UBC Theses and Dissertations

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UBC Theses and Dissertations

A Pulsed N.M.R. study of the ferromagnets Ni, Fe₂P and Fe₃P Koster, Evert 1972

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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= ^ + f<H z(t)H z(0)>dt (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 <s)> 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 <S> , 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 . - <L When no e x t e r n a l f i e l d i s a p p l i e d , t h e s i z e o f t h e two oppo-s i t e l y m a g n e t i z e d domains a r e e q u a l , and t h e average m a g n e t i -z a t i o n o f t h e p a r t i c l e i s z e r o . When an e x t e r n a l f i e l d i s a p p l i e d p a r a l l e l t o t h e b u l k m a g n e t i z a t i o n M , t h e w a l l s h i f t s u n t i l t h e sum o f t h e i n t e r a c t i o n and d e m a g n e t i z i n g e n e r g i e s i s a minimum (see e.g. K o r r i s h , 1 9 6 5 ) . The i n t e r a c t i o n energy i s g i v e n by -H^aM, and the demagnetizing energy its approximately 2 g i v e n by -£N(AM) , where N i s t h e d e m a g n e t i z i n g f a c t o r . F o r 2 a sphere N=4?T/3. The minimum o f t h e sum -H^AM + ~ N (AM) o c c u r s f o r M s ^ / N s ( 3 / 4 i f ) H 1 . S i n c e , M = , , -, T x M = 3M -g-t o t a l volume s sd t h e r e f o r e x 1 d 4 TT M s As t h e domain w a l l s h i f t s by a d i s t a n c e x, t h e m a g n e t i z a t i o n r o t a t e s by an a n g l e ^ = Tfx S and t h e r e f o r e t h e component o f t h e i n t e r n a l f i e l d w h i c h i s p e r p e n d i c u l a r t o t h e e q u i l i b r i u m m a g n e t i z a t i o n i s Thus t h e enhancement f a c t o r i s H" n l H d n (2.20) H 1 4M b T h i s domain w a l l enhancement i s i n g e n e r a l one o r two o r d e r s of magnitude l a r g e r t h a n t h e domain enhancement. I n i r o n t h i s domain w a l l enhancement i s about 2000. I n p u l s e d N.M.R. expe-r i m e n t s t h e enhancement has two e f f e c t s . F i r s t , t h e magnitude o f t h e r e q u i r e d d r i v i n g f i e l d i s reduced by t h e f a c t o r S e c o n d l y , a f t e r removal o f t h e e x c i t a t i o n t h e p r e c e s s i n g n u c l e a r m a g n e t i z a t i o n i n d u c e s t h r o u g h t h e h y p e r f i n e i n t e r a c t i o n a c o h e r e n t p r e c e s s 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 z a t i o n . T h i s has th e e f f e c t o f e n h a n c i n g t h e s i g n a l by a f a c t o r r\ . (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 S t u d i e s o f t h e 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 , e.g. Weger(1962), have an e x p o n e n t i a l decay f o r l o n g t i m e s , w h i l e t h e s h o r t t i m e decay i s v e r y r a p i d and n o n - e x p o n e n t i a l . The r e l a x a t i o n t i m e i n c r e a s e s w i t h power l e v e l t o some l i m i t i n g v a l u e . T h i s v a l u e i s g e n e r a l l y assumed 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 i n domains. I t was o b s e r v e d by Weger t h a t i n Fe, N i and Co, t h e l i m i t i n g v a l u e s o f T^ were i n v e r s e l y p r o p o r t i o n a l t o t e m p e r a t u r e . T h i s s u g g e s t s t h a t t h e r e l a x a t i o n was due t o c o n d u c t i o n e l e c t r o n mechanisms ( K o r r i n g a , 1 9 5 0 ) . M o r i y a ( 1 9 6 4 ) has s u g g e s t e d t h a t f o r t h e domain n u c l e i t h e r e l a x a t i o n r a t e i s d e t e r m i n e d p r i m a r i l y by t h e 3-d e l e c t r o n s owing t o t h e 26 i n t e r a c t i o n o f t h e i r o r b i t a l c u r r e n t s w i t h t h e n u c l e a r s p i n d i p o l e s . T h i s mechanism g i v e s r i s e t o a T^T= c o n s t a n t r e l a -t i o n s h i p . The s h o r t t i m e and low power r a p i d r e l a x a t i o n must be a t t r i b u t e d t o domain w a l l mechanisms, s i n c e a t low power l e v e l s one d e t e c t s t h e e f f e c t o f t h o s e n u c l e i s i t u a t e d m a i n l y i n domain w a l l s . I t has been s u g g e s t e d by Weger(1962) t h a t t h e dominant r e l a x a t i o n mechanism i s t h a t due t o t h e 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 . To e s t i m a t e t h e o r d e r o f magni-tu d e o f t h i s r e l a x a t i o n c o n s i d e r a s m a l l 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, c o n s i s t i n g o f two e q u a l and o p p o s i t e domains w i t h a 180 degree domain w a l l between them. Imagine a l s o t h a t t h e o n l y low l y i n g w a l l e x c i t a t i o n i s a u n i f o r m d i s p l a c e m e n t . I f t h e w a l l s h i f t s by a d i s t a n c e x, a n e t m a g n e t i z a t i o n M-3M gx/d i s c r e a t e d . The d e m a g n e t i z i n g energy r e s u l t i n g from t h i s m a g n e t i z a t i o n i s 3 E = | M 2(2| ) (2.21) where N i s a d e m a g n e t i z i n g f a c t o r o f o r d e r 4^/3. A p p l y i n g t h e e q u i p a r t i t i o n theorem an average energy -jkT i s a s c r i b e d f o r each degree o f freedom, t h u s E = i k T s i n c e h e r e o n l y one degree o f freedom i s c o n s i d e r e d . The mean s q u a r e d d i s p l a c e m e n t i s t h u s g i v e n by < x2>= (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 <P ) i s random, so t h a t one must average o v e r a l l o r i e n t a t i o n s . F o r a domain w a l l w h i c h makes an a n g l e a? w i t h H^, t h e e f f e c t i v e component o f i s H^cos(<p ) . The m o t i o n o f t h e domain w a l l t h r o u g h a d i s t a n c e £x a t a p o s i t i o n x, d e f i n e d i n domain w a l l w i d t h u n i t s from t h e c e n t r a l p l a n e o f t h e w a l l , c o r r e s p o n d s t o a r o t a t i o n o f e l e c t r o n i c s p i n s t h r o u g h an a n g l e xd^/dx. The v a r i a t i o n d£/dx i s p r o p o r t i o n a l t o ( c o s h ( x ) ) ^. Thus t h e enhancement f a c t o r as a f u n c t i o n o f x and a n g l e <p i s g i v e n by I f we now t a k e i n t o a c c o u n t t h e d i s t r i b u t i o n i n a n g l e s and the v a r i a t i o n o f f\ w i t h x, t h e e x p r e s s i o n f o r t h e FID a m p l i t u d e becomes S =• C n s i n (jfqHjT) (4.1) (x,q>) = 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<Tlr^2» s e c h 2(T' < 5 - 1 2 ' 2 K i s r e l a t e d t o t n e a n i s o t r o p y f i e l d , H , by KS = g/^SH , where <g i s t h e Bohr magneton, and g i s t h e 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 . F i s c h e r ( 1 9 6 6 ) has d e t e r m i n e d g t o be 2.4 f o r Fe i n F e 2 B . S i n c e t h e r e i s no d a t a a v a i l a b l e f o r F e 2 P t h i s v a l u e w i l l be used. A c c o r d i n g t o Meyer and C a d e v i l l e (1962) S=1.32 and H a=23,000 oe.. K i s t h e n found t o be 4 . 1 8 x l 0 ~ 1 6 e r g s . 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 . T h i s has n o t been measured f o r F e 2 P . Gossard(1960) measured P f o r Co and found i t t o be " 1 0 1 0 s e c ~ 1 . I t w i l l be assumed t o be o f t h e same o r d e r f o r F e 2 P a t 4.2 K. From d a t a p r e s e n t e d i n t a b l e I I I o f K i t t e l and G a i t (1956) t h i s seems t o be a r e a s o -n a b l e a s s u m p t i o n . I n o r d e r t o e s t i m a t e J , a m o l e c u l a r f i e l d approach i s u s e d . Hence kT = SyWeHm c ' 8 m where H = *&I m /»B z i s t h e number o f n e a r e s t n e i g h b o u r s . F o r i r o n i n F e 2 P z i s 8, T c i s about 300 K, and S i s 1.32. J i s t h e n e s t i m a t e d -15 t o be 3x10 e r g s . The w a l l r e s o n a n c e f r e q u e n c y , A,- i s n o t known f o r F e 2 P b u t can be e s t i m a t e d i n t h e f o l l o w i n g way; r e c a l l i n g e q u a t i o n (2.19) t h e enhancement f a c t o r i s g i v e n by 86 2 H nM ssech(|)  T\ — ~ ~ 7y ~ 7~ =j—To (5.13) From t h i s e q u a t i o n t h e v a l u e o f can be deduced u s i n g t h e c 2 —1 measured v a l u e o f , t h e r e l a t i o n s h i p m o = {2^Y ) ( K i t t e l w and G a i t , 1 9 5 6 ) , where Y i s t h e e l e c t r o n g y r o m a g n e t i c r a t i o , 2 2 and t h e a s s u m p t i o n t h a t ((3/m w)tJ 0 i s s m a l l compared t o A - c j 0 ' . F o r a t y p i c a l f e r r o m a g n e t /^m = l O ^ s e c 1 . ^ has been d e t e r -m i n e d by F i s c h e r ( 1 9 6 6 ) f o r Fe i n Fe-jB t o be 2.4 . S i n c e t h e r e i s no d a t a a v a i l a b l e f o r Fe„P t h i s v a l u e w i l l be used. M i s 2 s about 700 oe., S i s o f t h e o r d e r o f 200 A°. U s i n g t h e measured v a l u e o f Oo f o r F e ( I ) i n e q u a t i o n ( 5 . 1 3 ) , w i t h x=0, y i e l d s 2 „ , „20 -1 A = 2.3x10 sec U s i n g e q u a t i o n (5.12) one o b t a i n s f o r t h e r e l a x a t i o n t i m e s a s s o c i a t e d w i t h t h e F e ( I ) s i t e and t h e P ( I I ) s i t e a t 1.5 K T^=~3 msec, and ~. 2 msec, r e s p e c t i v e l y . The o b s e r v e d v a l u e s a r e 1 msec, and .6 msec, r e s p e c t i v e l y . Thus i t appears t h a t t h e r m a l f l u c t u a t i o n s can a c c o u n t f o r t h e magnitude o f t h e r e l a x -a t i o n t i m e s a s s o c i a t e d w i t h t h e domain w a l l n u c l e i . S i n c e P i s i n g e n e r a l t e m p e r a t u r e dependent ( K i t t e l and G a i t , t a b l e I I I ^ , i t d e c r e a s e s w i t h t e m p e r a t u r e , t h e r e l a x a t i o n r a t e i s n o t e x p e c t e d t o be p r o p o r t i o n a l t o t e m p e r a t u r e . T h i s i s i n a c c o r -dance 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 s . I f . we now compare e q u a t i o n s (5.12) and (5.13) we see t h a t T^ i s 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 s q uare o f t h e enhancement f a c t o r . S i n c e t h e enhancement f a c t o r f o r P ( I ) n u c l e i i s about 87 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 , one e x p e c t s t h a t 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 f o r t h e P ( I ) n u c l e i would be about o n e - n i n t h t h a t f o r t h e P ( I I ) n u c l e i . T h i s i s i n good agreement 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 s . 2 From e q u a t i o n (5.12) we can w r i t e 1/T-^ 1/T^ sech (x/<5 ) , t h a t i s t o s a y , t h e r e w i l l be a d i s t r i b u t i o n o f 1 s w i t h i n t h e domain w a l l s . The s h o r t e s t t i m e b e i n g f o r x=0, i . e . a t th e c e n t e r o f t h e w a l l . Thus 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 can be a c c o u n t e d f o r . (b) T r a n s v e r s e R e l a x a t i o n Times I n o r d e r t o comment on t h e s e r e s u l t s i t i s u s e f u l t o r e c a l l e q u a t i o n (1.17) From t h i s e q u a t i o n we see t h a t i n t h e absence o f low f r e q u e n c y f i e l d f l u c t u a t i o n s t h e t r a n s v e r s e r e l a x a t i o n r a t e i s g i v e n by 1/2T 1. T h i s i s o b s e r v e d f o r t h e P ( I ) n u c l e i . The P ( I I ) r e s u l t s i n d i c a t e t h a t a t 77 K t h e t r a n s v e r s e r e l a x a t i o n has a l a r g e c o n t r i b u t i o n from t h e T^ p r o c e s s e s . T h i s i s r e f l e c t e d by t h e power dependence and t h e d i s t r i b u t i o n i n T2's. The r e l a -t i v e l y r a p i d and e x p o n e n t i a l r e l a x a t i o n f o r t h e F e ( I ) n u c l e i i n d i c a t e s t h a t t h e T, c o n t r i b u t i o n i s a m i n o r one. 2 (5.14) 1 88 CHAPTER VI F e 3 P (a) I n t r o d u c t i o n The m a g n e t i c p r o p e r t i e s o f Fe.jP have been t h e s u b j e c t o f p r e v i o u s i n v e s t i g a t i o n s . I t s C u r i e p o i n t was f i r s t d e t e r -mined by Le C h a t e l i e r and L o l o d g i n e (1909) t o be i n t h e range 706 K t o 717 K. More r e c e n t l y Meyer and C a d e v i l l e (1962) have s t u d i e d t h e b u l k m a g n e t i c p r o p e r t i e s o f Fe^P. They r e p o r t e d a C u r i e p o i n t o f 714 K and a s a t u r a t i o n m a g n e t i z a t i o n a t room t e m p e r a t u r e o f 1025 oe. . They deduced a v a l u e o f 1.84/^0 f o r the average m a g n e t i c moment p e r i r o n atom. L a t e r measurements by F r u c h a r t e t a l . (1964) y i e l d e d a C u r i e t e m p e r a t u r e o f 6 86 K and an average m a g n e t i c moment o f 1.91yJ9 p e r i r o n atom. R u n d q u i s t ( 1 9 6 2 ) has d e t e r m i n e d t h e c r y s t a l s t r u c t u r e o f Fe^P. I t s c r y s t a l s t r u c t u r e i s a t e t r a g o n a l (DOe) t y p e ( P e a r s o n , 1 9 6 7 ) , w i t h space group 14", a=9.107 A° and c=4.46 A°. I t has 32 atoms p e r u n i t c e l l . There a r e t h r e e 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 ) , F e ( I I ) , and F e ( I I I ) , and one phosphorous s i t e . F e ( I ) has two phosphorous n e a r e s t n e i g h b o u r s , F e ( I I ) has f o u r and F e ( I I I ) has t h r e e . The c r y s t a l s t r u c t u r e i s i l l u s t r a t e d i n f i g u r e 6-1. ." • . : Mossbauer i n v e s t i g a t i o n s o f Fe^P by B a i l e y and Duncan (1966) and Wa p p l i n g e t a l . (1971) have i n d i c a t e d t h a t t h e ma g n e t i c s t r u c t u r e o f Fe^P i s not as s i m p l e as i t s c r y s t a l s t r u c t u r e . B a i l e y and Duncan deduced h y p e r f i n e f i e l d s o f 89 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 90 295 koe. , 265 koe. and 185 koe. f o r t h e t h r e e i r o n s i t e s a t 90 K. Wapplin g e t a l . found t h a t a t l e a s t f o u r m a g n e t i c a l l y n o n - e q u i -v a l e n t t y p e s o f i r o n atoms c o u l d be d i s t i n g u i s h e d from t h e Mossbauer spectrum. The c o r r e s p o n d i n g h y p e r f i n e f i e l d s , a t 300 K, a r e 278.7 koe., 251.7 koe., 228.4 koe., and 175.6 koe.. The quoted a c c u r a c y i s + 0.1 koe.. A 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 i s t h e d e t e r m i n a 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 s s o c i a t e d w i t h t h e v a r i o u s s i t e s as t h e s e r e s u l t s c o u l d h e l p 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 o f Fe^P. F o r t h e p r e s e n t s t u d i e s two samples were employed, a comm e r c i a l one and a 'home-made' one. The 'home-made sample was p r e p a r e d i n t h e same manner as t h e F e 2 P sample ( c h a p t e r 5 s e c t i o n a ) . The c r y s t a l s t r u c t u r e s o f t h e samples were v e r i f i e d by X-ray powder a n a l y s i s . The samples were a l s o s u b j e c t e d t o c h e m i c a l a n a l y s i s . The com m e r c i a l sample a n a l y s e d as Fe-, ,,P, t h e o t h e r as F e 0 n ^ P . 3.16 3.06 (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 Resonances 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 -meter d e s c r i b e d i n c h a p t e r 3, w h i c h was swept o v e r t h e range 10-200 MHz. Bot h samples were used and t h e same N.M.R. spe c t r u m was o b t a i n e d . Three s e t s o f d o u b l e t s were o b s e r v e d ; one was o n l y p a r t i a l l y r e s o l v e d t h e o t h e r two were a l m o s t c o m p l e t e l y r e s o l v e d . R e p r e s e n t a t i v e t r a c e s o f t h e o b s e r v e d s p e c t r a a t 1.5 K a r e g i v e n i n f i g u r e s 6-2, 6-3 and 6-4. The r e s o n a n c e s o c c u r a t 41.7 MHz, 37.2 MHz, 34.5»MHz, 27.5 MHz and 24.8 MHz. in €\J o CVJ ^ a o C. U Ci) ! G •H OJ cn r-i (1) •H fa 0 U 0) N CN I •H fa CM KD FREQUENCY (MHz) F i g . 6-3 Zero F i e l d Spin-echo Spectrum of F e 3 P a t 1.5 K F R E Q U E N C Y ( M H z ) F i g . 6-4 Zero F i e l d S p i n - e c h o S p e c t r u n o f F e 3 P a t 1.5 K 94 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 t h e r e f e r e n c e s i g n a l from a v . h . f . s i g n a l gene-r a t o r , t h e o u t p u t f r e q u e n c y o f w h i c h was m o n i t o r e d by a f r e q f r e q u e n c y c o u n t e 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 + .2 MHz. Poor s i g n a l t o n o i s e r a t i o s p r e c l u d e d measurements a t t e m p e r a t u r e s g r e a t e r t h a n 1.5 K. ( 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 . Due t o t h e T ^ ' n i d r l p c s v t i t " 1 0 i t was n o t p o s s i b l e t o s t u d y t h e b e h a v i o u r o f t h e FID, 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 i o f t h e r . f . f i e l d s t r e n g t h . I n f i g u r e 6-5 i s shown a p l o t o f t h e s p i n echo a m p l i t u d e f o r t h e 41.7 MHz. l i n e 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 a t 1.5 K. The two p u l s e sequence f o r s t i m u l a t i n g t h e echo used p u l s e l e n g t h s o f 1 and 2 m i c r o s e c o n d s f o r t h e 90 and 180 degree p u l s e s r e s p e c t i v e l y . ( i i i ) . N u c l e a r R e l a x a t i o n Times 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 2, were measured a t 1.5 K f o r t h e 41.7 MHz l i n e . T y p i c a l 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 c u r v e s a r e g i v e n i n f i g u r e s 6-6 and 6-7 r e s p e c t i v e l y . As was 95 0 .1 ,2 .3 M 3 .6 .7 .8 .9 1.0 1.1 1.2 1.3 U H j I N G A U S S F i g . 6-5 H 1 dependence o f the Fe(I) spin-echo amplitude i n Fe^P at 1.5 K 96 97 98 t h e c a s e f o r F e 2 P a 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 and a power dependence o f t h e r e l a x a t i o n t i m e s i s o b s e r v e d . The ob s e r v e d T^'s range from 2.4 + .2 msec, t o 14 + 1 m s e c . The t r a n s v e r s e r e l a x a t i o n c u r v e s a r e e x p o n e n t i a l and y i e l d T 2 ' s o f 4.8 + .4 and 15 + 1.5 m s e c a t power l e v e l s o f 0 db and -10 db r e s p e c t i v e l y . (c) D i s c u s s i o n o f t h e E x p e r i m e n t a l R e s u l t s ( i ) Zero F i e l d Resonances S i n c e t h e average m a g n e t i c moment per i r o n atom i n Fe^P, 1.84/Jg, i s l a r g e r t h a n t h a t i n F e 2 P , 1.32yU 0, i t i s r e a s o n a b l e t o e x p e c t t h a t t h e h y p e r f i n e f i e l d a t t h e P n u c l e u s and hence i t s r e s o n a n c e f r e q u e n c y i n Fe^P w i l l be g r e a t e r t h a n t h e r e s o -nance f r e q u e n c y i n F e 2 P , i . e . g r e a t e r t h a n 77 MHz.. F o r t h i s r e a s o n i t i s l i k e l y t h a t a l l t h e o b s e r v e d r e s o n a n c e a r e due t o t h e i r o n n u c l e i . The o b s e r v e d r e s o n a n c e f r e q u e n c i e s 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 304 + 2 koe., 271 + 2 koe., 251 + 2 koe., 200 + 1 koe., and 180 + 1 koe.. S i n c e t h e s e f a l l i n t h e range o f t h e Mossbauer r e s u l t s p r e s e n t N.M.R. r e s u l t s a r e n o t i n c o n -s i s t e n t w i t h t h e Mossbauer r e s u l t s . I t i s c l e a r however t h a t t h e Mossbauer r e s u l t s are n o t u s e f u l . Our N.M.R. r e s u l t s s u g g e s t t h a t t h e Mossbauer d a t a s h o u l d be r e i n t e r p r e t e d assuming t h a t t h e r e a r e 5 m a g n e t i c a l l y n o n - e q u i v a l e n t i r o n s i t e s . The a ssignment o f t h e o b s e r v e d h y p e r f i n e f i e l d s t o p a r t i -c u l a r c r y s t a l l o g r a p h i c s i t e s i s c o m p l i c a t e d by the f a c t t h a t t h e r e a r e o n l y t h r e e c r y s t a l l o g r c f 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 . S i n c e t h e r e a r e t h r e e s e t s o f d o u b l e t s i t i s r e a s o n a b l e t o 99 a s s i g n each s e t t o one i r o n s i t e . The average h y p e r f i n e f i e l d s f o r t h e d o u b l e t s a r e 304 koe., 261 koe. and 190 koe.. I f we assume t h a t t h e i r o n h y p e r f i n e f i e l d s a r e 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 s s o c i a t e d w i t h t h e p a r t i c u l a r i r o n s i t e we can deduce t h e f o l l o w i n g m a g n e t i c moments; 2.21/^, 1.91/^ 0, and 1.38f9. The average moment i s l e s s t h a n t h a t o b s e r v e d i n p u re i r o n . . T h i s s u g g e s t s t h a t t h e r e i s e l e c t r o n d o n a t i o n from t h e phosphorous v a l e n c e band t o t h e i r o n 3-d bands. A s i m p l e e l e c t r o n d o n a t i o n model was p r e s e n t e d i n c h a p t e r 5 s e c t i o n a - i i , t h i s w i l l be f o l l o w e d h e r e . Each P i s assumed t o donate 2.6 e l e c t r o n s w h i c h a r e s h a r e d among i t s 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 . Then f o r F e ( I ) w h i c h has two P n e a r e s t n e i g h b o u r s t h e model p r e d i c t s ^ F e ( I ) = 2.7 - 2x2.6/9 = 2.12yUe (6.1) Fo r F e ( I I ) w h i c h has f o u r P n e a r e s t n e i g h b o u r s we g e t ^ p e ( n ) = 2.7 - 4x2.6/9 = 1.54yU0 (6.2) F o r F e ( I I I ) w h i c h has t h r e e P n e a r e s t n e i g h b o u r s we g e t ^ ( I I l T 2.7 - 3x2.6/9 = 1.83/^g (6.3) On t h e b a s i s o f t h e s e r e s u l t s we can a s s i g n t h e 41.7 MHz l i n e t o t h e F e ( I ) s i t e , t h e 36 MHz d o u b l e t t o t h e F e ( I I I ) . s i t e and th e 26 MHz d o u b l e t t o t h e F e ( I I ) s i t e . The p h y s i c a l r e a s o n f o r t h e p r e s e n c e o f t h e d o u b l e t s i s n o t y e t u n d e r s t o o d . There 100 are at present neutron s c a t t e r i n g experiments underway (Wilkinson,1971) which may help t o c l a r i f y the s i t u a t i o n . P r e l i m i n a r y r e s u l t s show t h a t Fe^P i s not simple magneti-c a l l y . Although the s t a t i s t i c s are poor i t does not seem t h a t j u s t three magnetic s t a t e s f i t the data. A simple estimate of the expected P h y p e r f i n e f i e l d , and hence the resonance frequency, can be made i f we assume t h a t the P 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 the sum of the nearest neighbour i r o n moments. This sum f o r Fe^P i s 15.72, f o r Fe 2P i t i s 11.88. Taking the constant of p r o p o r t i o n a l i t y to be the same f o r both Fe^P and Fe^P the expected resonance frequency should be about 115 MHz. However, no resonance was observed above 41.7 MHz. I t i s p o s s i b l e t h a t the P resonance was so broad as t o make i t undetectable on the apparatus used. Otherwise the resonance i s out of the frequency range swept by the spectrometer. ( i i ) Enhancement Factors The curve of the s p i n echo amplitude versus r . f . f i e l d s t r e n g t h given i n f i g u r e 6-5 bears a q u a l i t a t i v e resemblance to the n i c k e l FID curve, f i g u r e 4-1. The dashed l i n e i n f i g u r e 6-5 was obtained employing the drumhead model w i t h a maximum enhancement f a c t o r of 14000. I t i s evident t h a t the model does d e s c r i b e the general behaviour but does not g i v e a good account o f the o b s e r v a t i o n s . Using equation (3.2) an average enhancement f a c t o r can be deduced from the p o s i t i o n 101 o f t h e maximum by H. n (6.4) T h i s g i v e s n = 4400. A c c o r d i n g t o e q u a t i o n (2.20) t h e enhancement f a c t o r due t o domain w a l l m o t i o n i s g i v e n by 4M 5 (6.5) s F o r F e 0 P M i s about 10 oe. and 6 i s t h e o r d e r o f 300 A. 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 H = 300 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 o f 7000 w h i c h 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 o b s e r v e d v a l u e . a c c o u n t e d f o r . The enhancement f a c t o r f o r domain n u c l e i i n Fe^P i s about 50 so t h a t domain n u c l e i a r e not e x p e c t e d t o make a s i g n i f i c a n t c o n t r i b u t i o n t o t h e o b s e r v e d s i g n a l . ( i i i ) N u c l e a r S p i n R e l a x a t i o n Times S i n c e t h e domain n u c l e i do n o t 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 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 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 n 102 r a t e i s g i v e n by 1 = u ^ k T 1 6 T T J S (6.6) F o r F e 0 P K i s -8x10 -17 e r g s , S=1.86 and J= 3x10 -15 e r g s . P has not been d e t e r m i n e d f o r Fe^P so i t i s t a k e n t o be about l O ^ s e c 1 as f o r Fe,,P. The w a l l r esonance f r e q u e n c y i s e s t i -mated as f o r t h e F e 2 P case ( c h a p t e r 5-c s e c t i o n i v ) . The : resonance f r e q u e n c y i s e s t i m a t e d t o be ~ 4 . 5 x l 0 1 ( ^ s e c U s i n g e q u a t i o n (6.6) one o b t a i n s T ^ = 4 m i l l i s e c o n d s . The s h o r t e s t o b s e r v e d T^ i s 2.4 m i l l i s e c o n d s . I t i s seen t h e n 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 can ac c o u n t f o r th e o b s e r v e d r e l a x a t i o n t i m e s . The s h o r t e s t t r a n s v e r s e r e l a x a t i o n t i m e i s , w i t h i n e x p e r i -m e n t a l e r r o r , - t w i c e t h e s h o r t e s t l o n g i t u d i n a l r e l a x a t i o n t i m e . T h i s s u g g e s t s t h a t t h e dominant c o n t r i b u t i o n t o t h e t r a n s v e r s e r e l a x a t i o n r a t e i s from t h e s p i n - l a t t i c e p r o c e s s e s . T h i s c o n t r i b u t i o n i s r e f l e c t e d i n t h e power dependence o f t h e t r a n s v e r s e r e l a x a t i o n . 103 CHAPTER VII CONCLUSIONS The p u l s e d N.M.R. technique has proved to be u s e f u l i n the study o f the dynamic and s t a t i c p r o p e r t i e s o f the hyper-f i n e i n t e r a c t i o n s i n N i , Fe 2 P and Fe^P. The pr e s e n t r e s u l t s i n d i c a t e t h a t the motion o f domain w a l l s i n n i c k e l may be l i k e n e d to t h a t o f a c i r c u l a r membrane pinned at i t s c i r c u m -f e r e n c e . T h i s 'drumhead' model accounts f o r the g e n e r a l behaviour o f the exp e r i m e n t a l r e s u l t s but does not g i v e good agreement w i t h the r e s u l t s i n F e 2 P and Fe^P. T h i s suggests t h a t the motion of domain w a l l s i n these systems i s more com p l i c a t e d than t h a t o f a v i b r a t i n g membrane. The r e l a x a t i o n o f the domain w a l l n u c l e i i n Fe 2 P and Fe.jP can be a t t r i b u t e d to thermal f l u c t u a t i o n s o f the domain w a l l s . T h i s assumption accounts f o r both the d i s t r i b u t i o n and magni-tude of the observed l o n g i t u d i n a l r e l a x a t i o n t i m e s . We have determined the h y p e r f i n e f i e l d s a s s o c i a t e d w i t h 57 the v a r i o u s Fe s i t e s i n Fe 2P and F e 3 P . These r e s u l t s suggest t h a t the bonding i n these systems i n v o l v e s d o n a t i o n o f phospho-rous v a l e n c e e l e c t r o n s to the i r o n d bands wi t h a r e s u l t a n t d e p r e s s i o n o f the i r o n moments from the pure i r o n v a l u e . The magnetic s t r u c t u r e o f F e 2 P was r e a d i l y determined. The s i t u a t i o n i n Fe^P i s not so c l e a r . There appear t o be s i x m a g n e t i c a l l y n o n - e q u i v a l e n t i r o n s i t e s w h i l e t h e r e are o n l y 104 t h r e e 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 . The r e a s o n f o r t h i s i s not y e t u n d e r s t o o d . N e u t r o n d i f f r a c t i o n e x p e r i -ments may h e l p t o c l a r i f y the m a g n e t i c s t r u c t u r e o f Fe^P. The p r e s e n t measurements show the u s e f u l n e s s o f t h e N.M.R. r e s u l t s as compared t o t h e Mossbauer measurements. P r e v i o u s Mossbauer measurements o f F e 2 P and Fe^P have e x h i b i t e d d i s a -greement i n t h e magnitude o f t h e h y p e r f i n e f i e l d s . I n t h e case o f Fe^P the Mossbauer measurements a l s o e x h i b i t d i s a -greement i n t h e number o f m a g n e t i c a l l y d i s t i n c t i r o n s i t e s . These d i s a g r e e m e n t s can be a t t r i b u t e d t o the c o m p l i c a t e d u n f o l d -i n g p r o c e d u r e r e q u i r e d t o e x t r a c t h y p e r f i n e f i e l d s f r o m t h e Mossbauer,-spectrum. To qach h y p e r f i n e f i e l d t h e r e c o r r e s p o n d s i x l i n e s so t h a t when s e v e r a l h y p e r f i n e f i e l d s a r e b e i n g c o n s i -d e r e d the u n f o l d i n g p r o c e d u r e can become v e r y c o m p l i c a t e d . a n d t h e r e s u l t i s by no means unambiguous. The N.M.R. e x p e r i m e n t though i n p r i n c i p l e l e s s s e n s i t i v e t h a n the Mossbauer e x p e r i m e n t has t h e advantage o f y i e l d i n g an unambiguous r e s u l t as i t y i e l d s I t i s n o t c l e a r w h i c h mechanisms a r e 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 s a t t h e phosphorous n u c l e i i n F e 2 P and F e 3 P . The p o s i t i v e s i g n o f t h i s f i e l d i n F e 2 P i s c o n s i s t e n t w i t h e x p e r i m e n t a l o b s e r v a t i o n s and t h e o r e t i c a l c o n s i d e r a t i o n s t h a t p 3 elements d i s s o l v e d i n i r o n s h o u l d have p o s i t i v e h y p e r -f i n e f i e l d s . The t h e o r e t i c a l c o n s i d e r a t i o n s assume t h a t 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 i s t h e dominant mechanism. 31 I t i s u n f o r t u n a t e t h a t t h e P reso n a n c e i n F e 3 P was n o t ob s e r v e d as i t c o u l d have h e l p e d t o c l a r i f y t h e mechanisms 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 s . 105 BIBLIOGRAPHY Abragam, A. 1961, The P r i n c i p l e s o f N u c l e a r Magnetism ( O x f o r d U n i v e r s i t y P r e s s ) A n d e r s o n , P.W. and C l o g s t o n , A.M. 1961, B u l l . Am. Phy s . 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