t h t h e p r e a m p l i f i e r was about 6 MHz. The p r e a m p l i f i e r has a g a i n o f about 30 db, and has l o w - n o i s e and f a s t r e c o v e r y ch c h a r a c t e r i s t i c s . I t p r o v e d t o be u s e f u l o v e r t h e f r e q u e n c y range 10 MHz t o 100 MHz. The custom b u i l t a m p l i f i e r i s a low n o i s e f i g u r e (6 d b ) , f a s t r e c o v e r y u n i t w h i c h was c o n s t r u c t e d c o m m e r c i a l l y t o our s p e c i f i c a t i o n s . I t has a f r e q u e n c y r e s p o n s e w h i c h i s f l a t t o w i t h i n 1.0 db from 40 MHz t o 110 MHz and a g a i n w h i c h i s v a r i a b l e between 60 db and 80 db. The r e c o v e r y t i m e i s d e f i n e d as t h e t i m e e l a p s e d b e f o r e t h e a m p l i f i e r n o i s e i s v i s i -v i s i b l e a f t e r t h e a m p l i f i e r has been s u b j e c t e d t o an . o v e r l o a d . W i t h t h e a m p l i f i e r i n t h e r . f . o u t p u t mode t h e r e c o v e r y t i m e was about 2 m i c r o s e c o n d s , w h i l e i n t h e d e t e c t e d o u t p u t mode i t was about 4 m i c r o s e c o n d s . I n p r a c t i s e t h e i n f l u e n c e o f th e r e c o v e r y c h a r a c t e r i s t i c s o f t h e a m p l i f i e r can be m i n i m i z e d by o b s e r v i n g t h e echo, w h i c h can be made t o appear w e l l a f t e r F i g . 3-5 P r e a m p l i f i e r 38 t h e r e c e i v e r has r e c o v e r e d from t h e o v e r l o a d . The c i r c u i t d i agrams o f t h e wideband a m p l i f i e r a r e shown i n f i g u r e s 3-6 and 3-7. The f i x e d f r e q u e n c y r e c e i v i n g systems j u s t d e s c r i b e d a l l o w e d a 2 m i c r o v o l t peak-to-peak i n p u t s i g n a l t o be d e t e c t e d w i t h a one-to-one s i g n a l t o n o i s e r a t i o . I n t h e f r e q u e n c y swept mode o f o p e r a t i o n wide-band r e c e i v i n g systems were employed. I n t h e r a n g e 10 MHz t o 40 MHz t h e r e c e i v e r c o n s i s t e d on t h e p r e v i o u s l y d e s c r i b e d p r e a m p l i f i e r f o l l o w e d by t h e A r e n b e r g wideband a m p l i f i e r . The p r e a m p l i f i e r was s e t t o have a bandpass of about 6 MHz and i t s c e n t e r f r e q u e n c y a l t e r e d as t h e s p e c t r o m e t e r was swept t h r o u g h t h e 10 MHz t o 40 MHz range. F o r sweeping o v e r t h e range 4 0 MHz t o 110 MHz t h e a f o r e mentioned custom b u i l t w i d e -band a m p l i f i e r was employed as a p r e a m p l i f i e r , and t h i s was f o l l o w e d by a H e w l e t t - P a c k a r d model 461A wideband a m p l i f i e r , t h e o u t p u t o f w h i c h was d e t e c t e d . These r e c e i v e r s a l l o w e d a 4 m i c r o v o l t peak-to-peak i n p u t s i g n a l t o be d e t e c t e d w i t h a one t o one s i g n a l t o n o i s e r a t i o . F o r a l l t h e above c a s e s t h e d e t e c t e d o u t p u t was f e d i n t o a P r i n c e t o n A p p l i e d R e s e a r c h Corp. model 160 b o x c a r i n t e g r a t o r i n o r d e r t o improve t h e s i g n a l t o n o i s e r a t i o . The o u t p u t o f t h e b o x c a r i n t e g r a t o r was m o n i t o r e d w i t h a s t r i p - c h a r t r e c o r d e r . (v) T i m i n g A p p a r a t u s A s u i t a b l e c o m b i n a t i o n o f T e k t r o n i x p u l s e and waveform 100 • A M / ^ — > + 1 5 0 V Capac i to rs i n p f . T = 1000 v F i g . 3-6 Cascode Input s tage and f i r s t Gain C o n t r o l l e d s tage F i g . 3-7 Second gain C o n t r o l l e d , Output and Detector Stages 41 g e n e r a t o r s was used t o s u p p l y t h e sequence o f p u l s e s used t o g a t e t h e p u l s e d o s c i l l a t o r s and t h e b o x c a r i n t e g r a t o r . F o r th e measurements a 180°-90°-180° p u l s e sequence was u s e d , o t h e r w i s e a 90°-180° p u l s e sequence was use d . I n b o t h c a s e s t h e o v e r a l l r e p e t i t i o n r a t e was c o n t r o l l e d by a f r e e r u n n i n g T e k t r o n i x t y p e 162 waveform g e n e r a t o r . F o r t h e T^ measurements t h i s g e n e r a t o r s u p p l i e d a sawt o o t h v o l t a g e w h i c h t r i g g e r e d two t y p e 163 p u l s e r g e n e r a t o r s . One s u p p l i e d t h e 180° p u l s e and t h e o t h e r s u p p l i e d a d e l a y e d p u l s e w h i c h t r i g g e r e d a p a i r o f 163 p u l s e g e n e r a t o r s used t o s u p p l y t h e p u l s e s f o r t h e 90°-180° sequence. I n p r a c t i c e t h e t i m e between t h e f i r s t and second p u l s e s was swept l i n e a r l y w i t h t i m e and t h e ti m e between t h e second and t h i r d k e p t f i x e d . The t i m e between t h e f i r s t and second p u l s e s was r e c o r d e d by a H e w l e t t - P a c k a r d model 5245C e l e c t r o n i c c o u n t e r . F o r t h e non-T^ measurements t h e f r e e r u n n i n g waveform g e n e r a t o r s u p p l i e d a g a t e w h i c h was used t o t r i g g e r a n o t h e r 162 waveform g e n e r a t o r w h i c h i n t u r n t r i g g e r e d t h e two t y p e 163 p u l s e g e n e r a t o r s used t o p r o v i d e t h e 90°-180° sequence. More d e t a i l s about t h i s system can be found e l s e w h e r e ( K o s t e r , 1 9 6 8 ) . E x p e r i m e n t a l Technique ( i ) S e a r c h f o r Zero F i e l d N.M.R. L i n e s The s e a r c h f o r z e r o f i e l d N.M.R. l i n e s was made u s i n g t h e v a r i a b l e f r e q u e n c y p u l s e d N.M.R. s p e c t r o m e t e r w h i c h has been d e s c r i b e d i n th e f i r s t p a r t o f t h i s c h a p t e r . The specimen, 42 s i t u a t e d i n t h e t r a n s m i t t e r c o i l , was c o o l e d i n a b a t h o f l i q u i d h e l i u m and t h e s p e c t r o m e t e r swept t h r o u g h i t s e n t i r e range. On o b s e r v i n g a s p i n echo, t h e res o n a n c e f r e q u e n c y c o u l d be d e t e r m i n e d by b e a t i n g t h e N.M.R, s i g n a l w i t h t h e s i g n a l from an r . f . s i g n a l g e n e r a t o r t h e o p e r a t i n g f r e q u e n c y of w h i c h c o u l d by a c c u r a t e l y m o n i t o r e d . I n c a s e s where i t was n o t f e a s i b l e t o b e a t d i r e c t l y w i t h t h e N.M.R. s i g n a l i t was assumed t h a t t h e s i g n a l f r e q u e n c y was t h e same as t h e o p e r a t i n g f r e q u e n c y o f t h e p u l s e d s p e c t r o m e t e r . Dean and Urwin (1970) have shown t h a t t h i s i s a r e a s o n a b l e a s s u m p t i o n under t h e f o l l o w i n g c o n d i t i o n s , i f t h e maximum v a l u e o f i s u / y t h e n t h e shape f u n c t i o n c h a r a c t e r i z i n g t h e r e s o n a n c e l i n e - S(OJ_,+ AU>1. s h o u l d not change s i g n i f i c a n t l v i n t h e i n t e r v a l For measurements a t h i g h e r t e m p e r a t u r e s t h e sample was immersed i n b a t h s o f l i q u i d n i t r o g e n , l i q u i d methane, o r c o o l e d by a st r e a m o f c o l d n i t r o g e n gas. I n t h e l a t t e r c a s e the sample t e m p e r a t u r e was m o n i t o r e d w i t h a c a l i b r a t e d t h e r -m i s t o r thermometer. ( i i ) Measurement o f t h e Enhancement F a c t o r Measurement o f t h e enhancement f a c t o r r\\ was accom-p l i s h e d by o b s e r v i n g t h e a m p l i t u d e o f t h e f r e e i n d u c t i o n decay or s p i n echo as a f u n c t i o n o f t h e a p p l i e d r . f . f i e l d . I n a s i m p l i f i e d p i c t u r e t h e c o n d i t i o n f o r a viz p u l s e i s as f o l l o w s 1= ^Vw ( 3 - 1 } * where H = 1)H , i s t h e e f f e c t i v e r . f . f i e l d seen by t h e n u c l e u s and t i s t h e w i d t h o f t h e p u l s e . The enhancement w -f a c t o r i s t h e n g i v e n by 1 = V I T H ^ ( 3 ' 2 ) W X where v= (;VHN) /2TT i s t h e r e s o n a n c e f r e q u e n c y . The s i z e o f t h e r . f . f i e l d H was e s t i m a t e d by m e a s u r i n g t h e v o l t a g e i n d u c e d a c r o s s a s i n g l e t u r n p i c k - u p c o i l w h i c h was s i t u a t e d around t h e sample. The v o l t a g e i n d u c e d a c r o s s a c o i l o f c r o s s s e c t i o n a l a r e a A a t a f r e q u e n c y u) i s g i v e n by d t s i n c e . 9 = 2H A e 1 W t V = 2H A e l W t t h e n H = i j L (3.. 3) x 2Au> ( i i i ) Measurement o f R e l a x a t i o n Times (a) L o n g i t u d i n a l R e l a x a t i o n Time The l o n g i t u d i n a l 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^, was d e t e r m i n e d by c h a n g i n g t h e z component o f t h e n u c l e a r m a g n e t i -z a t i o n , M , from i t s e q u i l i b r i u m v a l u e , M , t o s a y , M ,, by Z \" ZO Z J_ a p p l y i n g an r . f . p u l s e a t t h e r e s o n a n t f r e q u e n c y and m e a s u r i n g M a t a l a t e r t i m e t . T h i s was a c c o m p l i s h e d by m o n i t o r i n g t h e 44 amplitude of the echo following a two pulse sequence that was applied at a time t aft e r the i n i t i a l saturating pulse as indi-cated i n the following diagram. t T - I The components of the magnetization i n the x,y plane following the two pulse sequence induce a voltage i n the pick up c o i l which i s proportional to the precessing magnetization .in the. x.y plane. The amplitude of the echo i s therefore d i r e c t l y proportional to the value of M j u s t before the two pulse sequence i s applied. For an exponential relaxation the echo amplitude i s propor-t i o n a l to -t/T, M (t) = M - (M - M , ) e ' 1 z zo zo z l ( 3 . 4 ) For the case of non-exponential relaxation often encountered i n ferromagnets an instantaneous r e l a x a t i o n rate, 1/T^, can be defined according to the following d e f i n i t i o n 1 T. aM z(t) / ( M z ( t ) - Mz (<*>)) ( 3 . 5 ) 45 (b) T r a n s v e r s e R e l a x a t i o n Time The t r a n s v e r s e r e l a x a t i o n t i m e , T 9, was d e t e r m i n e d by m o n i t o r i n g t h e a m p l i t u d e o f t h e s p i n echo as a f u n c t i o n o f t h e s p a c i n g between t h e 90° and 180° p u l s e s . I f t h e s p a c i n g between t h e s e p u l s e s i s t t h e n t h e echo a m p l i t u d e v a r i e s , f o r e x p o n e n t i a l r e l a x a t i o n , a c c o r d i n g t o F o r a n o n - e x p o n e n t i a l decay one can d e f i n e an i n s t a n t a n e o u s r e l a x a t i o n r a t e by t h e e q u a t i o n M(t) = M(0) e - 2 t / T 2 ( 3 . 6 ) 1 3M(t) / ( 2 M ( t ) ) ( 3 . 7 ) 46 CHAPTER IV NICKEL I t has been p o i n t e d o u t by S t e a r n s ( 1 9 6 7 ) and by S t e a r n s and Overhauser (1968), t h a t a s t u d y o f t h e v a r i a t i o n w i t h r . f . f i e l d s t r e n g t h and p u l s e l e n g t h o f t h e f r e e i n d u c t i o n decay (FID) s i g n a l can y i e l d i n f o r m a t i o n about t h e s t r u c t u r e and m o t i o n o f domain w a l l s . S t e a r n s s t u d i e d t h e FID s i g n a l i n i r o n ; we have p e r f o r m e d s i m i l a r e x p e r i m e n t s i n n i c k e l . The specimen s t u d i e d was an unannealed powder sample o f n i c k e l m e t a l o f p u r i t y 99.995%. The powder used i n t h e e x p e r i m e n t s ~ — „ ~ ,3 -u u — — i - — A n — — — - \" V -' - - ' . . . . i n p a r a f f i n wax t o s u p p r e s s m a g n e t o s t r i c t i v e l y e x c i t e d a c o u s t i c r e s o n a n c e s ( R u b e n s t e i n and S t a u s s , 1 9 6 8 ) . (a) E x p e r i m e n t a l R e s u l t s The e x p e r i m e n t a l d a t a was o b t a i n e d by s e t t i n g t h e s p e c t r o -meter t o t h e r e s o n a n t f r e q u e n c y , a d j u s t i n g t h e p u l s e l e n g t h t o a g i v e n v a l u e , T , and t h e n m o n i t o r i n g t h e FID a m p l i t u d e as a f u n c t i o n o f t h e r . f . f i e l d s t r e n g t h u s i n g a b o x c a r i n t e -g r a t o r . The e x p e r i m e n t s were p e r f o r m e d a t room t e m p e r a t u r e s i n c e , as S t r e e v e r and B e n n e t t (1961) have shown, t h e N.M.R. l i n e broadens c o n s i d e r a b l y a t l o w e r t e m p e r a t u r e s . I n f i g u r e 4-1 t h e v a r i a t i o n o f the FID a m p l i t u d e w i t h r . f . f i e l d s t r e n g t h i s shown. 47 H, I N G A U S S F i g . 4-1 FID Amplitude v e r s u s R.F. F i e l d S t r e n g t h '48 The v a r i a t i o n o f t h e FID a m p l i t u d e \" w i t h t r a n s m i t t e r f r e q u e n c y f o r a f i x e d f i e l d s t r e n g t h and p u l s e l e n g t h was a l s o s t u d i e d . A t y p i c a l measurement i s shown i n f i g u r e 4-2. (b) D i s c u s s i o n For an r . f . f i e l d p a r a l l e l t o t h e p l a n e o f t h e domain w a l l and a c o n s t a n t enhancement f a c t o r i\\ , t h e FID a m p l i t u d e i s g i v e n by where H i s t h e n u c l e a r g y r o m a g n e t i c r a t i o and C i s a c a l i -b r a t i o n c o n s t a n t f o r t h e d e t e c t i o n a p p a r a t u s . I n a sample o f many p a r t i c l e s t h e o r i e n t a t i o n o f w i t h t h e p l a n e o f t h e domain w a l l ( d e f i n e d bv an a n a l e

) = n 0 [ c o s h ( x ) ] cos ( 9 ) (4.2) (4.3) 49 25.0 26.0 27.0 28.0 FREQUENCY (MHZ) F i g . 4-2 Frequency Dependence o f t h e FID A m p l i t u d e 50 where f\\ i s as d e f i n e d i n equ a t i o n ( 4 . 2 ) . T h i s e x p r e s s i o n i s p l o t t e d i n f i g u r e 4-3. I t i s e v i d e n t t h a t t h i s does not d e s c r i b e the observed b e h a v i o u r . I t i s c l e a r then t h a t r e p r e s e n t i n g the w a l l s as r i g i d l y o s c i l l a t i n g w i t h p roper account taken o f the angular v a r i a t i o n ^ a n d the enhancement f a c t o r d i s t r i b u t i o n due t o the s p a t i a l arrangement of the s p i n s i n the domain w a l l does not agree w e l l a t a l l w i t h the observed FID behaviour. F o l l o w i n g Stearns i t i s now assumed t h a t the domain w a l l s v i b r a t e l i k e c i r c u l a r membranes of r a d i u s a, which are bound on t h e i r c i r c u m f e r e n c e s . The displacement o f the w a l l a t a 2 p o i n t r d i s t a n t from the c e n t e r i s p r o p o r t i o n a l t o [1 - (r/a) ]. The maximum displacement o f a g i v e n w a l l , a t the c e n t e r , i s denoted by h, and the p r o b a b i l i t y o f a nucleus being i n a w a l l w i t h t h i s maximum displacement i s P ( h ) . The g r e a t e s t v a l u e o f h i s h^. I f these parameters are averaged over the e x p r e s s i o n f o r the FID amplitude becomes S = C I J J I 4-N q s i n t f n j I ^ P t h J r s i n f f )d?dxdrdh 0 o 0 'O (4.4) where f\\ = Ho^-[l - (r/a) 2 ] c o s ( ^ ) [cosh (x) ] _ 1 m T h i s e x p r e s s i o n has been i n t e g r a t e d by computer f o r v a r i o u s v a l u e s o f r\\0 . i t i s found t h a t e x c e l l e n t f i t w i t h experiment f o r ^ 1.0 microsecond i s o b t a i n e d by t a k i n g P(h) as co n s t a n t and n 0= 4700 + 400. F i g u r e 4-1 shows the t h e o r e t i c a l and expe-r i m e n t a l v a l u e s f o r the FID amplitude. I t i s noted t h a t f o r 51 0 .1 . 2 .3 .4 .5 .6 .7 .9 LO 1 1 1 2 H 1 I N G A U S S F i g . 4-3 H, Dependence of the FID Amplitude: R i g i d Plane Model 52 h i g h v a l u e s o f H 1 , th e e x p e r i m e n t a l p o i n t s l i e c o n s i s t e n t l y -above a t h e o r e t i c a l c u r v e f i t t e d t o e x p e r i m e n t a l p o i n t s f o r low H^. T h i s i s a l m o s t c e r t a i n l y due t o t h e c o n t r i b u t i o n t o th e s i g n a l from n u c l e i i n t h e domains. T h i s c o n t r i b u t i o n can be s i g n i f i c a n t i n n i c k e l a t h i g h v a l u e s o f H^f, s i n c e t h e domain enhancement f a c t o r i s about 300 a t xoom t e m p e r a t u r e a c c o r d i n g t o t h e measurements o f Aubrun and Le Dang K h o i ( 1 9 6 6 ) . S t e a r n s e s t i m a t e d ^=67 00 f o r i r o n . I t i s n o t e d t h a t t h e r e i s r e a s o n a b l e agreement between t h e p u l s e d N.M.R. expe-r i m e n t s and t h e r o t a r y s a t u r a t i o n e x p e r i m e n t s o f Cowan and Anderson (1965). The p u l s e d N.M.R. measurements g i v e 1fi!H^)~.7, \"\"l o C T e V w h i l e t h e a b s o r p t i o n maxima i n t h e r o t a r y s a t u r a t i o n e x p e r i m e n t s r t ^ i r r o o ^ n n r l Ho C ^ ^ „ Q r\\r n A n r e o f l i o 1 a f f o r o v n o r i m o n f c d e t e r m i n e some average v a l u e o f n, , s i n c e t h e s i g n a l depends b o t h on r\\ and t h e number o f n u c l e i e x c i t e d . Domain W a l l D i a m e t e r The measured enhancement f a c t o r can be used t o o b t a i n an e s t i m a t e o f t h e maximum domain w a l l d i a m e t e r . F o r a domain w a l l moving l i k e a c i r c u l a r membrane p i n n e d a t i t s c i r c u m f e r e n c e t h e average enhancement f a c t o r i s -rJ»/3. By e q u a t i o n (2.20) we have H d 3 4M S K*'^} s 3 F o r n i c k e l M g i s 485 oe., H n i s about 75x10 oe., q„ i s 4700 and S i s about 260 A° ( L i l l e y , 1 9 5 0 ) . The domain w a l l d i a m e t e r i f found from t h e above e q u a t i o n t o be ~1 m i c r o n . T h i s r e s u l t 53 and the measured enhancement factor can be used to obtain an estimate of the relaxation time T^ for domain wall n u c l e i . Estimate of In chapter II section v the r e l a x a t i o n due to thermal fluctuations of the domain walls was considered. Here a s i m i l a r procedure w i l l be followed to obtain an expression for the relaxation time i n terms of the enhancement f a c t o r . Consider a small sphere of diameter, d, consisting o f two equal oppo-s i t e l y directed domains and a domain wall at the center. As a r e s u l t of a thermal e x c i t a t i o n of the domain wall a net magnetization, M, w i l l be created. The demagnetizing energy . 2 resu.1 t.i nc? \"From hhi s mainet i s a t 5 on i? N M . \\T/7 , Here V i s t h e > volume of the p a r t i c l e and N i s the demagnetizing factor. For a sphere N i s 4 t f / 3 . By the theorem of e q u i p a r t i t i o n of energy the average energy associated with t h i s degree of freedom i s 4kT. Hence we have kT NM 2 4 t f d 3 I A i = r T i ( 4- 6 ) The magnetization M can also be produced by an external f i e l d , H = NM, applied p a r a l l e l to the domain wa l l . From.equation ( 4 . 7 ) t h i s f i e l d i s given by H = (^|)* ( 4 . 7 ) d - 3 The n u c l e i w i l l see an enhanced f i e l d H = i\\ H. I f we assume that the fluctuations are associated with a Lorentzian 54 c o r r e l a t i o n s p e c t r u m P O ) = (4.8) I f d + urfc ) where T c i s t h e c o r r e l a t i o n t i m e . The r e l a x a t i o n r a t e caused by t h e f l u c t u a t i o n s i s g i v e n by i = 4 U H ) 2 P ( c u ) (4.9) ll X F o r n i c k e l y = 2300, H = 1 . 6 4 x l 0 8 s e c \" 1 , d =-1 m i c r o n , n<= 4700 _q and %= 4.3x10 s e c . ( B h a g a t and C h i c k l i s , 1 9 6 9 ) . S u b s t i t u t i n g t h e s e v a l u e s i n e q u a t i o n y i e l d s T^~ 70 m i c r o s e c o n d s a t room t e m p e r a t u r e . T h i s compares w e l l w i t h t h e v a l u e o f 40 m i c r o -seconds deduced by Reeves e t . a l . ( 1 9 7 0 ) from f a s t passage measurements on powdered n i c k e l . I n v i e w of t h e s e r e s u l t s t h e measured enhancement f a c t o r can be s a i d t o be r e a s o n a b l e . The v a r i a t i o n o f t h e FID a m p l i t u d e w i t h t r a n s m i t t e r f r e q u e n c y g i v e n i n f i g u r e 4-2 shows c o n s i d e r a b l e asymmetry, i . e . S (-*<*»')= S ( £ \" > ) . S i m i l a r b e h a v i o u r has been r e p o r t e d by S t e a r n s ( 1 9 6 7 ) f o r i r o n . The r e a s o n f o r t h i s asymmetry i s n o t u n d e r s t o o d . I t i s t e m p t i n g t o say t h a t i t i s caused by a f r e q u e n c y dependent enhancement f a c t o r . R e c a l l i n g e q u a t i o n ( 2 . 1 9 ) , t h e enhancement f a c t o r i s g i v e n by _ M s H n s e c h ( f ) (4.10) 5\"m w[(A 2- ^ 0 2) 2+(/3/m w) 2w. 2] I t i s seen t h a t a f r e q u e n c y dependence can be e x p e c t e d i f w0 i s c l o s e t o t h e domain w a l l r esonance f r e q u e n c y A . However 55 t h i s f r e q u e n c y i s e s t i m a t e d by W i n t e r ( 1 9 6 1 ) t o be o f t h e o r d e r o f 500 MHz f o r n i c k e l . S i n c e 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 i n n i c k e l i s about 30 MHz one would n o t e x p e c t t h e asymmetry t o a r i s e from domain w a l l r e s o n a n c e e f f e c t s . 56 CHAPTER V F e 2 P (a) I n t r o d u c t i o n The p h y s i c a l p r o p e r t i e s o f F e 2 P have been t h e s u b j e c t o f many i n v e s t i g a t i o n s i n r e c e n t y e a r s . There i s c o n s i d e r a b l e d i s a g r e e m e n t i n t h e r e p o r t e d C u r i e p o i n t s and m a g n e t i c moments o b t a i n e d from b u l k m a g n e t i z a t i o n measurements. The C u r i e t e m p e r a t u r e o f F e 2 P was r e p o r t e d t o be 353 K by Le C h a t e l i e r and Wolodgine (1909), 306 K by Chiba(1960) and 266 K by Meyer and C a d e v i l l e (1961). B e l a v a n c e e t a l . (1970) r e p o r t a C u r i e p o i n t o f 255 K. The v a l u e o f t h e m a g n e t i c moment o b s e r v e d p e r i r o n atom v a r i e d f r om as r e p o r t e d by C h i b a t o 1.32/k as r e p o r t e d by Meyer and C a d e v i l l e . The l a t t e r c o r r e s p o n d s 3 t o a s a t u r a t i o n m a g n e t i z a t i o n p e r u n i t volume o f 70 8 Ce./cm . Meyer and C a d e v i l l e have shown t h a t n o n - s t o i c h i o m e t r i c F e 2 _ £ P e x h i b i t s extreme m a g n e t i c h a r d n e s s , t h i s makes i t d i f f i c u l t t o d e t e r m i n e t h e m a g n e t i c moment and may a c c o u n t f o r t h e d i s c r e p a n c i e s i n t h e r e p o r t e d v a l u e s o f t h e m a g n e t i c moments p e r i r o n atom. I n v i e w o f t h i s t h e v a l u e o f t h e m a g n e t i c moment p e r i r o n atom g i v e n by Meyer and C a d e v i l l e i s a c c e p t e d by most p e o p l e as b e i n g t h e most r e l i a b l e ( e.g. W a p p l i n g e t at.,1971) and w i l l be used i n t h i s t h e s i s . The c r y s t a l s t r u c t u r e o f F e 2 P has been d e t e r m i n e d by R u n d q u i s t and J e l l i n e k (1956). I t i s a h e x a g o n a l (C22) t y p e , w i t h space group P6~2m, and a=5.865 A° and c=3.546 A°(Pearson, 57 1967). The u n i t c e l l arrangement i s shown i n f i g u r e 5-1. There a r e two c r y s t a l l o g r a p h i c a l l y d i s t i n c t i r o n s i t e s , F e ( I ) and F e ( I I ) , and two d i s t i n c t phosphorous s i t e s , P ( I ) and P ( I I ) . F e ( I ) i s s u r r o u n d e d by an ap p r o x i m a t e t e t r a h e d r o n o f phospho-rous atoms, whereas F e ( I I ) i s n e a r the base o f a square p y r a m i d o f phosphorous atoms. The d i f f e r e n t s i t e s and t h e i r n e a r e s t n e i g h b o u r c o n f i g u r a t i o n s a r e i l l u s t r a t e d i n f i g u r e 5-2. F e 2 P has been t h e s u b j e c t o f Mossbauer e x p e r i m e n t s . The r e s u l t s o f t h e s e e x p e r i m e n t s a l s o e x h i b i t d i s a g r e e m e n t . Mossbauer s t u d i e s were p e r f o r m e d by Duncan and B a i l e y (1967) and more r e c e n t l y by Sato e t a l . (1969) and Wuppling e t a l . (1971). Duncan and B a i l e y measured h y p e r f i n e f i e l d s o f 110 koe. and 14 0 koe. a t 90 K f o r t h e two i r o n s i t e s whereas S a t o e t a l . r e p o r t e d h y p e r f i n e f i e l d s o f 117 koe. and 175 koe.. W a p p l i n g e t a l . r e p o r t h y p e r f i n e f i e l d s o f 109 koe. and 169 koe.. The m o t i v a t i o n f o r t h e N.M.R. r e s u l t s i s t h e measurement o f t h e h y p e r f i n e f i e l d s i n Fe and P atoms. A l s o we hope t o c l a r i f y t h e m a g n e t i c s t r u c t u r e . Two samples were employed f o r t h e N.M.R. e x p e r i m e n t s . One was o b t a i n e d c o m m e r c i a l l y and was c h e m i c a l l y a n a l y z e d as F e 2 Qg P' t n e o t h e r was p r e p a r e d as d e s c r i b e d below and a n a l y z e d as Fe^ 9g p« Powders o f 99.99% pure i r o n (325 mesh) and 99.9% pure r e d phosphorous (100 mesh) were weighed o u t i n t h e d e s i r e d p r o p o r t i o n s , mixed w e l l i n a m o r t a r and e n c l o s e d i n an e v a c u -a t e d s i l i c a g l a s s t u b e . S i n c e t h e b o i l i n g p o i n t o f r e d phosphorous i s 416 °C, r a p i d h e a t i n g o f t h e m i x t u r e above t h i s 58 • Fe cnc=o,i (3 Fe (II) c=v2 O P CD c=v2 ® P(I I ) c=o,i 5-1 Diagram of Fe^P C r y s t a l S t r u c t u r e 59 ® FeCl) cj Fe CII) F i g . 5-2 N e a r e s t N e i g h b o u r C o n f i g u r a t i o n s i n F e 2 P 60 p o i n t c o u l d i n d u c e an e x p l o s i o n o f t h e r e a c t i o n tube due t o the h e a t o f t h e r e a c t i o n and t h e v a p o r p r e s s u r e o f t h e phosphorous. T h e r e f o r e , t h e m i x t u r e was f i r e d i n an e l e c t r i c f u r n a c e i n i t i a l l y a t 400 °C f o r 24 hours and t h e n h e a t e d up t o 1000 C a t t h e r a t e o f 20 degrees p e r hour. The m i x t u r e was t h e n h e a t e d f o r a n o t h e r 24 hours a t 1000 °C. The r e s u l t a n t p r o d u c t c o u l d e a s i l y be r e d u c e d t o a powder w i t h a m o r t a r and p e s t l e . The powder was t h e n a n n e a l l e d a t 500 °C f o r 48 hours t o remove s t r a i n s i n d u c e d by t h e c o l d w o r k i n g . The c r y s t a l s t r u c t u r e o f t h e samples were v e r i f i e d by X - r a y powder a n a l y s i s . (b) E x p e r i m e n t a l R e s u l t s ( i ) Zero F i e l d S p e c t r a The z e r o f i e l d r e s o n a n c e s were sought e m p l o y i n g t h e s p e c t r o m e t e r d e s c r i b e d i n c h a p t e r 3. B o t h samples were used and t h e same N.M.R. spectrum was o b t a i n e d . F o u r r e s o n a n c e s were o b s e r v e d and t h e s e a r e a s s i g n e d t o t h e f o u r c r y s t a l l o -g r a p h i c a l l y d i s t i n c t s i t e s i n Fe2P. R e p r e s e n t a t i v e t r a c e s a r e shown i n f i g u r e s 5-3 and 5-4. The r e s o n a n c e s o c c u r a t 20.5 MHz, 17.5 MHz, 7 7.7 MHz and 86.6 MHz a t 1.5 K. The r e s o n a n t f r e q u e n c i e s were d e t e r m i n e d by b e a t i n g t h e n u c l e a r s i g n a l w i t h a r e f e r e n c e s i g n a l f r om a V.H.F. s i g n a l g e n e r a t o r . The a c c u r a c y o f t h i s d e t e r m i n a t i o n was l i m i t e d by t h e f i n i t e w i d t h o f t h e echo t o + 0.2 MHz. The l i n e s a t 17.5 MHz and 20.5 MHz a r e r e l a t i v e l y weak and have a f u l l w i d t h a t h a l f h e i g h t o f about 2 MHz and 1 MHz r e s p e c t i v e l y . The h i g h f r e q u e n c y l i n e s a r e much s t r o n g e r . 1 6 17 1 8 19 2 0 2 1 FREQUENCY (MHz) F i g . 5-3. Zero F i e l d Frequency Dependence of t h e Spin-Echo A m p l i t u d e i n Fe~P a t 1.5 K FREQUENCY (MHz) F i g . 5-4 Zero F i e l d Frequency Dependence o f the Spin-Echo Amplitude i n Fe-P at 1.5 K 63 The r e l a t i v e i n t e g r a t e d i n t e n s i t i e s o f t h e 77.7 MHz and t h e 86.6 MHz l i n e s a r e about 2 t o 1. ( i i ) Temperature and F i e l d Dependence o f t h e Resonant Frequency The s t r o n g e s t r e s o n a n c e , t h e 77.7 MHz l i n e , w h i c h ( as 31 W i l l be d i s c u s s e d i n p a r t c o f t h i s c h a p t e r ) i s a P r e s o n a n c e , was s t u d i e s as a f u n c t i o n o f e x t e r n a l f i e l d and as a f u n c t i o n o f t e m p e r a t u r e . F i g u r e 5-5 shows t h e change i n t h e r e s o n a n c e f r e q u e n c y as a f u n c t i o n o f t h e a p p l i e d f i e l d . 3\"! The t e m p e r a t u r e dependence o f t h e l o w e r and s t r o n g e r ~P r e s o n a n c e f r e q u e n c y i s summarized i n t h e f o l l o w i n g t a b l e 31 TABLE I : V a r i a t i o n o f P N.M.R. f r e q u e n c y w i t h t e m p e r a t u r e T(K) (MHz) 4.2 77.7 + .2 77.7 72.5 II 112 + 2 67.5 II 122 + 2 64.8 II 136 + 2 62.7 II 147 + 2 60.0 64 F i g . 5-5 Change i n P Resonance Frequency w i t h A p p l i e d F i e l d a t 1.5 K 65 ( i i i ) Enhancement F a c t o r s As was d e m o n s t r a t e d i n c h a p t e r 4, a s t u d y o f t h e s i g n a l i n t e n s i t y as a f u n c t i o n o f t h e a p p l i e d r . f . f i e l d s t r e n g t h can y i e l d i n f o r m a t i o n about t h e d i s t r i b u t i o n o f enhancement f a c t o r s w i t h i n a domain w a l l . The FID decay t i m e was t o o s h o r t t o e n a b l e a s t u d y o f i t s b e h a v i o u r , and i n s t e a d , t h e a m p l i t u d e o f t h e s p i n echo was d e t e r m i n e d as a f u n c t i o n o f t h e r . f . f i e l d s t r e n g t h . R e s u l t s o f t h e measurements f o r t h e P ( I I ) and P ( I ) s i t e s a r e g i v e n i n f i g u r e s 5-6 and 5-7 r e s p e c t i v e l y . ( i v ) N u c l e a r S p i n R e l a x a t i o n i n Fe^P L o n g i t u d i n a l 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^, and t r a n s v e r s e r e l a x a t i o n t i m e s , T ?, were d e t e r m i n e d f o r t h e P ( I ) , P ( I I ) and F e ( I ) n u c l e i . F o r t h e P ( I I ) n u c l e i t h e r e l a x a t i o n t i m e s were d e t e r m i n e d a t 1.5 K, 4.2 K and 7 7 K. P ( I ) n u c l e a r r e l a x a t i o n t i m e s were d e t e r m i n e d a t 1.5 K and 4.2 K. F e ( I ) r e l a x a t i o n t i m e s were d e t e r m i n e d o n l y a t 1.5 K due t o poor s i g n a l t o n o i s e . T y p i c a l l o n g i t u d i n a l r e l a x a t i o n c u r v e s f o r the P ( I ) , P ( I I ) and F e ( I ) s i t e s a t 1.5 K and v a r i o u s power l e v e l s a r e g i v e n i n f i g u r e s 5-8, 5-9 and 5-10 r e s p e c t i v e l y . These c u r v e s i n d i c a t e t h a t t h e r e l a x a t i o n i s n o n - e x p o n e n t i a l and power dependent. An i n s t a n t a n e o u s r e l a x a t i o n r a t e can be d e f i n e d as f o l l o w s 1 dM (t) ± = - j f - / [ M z ( t > - M z(<*)] (5.1) where M(t) i s t h e a m p l i t u d e o f t h e echo a t t i m e t . The e x p e r i -m e n t a l r e s u l t s i n d i c a t e t h a t t h e i n i t i a l r e l a x a t i o n r a t e a t H. IN GAUSS F i g . 5-6 Spin-Echo Amplitude vs R.F. F i e l d S t r e n g t h : P(II) 1.5 K F i g . 5-7_ Spin-Echo Amplitude vs R.F. F i e l d S t r e n g t h : P(I) 1.5 K 68 69 70 71 low power l e v e l s i s most rapid, and that the r e l a x a t i o n rate decreases with time and power l e v e l . Representative transverse relaxation curves for the P ( I ) , P(II) and Fe(I) s i t e s are presented i n figures 5-11, 5-12 and 5-13 re s p e c t i v e l y . The transverse relaxation curves for the P(II) nuclei at 77 K (figure 5-12b) ex h i b i t a d i s t r i b u t i o n i n times, T 2, and a power l e v e l dependence s i m i l a r to that of the l o n g i t u d i n a l relaxation curves. At 4.2 K (figure 5-12a) and at 1.5 K, the d i s t r i b u t i o n and the power dependence of the T 2 s are not very great. The P(I) relaxation curves exh i b i t some power dependence. The Fe(I) T 2 i s much less than T^, and the re l a x a t i o n i n exponential. The r e s u l t s of the relaxa t i o n time measurements are summarized i n the following table TABLE II : Nuclear spin l o n g i t u d i n a l and transverse relaxation times. atom T(K) ^(msec.) T 2(msec.) P(I) 1.5 0.10 - 0.35 0.20 4.2 - 0.05 - 0.35 0.12 P(II) \" 1.5 0.60 - 8.50 0.45 4.2 0.40 - 6.40 0.20 - 0.35 77.7 0.04 - 0.40 0.06 - 0.36 Fe(I) 1.5 1.0 - 10 0.18 72 75 The r e l a x a t i o n t i m e s l i s t e d i n t a b l e I I have an u n c e r t a i n t y o f about 10%. T h i s a r i s e s because t h e r e was some u n c e r -t a i n t y i n t h e e x p e r i m e n t a l d a t a and hence i n t h e r e l a x a t i o n t i m e s w h i c h were deduced from t h e s l o p e s o f t h e r e l a x a t i o n c u r v e s . (c) D i s c u s s i o n o f E x p e r i m e n t a l R e s u l t s ( i ) Zero F i e l d S p e c t r a Four r e s o n a n c e s a r e o b s e r v e d . S i n c e t h e r e a r e f o u r d i s t i n c t s i t e s one l i n e w i l l be a s s i g n e d t o each s i t e . I t was n o t e d i n c h a p t e r 2 s e c t i o n i i i t h a t t h e h y p e r f i n e f i e l d i s p r o p o r t i o n a l t o t h e e l e c t r o n i c m a g n e t i c moment. I n F e 2 P t h e average m a a n e t i c moment p e r i r o n atom i s 1.32/A* wh-Me i n p ure Fe i t i s about 2.2jJg. Thus we e x p e c t t h e h y p e r f i n e f i e l d a t t h e i r o n n u c l e i t o be d e p r e s s e d r e l a t i v e t o t h e p u r e i i r o n v a l u e . The r e s o n a n c e f r e q u e n c y i n pure i r o n i s about 45 MHz, t h e r e f o r e t h e two low f r e q u e n c y l i n e s i n t h e F e 2 P 57 spectrum a r e u n d o u b t a b l y Fe r e s o n a n c e s . These c o r r e s p o n d t o h y p e r f i n e f i e l d s o f 123 + 2 koe. and 148 + 2 koe.. These r e s u l t s a r e i n f a i r l y good agreement w i t h t h o s e o f B a i l e y and Duncan (1967). The two h i g h f r e q u e n c y l i n e s a r e a s s i g n e d t o t h e phospho-rou s s i t e s . S i n c e t h e u n i t c e l l c o n t a i n s one P ( I ) s i t e and two P ( I I ) s i t e s , c o n s i d e r a t i o n o f 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 two l i n e s l e a d s us t o a s s i g n t h e 77.7 MHz l i n e t o t h e P ( I I ) s i t e . The deduced h y p e r f i n e f i e l d s f o r t h e two s i t e s 76 a r e 45.0 + .1 koe. and 50.2 + .1 koe.. These r e s u l t s a re summarized i n t h e f o l l o w i n g t a b l e . TABLE I I I : N.M.R. d a t a f o r Fe„P a t h e l i u m t e m p e r a t u r e s Vo (MHz) AV(MHz) N u c l e u s S i t e H n(Koe.) 17. 0 + 0.2 2 5 7 F e F e ( I I ) 123 + 2 20. 5 4- 0.2 1 5 7 F e F e ( I ) 148 + 2 77.5 + 0.2 0.6 3 1 P P ( I I ) 45.0 + 0.1 86.6 + 0.2 1.2 3 1 p P (D 50.2 + 0.1 The m a g n e t i c s t r u c t u r e o f F e 2 P can be i n t e r p r e t e d by-assuming t h a t t h e h y p e r f i n e f i e l d s o b s e r v e d a t t h e d i f f e r e n t s i t e s a r e d i r e c t l y p r o p o r t i o n a l t o t h e m a g n e t i c moment a t t h o s e s i t e s . The o b s e r v e d s a t u r a t i o n moment o f 1.32/Js p e r i r o n atom can t h e n be a p p o r t i o n e d between t h e two i r o n s i t e s t o g i v e 1.21fi» and 1.44/^8 f o r t h e moments a s s o c i a t e d w i t h t h e F e ( I I ) and F e ( I ) s i t e s r e s p e c t i v e l y . From t h e b u l k m a g n e t i c measurements o f Meyer and C a d e v i l l e (1962) i t i s known t h a t t h e d i r e c t i o n o f t h e m a g n e t i z a t i o n and hence t h e d i r e c t i o n o f t h e a t o m i c moments i s p a r a l l e l t o the h e x a g o n a l a x i s . The v a l i d i t y o f t h e p r e c e e d i n g method o f a p p o r t i o n i n g t h e m a g n e t i c moments i s i l l u s t r a t e d by t h e work o f S h i r a n e 77 et a l . (1962) with Fe^N. The magnetic moments obtained by-apportioning the average magnetic moment were found to be i n excellent agreement with the moments obtained by neutron d i f f r a c t i o n . The study of a number of Laves phase compounds of the formula MFe2 by Wallace (1964) also shows a good corre-l a t i o n between the magnetic moment and the hyperfine f i e l d . An average value of Hn^J = 140 koe./^ 9 was found. This i s i n agreement with basic t h e o r e t i c a l considerations which predict that the hyperfine f i e l d i s proportional to the mag-netic moment. The observed iron hyperfine f i e l d s can be interpreted by assuming that the bonding i n Fe 2P involves donation of phosphorous valence electrons to the iron d bands thus reducing the average moment from that observed in pure i r o n . While t h i s i s contrary to the d i r e c t i o n expected from electronega-t i v i t y considerations, i t does provide a reasonable explanation of the reduced moments observed i n the i r o n phosphides. Fischer and Meyer (1967) have shown that for the iron series phosphides Fe^P/ Fe 2P and FeP, the average magnetic moment per iron atom va r i e s according to the r e l a t i o n M = M - y — _ (5.2) o 1 - c where c i s the concentration of P, and q i s the number of electrons donated by each phosphorous ion. They fi n d that for the i r o n phosphides q=2.6 for MQ= 2.7 (which i s the value observed for iro n i n strongly d i l u t e d a l l o y s ) . From these 78 v a l u e s t h e e x p e c t e d moments can now be e s t i m a t e d . The phosphorous atoms each have n i n e i r o n n e a r e s t n e i g h b o u r s , hence each phosphorous atom w i l l d o n a t e 2.6/9 e l e c t r o n s t o each o f i t s i r o n n e a r e s t n e i g h b o u r s . Thus f o r F e ( I ) w h i c h has f o u r phosphorous n e a r e s t n e i g h b o u r s t h e moment w i l l be g i v e n by JX = 2 . 7 - 4 x 2 . 6 / 9 = 1.55/^ (5.3) F e ( I ) F o r F e ( I I ) w h i c h has f i v e phosphorous n e a r e s t n e i g h b o u r s one e x p e c t s u = 2.7 - 5 x 2.6/9 = 1.26/^3 (5.4) F e ( I I ) The r a t i o o f t h e s e moments i s 1.23 w h i c h compares w e l l w i t h 1.20, t h e r a t i o o f t h e moments as deduced from t h e h y p e r f i n e f i e l d s . I f i t i s assumed t h a t t h e phosphorous h y p e r f i n e f i e l d s , are p r o p o r t i o n a l t o t h e sum o f t h e m a g n e t i c moments on t h e n e a r e s t n e i g h b o u r Fe s i t e s , t h e n one f i n d s from t h e model t h a t H [ P ( I ) ] DC £ /U F e = 13.08 (5.5) n nn ' nn H [ P ( I I ) ] 0 d L> A = 12.21 (5.6) n nn ' nn 79 The r a t i o p r e d i c t e d i s 1.07 w h i l e t h e o b s e r v e d v a l u e i s 1.11. T h i s good agreement may o n l y be f o r t u i t o u s as t h e a s s u m p t i o n t h a t t h e h y p e r f i n e f i e l d s :are p r o p o r t i o n a l t o t h e sum o f t h e i r o n moments i s a r a t h e r r e s t r i c t i v e one. I t i s most l i k e l y v a l i d i f t h e r e i s o n l y one dominant mechanism r e s p o n s i b l e f o r t h e t r a n s f e r r e d h y p e r f i n e f i e l d . I n F e 2 P b o t h c o n d u c t i o n e l e c t r o n p o l a r i z a t i o n and c o v a l e n c y e f f e c t s may be i m p o r t a n t ( c f . c h a p t e r 2 s e c t i o n i i i ) . However the r e s u l t i s c o n s i s t e n t w i t h t h e assumed model. ( i i ) Temperature and F i e l d Dependence o f t h e P ( I I ) Resonance Frequency The v a r i a t i o n w i t h t e m p e r a t u r e o f t h e f r e q u e n c y o f t h e 31 l o w e r and more i n t e n s e P r e s o n a n c e f r e q u e n c y was s t u d i e d and t h e r e s u l t s shown i n t a b l e I I . The d a t a were a n a l y z e d by computer u s i n g a l e a s t square f i t t e c h n i q u e . I t was found t h a t t h e d a t a f i t v e r y w e l l a r e l a t i o n V>(T) = V(0) [1-AT 2] (5.7) -5 -2 The a n a l y s i s shows a v a l u e o f A=(1.05 + . 0 3 ) x l 0 K . Here t h e q u o t e d i s t h e s t a n d a r d d e v i a t i o n o f t h e mean. The f i t i s i l l u s t r a t e d i n f i g u r e 5-14a where [ V( 0 ) - V ( T ) ] / V ( 0 ) i s 2 p l o t t e d a g a i n s t T . However, i t i s a l s o p o s s i b l e t o d e s c r i b e t h e t e m p e r a t u r e dependence by a r e l a t i o n s h i p V(T) = V(0) [1 - a T 3 / 2 - b T 5 / 2 ] (5.8) 81 The f i t i n t h i s c a s e i s much p o o r e r , t h e v a l u e s o f t h e c o n s t a n t s b e i n g ; a=(6.6 + 1 . 1 ) x l O _ 5 K ~ 3 / 2 , b=(4.1 + 0 . 8 ) x l O ~ 7 K ~ 5 / 2 . O b v i o u s l y f i t s o f v a r y i n g d e g r e e s o f a c c u r a c y cound be made w i t h any a d m i x t u r e o f e q u a t i o n s (5.7) and ( 5 . 8 ) . Thus, a l t h o u g h o u r 2 p r e s e n t r e s u l t s f a v o r a T dependence, i m p l y i n g s i n g l e - p a r t i c l e e x c i t a t i o n s , i t i s d i f f i c u l t o f a s c e r t a i n t h e c o n t r i b u t i o n o f spin-wave e x c i t a t i o n s . T h i s p r o b l e m has been d i s c u s s e d i n c c h a p t e r 2 s e c t i o n i i o f t h i s t h e s i s . I n p r e v i o u s work ( Weisman e t al., 1 9 6 9 ) on F e 2 B i t has been assumed t h a t t h e f r e q u e n c y o f t h e non-magnetic s i t e (B) i s p r o p o r t i o n a l t o t h e m a g n e t i z a t i o n . T h i s a s s u m p t i o n i s c o n f i r m e d 31 by o u r p r e s e n t r e s u l t s on t h e t e m p e r a t u r e v a r i a t i o n o f t h e P 2 N.M.R. f r e q u e n c y w h i c h f a v o r a T dependence, w h i c h we n o t e , i s a l s o t h e t e m p e r a t u r e dependence o f t h e b u l k m a g n e t i z a t i o n a c c o r d i n g t o t h e d a t a o f Meyer and C a d e v i l l e . The f i e l d dependence o f t h e change i n t h e re s o n a n c e f r e q u e n c y shown i n f i g u r e 5-5 i n d i c a t e s t h a t t h e a p p l i e d f i e l d i s i n i t i a l l y s h i e l d e d t o some e x t e n t . The i n i t i a l s h i e l d i n g e f f e c t can a r i s e from t h e random d i s t r i b u t i o n o f t h e n u c l e a r h y p e r f i n e f i e l d d i r e c t i o n s v / i t h r e s p e c t t o t h e a p p l i e d f i e l d . F o r domain n u c l e i t h e a p p l i e d f i e l d i s i n i t i a l l y compensated f o r by t h e d e m a g n e t i z i n g f i e l d s t h a t a r i s e as t h e domain w a l l s a r e swept o u t . T h i s may a l s o have a s h i e l d i n g e f f e c t on t h e domain w a l l n u c l e i . I n m a g n e t i c a l l y h a r d m a t e r i a l s domain 82 w a l l m o t i o n and domain r o t a t i o n s a r e e x p e c t e d t o o c c u r a l m o s t s i m u l t a n e o u s l y . 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 t h e n u c l e a r h y p e r f i n e f i e l d s t e n d t o l i n e up a l o n g t h e a p p l i e d f i e l d . The r e s u l t i s t h a t a t h i g h f i e l d s , i n o u r case above 6 koe., t h e f r e q u e n c y changes a l m o s t l i n e a r l y w i t h a p p l i e d f i e l d . The s l o p e o f t h e c u r v e i n t h e h i g h f i e l d r e g i o n i s e x p e c t e d t o be ^ / 2 T i , where # i s t h e n u c l e a r g y r o m a g n e t i c r a t i o . T h i s i s o b s e r v e d t o be t h e case as i n d i c a t e d by t h e dashed l i n e i n f i g u r e 5-5. The f r e q u e n c y s h i f t w i t h a p p l i e d f i e l d i s p o s i t i v e , hence, t h e h y p e r f i n e f i e l d i s p o s i t i v e . T h i s i s n o t s u r p r i s i n g s i n c e 3 . . . p e l e m e n t s d i s s o l v e d i n i r o n a r e e x p e c t e d t o e x h i b i t p o s i t i v e h y p e r f i n e f i e l d s ( c f . c h a p t e r 2 s e c t i o n i i i ) . ( i i i ) Enhancement F a c t o r s The s p i n - e c h o v e r s u s r . f . f i e l d s t r e n g t h c u r v e s p r e s e n t e d i n f i g u r e s 5-6 and 5-7 a r e q u a l i t a t i v e l y s i m i l a r t o t h e n i c k e l FID r e s u l t s ( f i g u r e 4-1). T h i s m o t i v a t e s an a n a l y s i s based on t h e model p r e s e n t e d i n c h a p t e r 4. To a p p l y t h i s model t h e term s i n ( H-^t) i n e q u a t i o n (4.4) must be r e p l a c e d by an e x p r e s s i o n w h i c h g i v e s t h e a m p l i t u d e o f t h e s p i n echo as a f u n c t i o n o f t h e p u l s e l e n g t h s t ^ , t 2 employed i n t h e two p u l s e sequence. A c c o r d i n g to: Bloom(1955) E ( t 1 , t 2 ) = s i n ( c u L t 1 ) s i n 2 ( i < ^ 1 t 2 ) (5.9) u;,= Yni-i, 83 W i t h t h i s m o d i f i c a t i o n e q u a t i o n (4.4 becomes S = C J J J j q E ( t l f t 2 ) P ( h ) s i n ( if )d(fdxdrdh 0 0 0 0 (5.10) T h i s e x p r e s s i o n has been e v a l u a t e d by computer. The dashed c u r v e i n f i g u r e 5-6 was o b t a i n e d f o r t^=1.3 s e c . and t 2=2.0 sec. u s i n g r\\o=1500 and P (h) c o n s t a n t . A compromise was made t o o b t a i n t h e b e s t f i t a t h i g h and low power l e v e l . F i t s w i t h P(h)= c o n s t a n t were a l s o t r i e d b u t gave worse agreement. I t i s e v i d e n t t h a t t h e model does d e s c r i b e t h e g e n e r a l b e h a v i o u r b u t does n o t g i v e a good ac c o u n t o f t h e o b s e r v a t i o n s . N e v e r -t h e l e s s we can use t h e r e s u l t s t o o b t a i n e s t i m a t e s o f t h e maximum enhancement f a c t o r s . These a r e found t o be 1500 + 200 and 4500 + 500 f o r t h e P ( I I ) and P ( I ) s i t e s r e s p e c t i v e l y . S i m i l a r measurements on t h e F e ( I ) s i t e gave 3000 + 400 f o r t h e maximum enhancement,, f a c t o r . I t s h o u l d be n o t e d t h a t t h e d i s c r e p a n c i e s a t h i g h e r power l e v e l s c a nnot be a t t r i b u t e d t o domain n u c l e i c o n t r i b u t i n g t o t h e s i g n a l . The domain enhancement f a c t o r i s g i v e n a p p r o x i -m a t e l y by H n/H a. F o r F e 2 P H i s about 23000oe. and hence, t h e domain enhancement f a c t o r i s about 2. T h i s p r e c l u d e s any s i g n i f i c a n t c o n t r i b u t i o n by t h e domain n u c l e i t o t h e o b s e r v e d s i g n a l . The magnitude o f t h e o b s e r v e d enhancement f a c t o r s can be u n d e r s t o o d i n terms o f t h e f o l l o w i n g c a l c u l a t i o n . I t was shown i n c h a p t e r 2 t h a t f o r a s p h e r i c a l p a r t i c l e w i t h a s i n g l e domain w a l l , t h e enhancement f a c t o r due t o domain w a l l 84 m o t i o n i s g i v e n a p p r o x i m a t e l y by H d s F o r Fe„P M i s about 700 oe., S i s o f t h e o r d e r o f 200 A°. 2 s Then f o r d i n t h e range 20,000 A° t o 40,000 A°, one f i n d s f o r II =50 koe. t h a t t h e enhancement f a c t o r w i l l be o f t h e o r d e r n o f 2000. T h i s i s i n r e a s o n a b l e a c c o r d w i t h t h e e x p e r i m e n t a l r e s u l t f o r t h e P ( I I ) n u c l e i . I t i s n o t u n d e r s t o o d why t h e enhancement f a c t o r a s s o c i a t e d w i t h t h e P ( I ) s i t e i s about t h r e e t i m e s t h a t o f t h e P ( I I ) n u c l e i . However, 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 o be d i s c u s s e d ) a r e a l s o c o n s i s t e n t w i t h n b(p(D)=-3n 0(p(ii). ( i v ) N u c l e a r S p i n R e l a x a t i o n (a) L o n g i t u d i n a l 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 s o f t h e T^ measurements were summarized i n t a b l e t a b l e I I . S i n c e t h e domain n u c l e i do not c o n t r i b u t e s i g n i f i -c a n t l y t o t h e n u c l e a r s i g n a l (see s e c t i o n i i i ) t h e o b s e r v e d d i s t r i b u t i o n i n r e l a x a t i o n t i m e s must be c h a r a c t e r i s t i c o f th e domain w a l l s . From e q u a t i o n (2.25) t h e s h o r t e s t r e l a x -a t i o n t i m e i s t a k e n t o be c h a r a c t e r i s t i c o f n u c l e i s i t u a t e d a t t h e c e n t e r o f t h e domain w a l l s . The p r e s e n t r e s u l t s can be a c c o u n t e d f o r by assuming t h a t t h e r m a l f l u c t u a t i o n s o f t h e domain w a l l s p r o v i d e t h e dominant r e l a x a t i o n mechanism. R e c a l l i n g e q u a t i o n ( 2 . 2 5 ) , t h e s p i n - l a t t i c e r e l a x a t i o n 85 r a t e i s g i v e n by k~ r6W§s<§) / 2 t a n\" 1