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Submitted on 1 Jan 1978
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NUCLEAR MAGNETIC ORDERING
A. Abragam, V. Bouffard, M. Goldman, Y. Roinel
To cite this version:
A. Abragam, V. Bouffard, M. Goldman, Y. Roinel. NUCLEAR MAGNETIC ORDERING. Journal de
Physique Colloques, 1978, 39 (C6), pp.C6-1436-C6-1443. �10.1051/jphyscol:19786584�. �jpa-00218076�
JOURNAL DE PHYSIQUE
Colloque
C6,supplkment au no
8,Tome
39,aotir
1978,page
~ 6 - 1 4 3 6NUCLEAR MAGNETIC ORDERING
A. Abragam, V. Bouffard, M.
oldm man+
and Y. BoinelC.E.N/SACLAY, B . P . N02, 91190 Cif sur Y v e t t e , F r a n c e
+ CoZZege de F r a n c e
R6sumd.- AprPs un expos6 d e s concepts e t d e s mdthodes u t i l i s d s pour l a p r o d u c t i o n e t l ' o b s e r v a t i o n de l ' o r d r e magndtique dans l e s systzmes de s p i n s n u c l b a i r e s , nous p r s s e n t o n s d e s r 6 s u l t a t s prdlimi- n a i r e s de d i f f r a c t i o n d e n e u t r o n s s u r un 6 t a t a n t i f e r r o m a g n e t i q u e n u c l C a i r e de l ' h y d r u r e d e l i t h i u m , p r o d u i t par d 6 s a i m a n t a t i o n a d i a b a t i q u e dans l e r d f d r e n t i e l t o u r n a n t .
A b s t r a c t . - A f t e r a d e s c r i p t i o n of t h e concepts and methods used f o r t h e p r o d u c t i o n and o b s e r v a t i o n of magnetic o r d e r i n g i n systems of n u c l e a r s p i n s , we p r e s e n t p r e l i m i n a r y r e s u l t s of n e u t r o n d i f f r a c - t i o n on a n u c l e a r a n t i f e r r o m a g n e t i c s t a t e of l i t h i u m h y d r i d e , produced by a d i a b a t i c demagnetization i n t h e r o t a t i n g frame.
1. PRODUCTION AND OBSERVATION OF NUCLEAR MAGNETIC r a l r e p o r t s a t conferences on NMR o r Magnetism t h i s
ORDER.
-
i s t h e f i r s t time t h a t n u c l e a r magnetic o r d e r i n g i s1.1. Introduction.- The s t u d y of nuclear a t a Low Temperature c o n f e r e n c e . he con- tism s t a r t e d in late 1945 with the f i r s t observation c e p t s and methods of magnetic resonance a p p l i e d t o of n u c l e a r magnetic resonance i n b u l k m a t t e r by n u c l e a r magnetic o r d e r i n g a r e s u f f i c i e n t l y d i f f e - P u r c e l l , Pound and Torrey a t Harvard and Bloch, r e n t from t h o s e used by t h e rank and f i l e low tem- Packard and Han'sen a t S t a n f o r d . I t immediately p e r a t u r e p h y s i c i s t t o w a r r a n t an i n t r o d u c t i o n t o spread a l l over t h e world and t h i r t y t h r e e y e a r s t h e second p a r t of t h i s t a l k : t h e r e r e c e n t r e s u l t s l a t e r i t i s s t i l l going s t r o n g . Besides i t s many w i l l b e p r e s e n t e d and c o n f r o n t e d t o t h e t h e o r e t i c a l o t h e r a t t r a c t i o n s , t h e r e i s l i t t l e doubt t h a t t h e p r e d i c t i o n s .
s t u d y of n u c l e a r paramagnetism by t h e methods of magnetic resonance owes much of i t s s u c c e s s t o t h e b e a u t i f u l s i m p l i c i t y of i t s t e c h n i q u e s . A magnet, and r f c i r c u i t w i t h a g e n e r a t o r , and a sample i s a l l t h a t i s needed and d e s p i t e c o n s i d e r a b l e sophis- t i c a t i o n and c o m p l i c a t i o n of t h e techniques i n l a - t e r y e a r s i t remains b a s i c a l l y v e r y simple.
By c o n t r a s t t h e s t u d i e s of n u c l e a r magnetic o r d e r i n g , ferromagnetism and antiferromagnetism, undertaken i n t h e l a b o r a t o r y of Nuclear Magnetism a t Saclay -1.irteen y e a r s ago, never had s o f a r any c o m p e t i t i o n from elsewhere. Whether a boon o r a c u r s e , t h i s monopoly follows a t l e a s t i n p a r t from t h e f a c t t h a t t o produce and t o observe n u c l e a r ma- g n e t i c o r d e r i n g i s n o t t h e e a s i e s t t h i n g i n t h e
Before going any f u r t h e r i t should b e s p e c i - f i e d t h a t two t o p i c s a r e excluded from t h i s s u r v e y : The f i r s t i s t h e n u c l e a r o r d e r i n g i n s o l i d 3 ~ e , which i s covered e x t e n s i v e l y elsewhere, i n t h i s Conference.
The seond s u b j e c t i s t h a t of compounds where l a r g e induced e l e c t r o n i c magnetism i s r e s p o n s i b l e f o r t h e magnetic behaviour of t h e n u c l e i . We c a l l such s t u d i e s "pseudo-nuclear magnetism" ( n o t t o b e confused w i t h n u c l e a r pseudo-magnetism t o b e d e f i - ned l a t e r o n ) . I n any c a s e t h e r e i s an o p e r a t i o n a l d i s t i n c t i o n between our work and t h e s e two t o p i c s : a gap of t h r e e o r d e r s of magnitude i n t h e c r i t i c a l temperatures.
world
.
1.2. P r o d u c t i o n of n u c l e a r magnetic o r d e r i n g :The purpose of t h e f i r s t p a r t of t h i s t a l k i s ADRF and DNP.- The c r i t i c a l temperature Tc f o r ma- t h e following. A new s t a g e has been reached recen- g n e t i c o r d e r i n g of n u c l e i through t h e i r d i p o l a r t l y w i t h t h e o b s e r v a t i o n of long r a n g e n u c l e a r ma- i n t e r a c t i o n s , i s g i v e n roughly by kgT; = y f i % where g n e t l c o r d e r by n e u t r o n d i f f r a c t i o n and t h i s seems H i s t h e l o c a l n u c l e a r magnetic f i e l d , of t h e o r -
L
t o b e a good time t o s k e t c h t h e h i s t o r i c a l develpp- d e r of a few g a u s s , and y t h e n u c l e a r gyromagnetic ment of i d e a s and f a c t s t h a t have l e d t o t h e pre- r a t i o , and i t f a l l s i n t o t h e m i c r o k e l v i n range. The s e n t s i t u a t i o n . f i r s t g o a l i s t h e n t h e p r o d u c t i o n of such tempera-
Although o v e r t h e y e a r s t h e r e have been seve- t u r e s .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786584
The most d i r e c t method f o r t h e c o o l i n g of nu- c l e a r moments i s t h e i r a d i a b a t i c demagnetization from an i n i t i a l f i e l d H a s high a s p o s s i b l e . The f i n a l temperature Tf i s given i n o r d e r of magnitude by Tf = To HL/Ho. A t p r e s e n t , thanks t o t h e progress of d i l u t i o n r e f r i g e r a t o r s , and of superconducting s o l e n o i d s i t i s p o s s i b l e t o produce i n i t i a l tempe- r a t u r e s i n t h e range of a few m i l l i k e l v i n s i n f i e l d s of t h e o r d e r of t e n t e s l a s , o r more, l e a d i n g hope- f u l l y t o f i n a l temperatures i n t h e r e q u i r e d micro- k e l v i n range. Superconducting magnetometers (squids) a r e a v a i l a b l e f o r n u c l e a r magnetic measurements i n v e r y low a p p l i e d f i e l d s .
T h i s was not t h e method we used f o r t h e v e r y good r e a s o n t h a t a t t h e s t a r t of our s t u d i e s o r in- deed d u r i n g t h e f i r s t s u c c e s s f u l o b s e r v a t i o n of nu- c l e a r antiferrornagnetism i n 1969, we had a t o u r d i s - p o s a l an i r o n magnet with a maximum f i e l d of 2 . 7 T, a 3 ~ e r e f r i g e r a t o r w i t h a temperature of 0 . 3 K , and no squid. On t h e o t h e r hand we had good equipment f o r observing NMR i n high f i e l d s .
A) A D R F.- The absence of measuring d e v i c e i n ve- r y low f i e l d made i t imperative t o be a b l e t o a c h i e - ve t h e a d i a b a t i c n u c l e a r demagnetization w h i l e r e - maining a l l t h e time i n a high magnetic f i e l d . There i s no c o n t r a d i c t i o n e i t h e r i n terms s i n c e t h e word demagnetization means r e d u c t i o n of t h e magnetization, n o t of t h e f i e l d , o r i n f a c t , f o r such a demagneti- z a t i o n can be e a s i l y achieved i n p r a c t i c e , u s i n g an r f f i e l d . The p r i n c i p l e of t h i s o p e r a t i o n c a l l e d ADRF ( a d i a b a t i c demagnetization i n t h e r o t a t i n g frame) i s b e s t understood u s i n g t h e f a m i l i a r concept of t h e r o t a t i n g frame.
The behaviour of a system of n u c l e a r s p i n s i n a l a r g e d c f i e l d Ho and a s m a l l n e a r l y r e s o n a n t r f f i e l d of amplitude H I , r o t a t i n g a t a frequency w i n t h e neighbourhood of t h e Larmor frequency yH of t h e s p i n s , i n a p l a n e p e r p e n d i c u l a r t o Ho, i s des- c r i b e d most simply i n a frame r o t a t i n g arround H w i t h t h e a n g u l a r v e l o c i t y w. I n t h a t frame t h e nu- c l e a r s p i n s b e h a v e a s i f t h e y were "seeing" s t a t i c f i e l d s only : a dc f i e l d p a r a l l e l t o Ho b u t of am- p l i t u d e AH = Ho
-
and a dc f i e l d of amplitude HI a tY r i g h t a n g l e t o i t .
The Q i p o l a r Hamiltonian of t h e s p i n s which c a n be w r i t t e n
i s r e p l a c e d i n t h e r o t a t i n g frame by t h e so c a l l e d t r u n c a t e d Hamiltonian where a l l elements of ( 1 ) which do n o t commute w i t h t h e Zeeman Hamiltonian :
- YH
H -1 =- YMH
I a r e thrown o u t :-0
-
0 zwhere
eij
i s t h e a n g l e of t h e u n i t v e c t o r ? -i j w i t h t h e dc f i e l d Ho. I n a c r y s t a l t h e t r u n c a t e d Hamilto- n i a na$lD
depends on t h e o r i e n t a t i o n of t h e d c f i e l d H w i t h r e s p e c t t o t h e c r y s t a l axes. The Hamiltonian of t h e system can t h e n be w r i t t e n :=
-
y6 AH Iz- ~b
Ix + XID ( 3 )This i s t h e Hamiltonian of a system of s p i n s i n a s t a t i c f i e l d AH2 + H 2, i n t e r a c t i n g through
1
t h e t r u n c a t e d Hamiltonian
aD
of e q u a t i o n ( 2 ) . It i s p l a u s i b l e and h a s been v e r i f i e d e x p e r i ~ n e n t a l l y t h a t applying t h e r f f i e l d f o r o f f resonance, then sweeping t h e frequency ( o r t h e dc f i e l d ) s o a s t o reduce AH t o z e r o , and f i n a l l y s u p p r e s s i n g t h e r f f i e l d i t s e l f , l e a d s t o a c o o l i n g of t h e d i p o l a r energy ) & I D i n a r a t i o H o / H V L , comparable t o , b u t somewhat d i f f e r e n t from, H /HL, ( t h e t r u n c a t e d Hamil t o n i a nXtD
y i e l d s a somewhat d i f f e r e n t v a l u e H I L f o r t h e l o c a l f i e l d ) . Besides l e a v i n g t h e dipo-l a r i n t e r a c t i o n cold i n high f i e l d , and allowing a w e a l t h of Hamiltonians
aD
by changing t h e o r i e n -t a t i o n of t h e f i e l d H w i t h r e s p e c t t o t h e c r y s t a l a x e s , t h e ADRF procedure h a s y e t a t h i r d a d v a n t a g e : by choosing a t w i l l t h e i n i t i a l s i g n of AH = (H -w/y), t h e e f f e c t i v e f i e l d b e f o r e t h e ADRF, n e g a t i v e a s w e l l p o s i t i v e temperatures can b e given t o t h e trun- c a t e d d i p o l a r energy
XvD.
This whole procedure of ADRF may appear a s a c o n j u r i n g t r i c k and a q u e s t i o n i n p a r t i c u l a r o f t e n r i s e s : how c a n an ordered s t a - t e of n u c l e a r s p i n s , where t h e l o c a l o r d e r i n g f i e l d s a r e of t h e o r d e r of a few gauss a t most, s u r v i v e i n t h e presence of a dc f i e l d H of s e v e r a l t e s l a s . T h e answer i s t h a t a s soon a s t h e r f f i e l d i s c u t o f f t h e r e i s no way f o r t h e Zeeman energy which i s quan- t i z e d i n u n i t s o f hundreds of megahertz t o flow in- t o t h e d i p o l a r energy whose spread i s a t most a few t e n s of k i l o h e r t z p e r s p i n .B) D N P.- The a d i a b a t i c demagnetization p r o v i d e s a c o o l i n g r a t i o of t h r e e t o f o u r o r d e r s of magnitude.
However even i f f i e l d s of t e n t e s l a s and l a t t i c e temperatures of a few m i l l i k e l v i n s a r e a v a i l a b l e ,
JOURNAL DE PHYSIQUE
t h e r e i s s t i l l a problem f o r r e a c h i n g t h e f i n a l m i - c r o k e l v i n range. At l e a s t i n i n s u l a t o r s t h e n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t i m e s a t such f i e l d s and tem- p e r a t u r e s , (and even f o r f i e l d s lower by a f a c t o r t h r e e and temperatures h i g h e r by a f a c t o r t e n ) a r e s o long t h a t t h e n u c l e a r s p i n s never reach t h e tem- p e r a t u r e of t h e r e f r i g e r a t o r (you can take t h e h o r s e t o t h e water b u t you cannot make i t d r i n k ) . The s i - t u a t i o n i s b e t t e r i n m e t a l s b u t one would e x p e c t t h e r e d i f f i c u l t i e s w i t h t h e ADRF. There e x i s t s howe- v e r a method of dynamic n u c l e a r p o l a r i z a t i o n (DNP)
,
widely used i n t h e making of p o l a r i z e d t a r g e t s f o r n u c l e a r and p a r t i c l e p h y s i c s , which can b r i n g nu- c l e a r s p i n s t o temperatures of a few m i l l i k e l v i n s i n f i e l d s of a t e s l a s i n a few hours.
The p r i n c i p l e of t h i s method, o r i g i n a l l y c a l - led t h e j ' s o l i d e f f e c t " h a s been d e s c r i b e d i n many d i f f e r e n t ways. The d e s c r i p t i o n g i v e n h e r e , should appeal, one hopes, t o low temperature p h y s i c i s t s .
Paramagnetic e l e c t r o n i c i m p u r i t i e s a r e i n t r o - duced i n t o an otherwise diamagnetic sample a t con- c e n t r a t i o n s of t h e o r d e r of ( w i t h i n an o r d e r of magnitude) and,because of t h e s h o r t e l e c t r o n i c spin- l a t t i c e time have no d i f f i c u l t y i n r e a c h i n g t h e tem- p e r a t u r e of t h e l a t t i c e (and of t h e r e f r i g e r a t o r ) which i s of t h e o r d e r of h a l f a k e l v i n o r so. The e l e c t r o n i c s p i n s i n t e r a c t w i t h each o t h e r through a t r u n c a t e d e l e c t r o n i c d i p o l a r i n t e r a c t i o n
71&';
which corresponds t o an i n t e r n a l e l e c t r o n i c magnetic f i e l dof t h e o r d e r of s a y twenty gauss. A c t u a l l y t h i s concept of l o c a l e l e c t r o n i c f i e l d f o r a randomly d i - l u t e system of s p i n s should b e used with c a u t i o n . For most p a i r s of e l e c t r o n i c s p i n s i t w i l l b e much
l e s s and f o r a few i t would b e a good d e a l more. The main p o i n t i s t h a t because of t h e l a r g e e l e c t r o n i c
gyromagnetic f a c t o r ye, t h e spread of t h e energy spectrum oq
a&';,
of t h e o r d e r of yeH;/2n 50 MHz w i l l have wings r e a c h i n g i n t o t h e n u c l e a r Larmor frequency of t h e o r d e r of a hundred MHz. The n u c l e a r Zeeman energy Zn and t h e e l e c t r o n i c t r u n c a t e d dipo-l a r energy a r e t h u s "on speaking terms" and a t t h e same s p i n temperature.
I f now we perform an ADRF on t h e e l e c t r o n i c s p i n s w i t h a microwave g e n e r a t o r n e a r t h e e l e c t r o n i c Larmor frequency which i s i n t h e r a n g e of a hundred GHz, we should c o o l t h e e l e c t r o n i c d i p o l a r energy by a f a c t o r of t h e o r d e r of H ~ / H : t h a t i s t h r e e o r d e r s of magnitude. Since
a&';
and Z a r e on "spreakingn
terms" t h i s r e s u l t s i n a c o o l i n g of t h e n u c l e a r Zeeman energy Zn b u t by a f a r s m a l l e r amount because
of t h e h e a t c a p a c i t y of Z much h i g h e r t h a n t h a t n'
of
;)pol;.
However once t h e ADRF i s o v e r , because oft h e s h o r t e l e c t r o n i c r e l a x a t i o n time, one can r e p e a t i t a g a i n and a g a i n u n t i l Z h a s reached a tempera-
n
t u r e s m a l l e r t h a n t h a t of t h e l a t t i c e by a f a c t o r of t h e o r d e r of H /He t h a t i s reaching i n t o t h e m i l -
0 L
l i k e l v i n range. I n p r a c t i c e , i n s t e a d of r e p e a t i n g t h e e l d c t r o n i c ADRF many times one o b t a i n s a compa- r a b l e r e s u l t by applying t h e microwave f i e l d c o n t i - nuously a t a d i s t a n c e from t h e e l e c t r o n i c resonance
of t h e o r d e r of
q.
Depending on t h e s i d e of t h e resonance a t which t h i s microwave i s a p p l i e d , tem- p e r a t u r e s of e i t h e r s i g n a r e obtained f o r Z Cut-n' t i n g o f f t h e microwave f i e l d one i s t h e n ready f o r a n u c l e a r ADRF which b r i n g s t h e n u c l e a r d i p o l a r tem- p e r a t u r e down i n t o t h e m i c r o k e l v i n range. The l i f e - time of t h e ordered n u c l e a r s t a t e which o b t a i n s i f t h e f i n a l temperature i s below t h e c r i t i c a l tempera- t u r e T i s of t h e o r d e r of t h e s p i n - l a t t i c e r e l a x a - t i o n time TID f o r t h e n u c l e a r d i p o l a r energy. This time i s v e r y much s h o r t e r t h a n t h e r e l a x a t i o n time T I Z f o r t h e n u c l e a r Zeeman energy Z because a t low
n
l a t t i c e temperatures t h e spectrum of t h e f l u c t u a t i n g magnetic l o c a l f i e l d s r e s p o n s i b l e f o r t h e n u c l e a r
r e l a x a t i o n does n o t c o n t a i n t h e high (100 MHz) nu- c l e a r Lannor frequency, whereas i t does c o n t a i n t h e low f r e q u e n c i e s spanned by t h e spectrum of t h e nu- c l e a r d i p o l a r energy. I n p r a c t i c e r e l a x a t i o n times TID between a few minutes and a few hours have been
o b t a i n e d .
1.3. Observation of n u c l e a r magnetic o r d e r i n g . - Li- ke e l e c t r o n i c magnetic o r d e r i n g i t i n v o l v e s t h r e e types of measurements.
A ) Macroscopic magnetic measurements.- What i s meant h e r e i s t h e use of magnetic f i e l d s homogeneous on a s c a l e comparable t o t h e s i z e of t h e sample. Whereas i n e l e c t r o n i c magnetism t h e s e f i e l d s a r e mostly s t a - t i c , i n high f i e l d n u c l e a r f e r r o o r antiferromagne- t i s m t h e s e a r e r f f i e l d s n e a r t h e Larmor frequency of t h e n u c l e i . The NMR s i g n a l of an ADRF s t a t e whe- t h e r paramagnetic o r ordered has z e r o n e t magneti- z a t i o n and t h e r e f o r e z e r o n e t a r e a . It can b e shown q u i t e g e n e r a l l y t h a t i t i s a n t i s y m m e t r i c a l with r e s p e c t t o t h e n u c l e a r Larmor frequency. Two such s i g n a l s of 7 ~ i i n LiH a r e shown i n f i g u r e 1. The f i r s t corresponds t o an a n t i f e r r o m a g n e t i c s t a t e a n d t h e second t o a paramagnetic s t a t e . The f i r s t one i s e a s y t o i n t e r p r e t : n u c l e a r moments l o c a t e d on t h e two a n t i f e r r o m a g n e t i c s u b l a t t i c e s have d i f f e -
rent Larmor frequencies because they see opposite Weiss fields. Those parallel to the high field Ho absorb energy from the N M R field and given an ab- sorption signal, those, on the other sublattice, antiparallel to H give an emission signal of oppo- site sign. The lower the spin temperature, the hi- gher, the narrower nd the farther apart are thetwo peaks.
Li NMR Signal
.g. 1 : NMR signal of 7 ~ i in LiH after ADRF at
< 0 with Ho parallel to
[loo]
: Antiferromagnetic state B : Paramagnetic state
In the paramagnetic ADRF state where there is no long-range order one still sees two peaks of opposite sign. This is explained by short range cor- relations between the spins and therefore also bet- ween the orientation of a spin and that of the local
field produced by its neighbours. Moments which are parallel to H and give a positive signal see local fields opposite in sign to those seen by moments antiparallel ti, Ho, whence the antisymmetrical struc- ture with two peaks of opposite sign. It is clear that from the looks of an ADRF signal it is diffi- cult to tell apart an antiferromagnetic state sligh- tly below the transition from a paramagnetic state slightly above.
It is possible however to extrait from the
ADRF NMR curve f(w) significant quantitative infor- mation. It can be shown that the first moment M1 of
f(w) with respect to the central frequency w is proportional to the dipolar energy of the spins if there is a single spin species I present in the sample :
If there are two spin species I and S the significance of the first moment M: is more invol- ved. It can be shown that
where
xis
is the dipolar interaction between the spins I and S.Another quantity of great importance is the transverse static susceptibility of the nuclear spins which is given by the relation :
It is well known that for an antiferromagnet the transverse susceptibility is very nearly inde- pendent of the temperature.
There is no simple way of measuring the tem- perature in the ADRF state, the relation
T./T
-
H /Hi being only a crude approximation. OnI f 0
the other hand the entropy is known in principle : if the ADRF is truly adiabatic, it is the same as before the demagnetization where it is a simple function of the initial nuclear polarization p
i' going from k Ln (2I+ 1) to zero as the polarization
B
goes from zero to unity. Figure 2 shows a plot of X against p. for 1 9 ~ . The plateau characteristic of antiferromagnetism is unmistakable but the tran- L sition polarization not so easy to pinpoint.
B) Nuclear probes.- In electric antiferromagnetism the use of nuclear moments as probes which measure on a microscopic scale the local magnetic fields at various lattice sites has proven very fruitful.
The same technique has been successfully applied to the study of nuclear antiferromagnetism. These studies have been reported before and will be men- tioned here very briefly. The most spectacular suc- cess of this method is the discrimination between two states of the spins of 1 9 ~ in Ca Fp, antiferro- magnetism and domain ferromagnetism, which can both
C6-
1440 JOURNAL D E PHYSIQUE be produced in Ca F2 for different orientations ofthe magnetic field. Whereas the ADRF NMR signals of 'F look practically identical in both states, the NMR signals of the rare (0.13 %) isotope of ' 3 ~ a give a single resonance line for antiferromagnetism and two separate lines for ferromagnetism. Similarly the existence of antiferromagnetism in LiH was first demonstrated unambiguously from a splitting in the signal of the rare isotope '~i.
I I I I
I
I I I I0 0.1 0.2 0.3 0.1 0 5 0.6 0.7 O B 0 9 1.0
Initial polarization
Fig. 2 : Transverse susceptibility of "F in CaF2 after ADRF at T < 0 with H parallel to Eoo], as a function of the initial po!?arization. The plateau is as expected for an antiferromagnet.
One of the weaknesses of the method is that in contrast with electronic antiferromagnetism the nuclear probes do perturb the magnetic environment they are set to study. This is not offset by their small concentration : even if they perturb only small regions of the sample, it is these very re- gions that are observed.
C) Neutron diffraction.- As in electronic magnetism this is the method which brings the most detailed information by far. It will be dealt with in detail in the second part of this talk. One should at this stage warn the reader against undue pessimism : in spite of the fact that nuclear magnetic moments are three or four orders of magnitude. smaller than the electronic moments, neutron diffraction by nuclear
spins
isnot
a weak phenomenon. This is due to the fact that besides magnetic interactions there are sizeable nuclear interactions between the spin of the nucleus and that of the neutron which enable the neutron to "tell" a nuclear spin up from a nuclear spin down. The order of magnitude of these interac- tions is described conveniently by assigning to each nuclear species a hypothetical pseudo-magneticmoment % which would provide a magnetic scattering amplitude equal to the actual nuclear spin-dependent
scattering amplitude, of that nucleus. The pseudo- magnetic moments of most nuclei were very poorly known and original methods, for measuring these mo- ments have been developed at Saclay. The general name of nuclear pseudomagnetism has been proposed for these studies. It was a great disappointment that p%(19F) has turned out to be very small
(0.017 ) . Otherwise neutron diffraction studies of B
nuclear antiferromagnetism would have been reported at least five years earlier.
1.4. Landmarks in nuclear magnetic ordering.- 1958
-
Discovery of DNP by the solid effect 111 ,1960-
Proposal for observing nuclear ordering usingDNP followed by adiabatic demagnetization 121 1962
-
Proposal for using DNP followed by ADRF /3/1965
-
Experimental work on nuclear ordering starts (M. Chapellier and M. Goldman)1968
-
Prediction of ordered nuclear structures 141 1969-
First observation of nuclear antiferromagne-tism in Ca F I51
2
1972 - First measurements of pseudo-magnetic moments /6,7/
197111974
-
Experimental work on LiF (Bouffard and Cox) I1011974
-
First use of nuclear probes and first obser- vation of nuclear domain ferromagnetism inCa F p /8,9/
1974
-
Experimental work starts on LiH (Bouffard and Roinel)1977
-
First observation of nuclear antiferromagne- tism in LiH1111
1978 - First superstructure Bragg diffraction in LiH 1121
2. NEUTRON DIFFRACTION STUDY OF ANTIFERROMAGNETISM IN LITHIUM HYDR1DE.- The possibility of performinga neutron diffraction study on a nuclear antiferroma- gnet is limited to substances whose nuclei have a sufficiently large pseudo-magnetic moment p x
.
Fur-thermore, for a first study it is advisable to choose a system as simple as possible where the pre- diction of antiferromagnetism has a good change to be correct. These considerations have led to the choice of lithium hydride : The pseudomagnetic mo- ment of the proton is the largest of all nuclei, p a (IH) = 5.4 pB, and that of lithium
7
isX
p (7~i) =
-
0.62 p B . As for the crystalline struc- ture of LiH, it is of the Na C1 type, i.e. it con-sists of two imbricated f.c.c. lattices of 'H and 7 ~ i . If one disregards for a moment the difference between I H and 7 ~ i , they form together a simple cu- '
bic lattice of magnetic moments of comparable magni- tude (they differ by about 15 I ) , for which it is plausible to expect the same ordered structures as i n a s.c. lattice of identical spins. Thesuccessful production of nuclear antiferromagnetism as deduced from magnetic measurements, in Ca F whose 1 9spins ~
2
form a s.c. structure was an incentive to trust the theoretical predictions for antiferromagnetism in LiH.
The successful observation of neutron diffrac tion on antiferromagnetic lithium hydride is very recent, and the results presented in this talk are still very preliminary.
2.1. Predicted antiferromagnetic structures.- The theoretical prediction of the ordered structures is made by a local mean field approximation. Figure 3 shows the antiferromagnetic structures expected both at positive and negative spin t?mperatures when the external field is parallel to a four-fold crystalline axis. This is the field orientation to which the neutron diffraction study has been limited so far. At positive temperature successive planes
(011) carry opposite magnetizations, and at negati- ve temperature it is successives planes (100) that carry opposite magnetizations. Each of the antifer- romagnetic sublattices contains spins of either species.
T > O T C O
Fig. 3 : Predicted antiferromagnetic structures in LiH at positive and negative tem eratures, following an aDRP with H parallel to
[lodg.
IH and 7 ~ i spins are black and Ghite, respectivelyThe qperimental arrangement, described in the next section, is such that the neutron diffraction w s t take place in a plane perpendicular to the field Ho.
that is on antiferromagnetic planes parallel to H
.
Since the neutrons "see" essentially the protons,
it is possibbe to performe an antiferromagnetic dif- fraction on the planes (011) both at positive and negative temperature (dashed planes in figure 3). One way to distinguish the two structures of figure 3 is that in a given (011) plane the proton and li- thium polarizations are parallel at T > 0 and anti- parallel at T < 0 ; these polarizations are rever- sed from one plane to the next.
2.2. Experimental procedure.- The whole experimental procedure : dynamic polarization and ADRF has to be performed in a high homogeneous field and at low temperature, that is in a superconducting magnet and with a dilution refrigerator. At the same time, free access must be provided to the incident and diffrac- ted neutron beams : an unacceptable absorption would result from their crossing the coil or an exessive thickness of dilute 3 ~ e .
The superconducting magnet is of the split- coil type, which allows neutron-diffraction experi- ments in a plane perpendicular to the (vertical) ma- gnetic field. The sample of LiH, in the fonn of a platelet of typical dimensions 5 x
4
x 0.5 nun is placed vertically in the cryostat. The thickness of the 6 %-
3 ~ e solution is limited to 0.5 mm on each crystal face, as a compromise between the necessi- ties of cooling the crystal and reducing neutron absorption. The whole cryostat can be rotated around a vertical axis, so as to bring the crystal to the Bragg-reflexion orientation.The cryogenic system, and the neutron-dif- fraction setup are described in separate papers at this conference.
The lithium hydride sample contains of the order of 2 x 1019 paramagnetic F-centres per cm3.
They are created by irradiation at liquid nitrogen temperature with a beam of 3-MeV electrons. The ma- gnetic field is 6.5 teslas, and the frequency of the microwave irradiation used for DNP is 185 GHz.
During the polarization period, the temperature of the bath is around 200 mK. The maximum polarization, after 2 to 3 days of irradiation, corresponds to :
After switching-off the microwave power, the bath temperature drops to 35 mK. The temperature of the sample itself is not known. The ADRF is perfor- med on both IH and 7 ~ i spins, by using two rf fields
of carefully adjusted frequencies, (of the order of 280 and 110
MHz,
respectively). The rf-field ampli- tudes are of the order of 30 mG, and the externalC6-
1442 JOURNAL DE PHYSIQUEfield is w e p t towards resonance at rate of 0.5 GIs. and nature have not been investigated yet. This re- laxation leads to a distribution of spin temperatu- res within the sample which becomes broader and broader as time proceeds. The methods used to over- come this drawback is to perform, after each ADRF, a series of partial saturations of the system, ho- mogeneous over the sample, in a time much shorter
than the shortest relaxation time. These saturations are performed by suitable rf irradiations. Following each saturation step the system has a relatively homogeneaus spin temperature, whose value increases at each step.
2.3. Experimental results.- We report some experi- mental results obtained on one sample at negative
spin temperature. The field is along a four-fold crystalline axis to within a fraction of a degree, as deduced from the observation of the crystalline neutron-diffraction reflexions 200 and 220.
Figure
4
shows the antiferromagnetic diffrac- tion line 110 observed immediately after an ADRF with initial polarizations pH = 0.95 and pLi = 0.80.On the same figure is shown for comparison the crys- talline diffraction line 220 observed with the un- polarized sample. The reality of a long-range nu- clear antiferromagnetic order whose structure is precisely that expected from theory, is thus direc- tly established. The diffraction of neutrons by this nuclear 'antiferromagnet is a large effect, as anti- cipated from the large value of the proton pseudo- magnetic moment. The width at half-intensity of the antiferromagnetic line, equal to 0.65O, is much lar- ger than that of the crystalline line 220 (% 0.2').
It is experimentally the same whatever the initial polarizations and the antiferromagnetic line inten- sity. This broadening is attributed to the existence of antiferromagnetic domains, and it yields an ave-
0
rage value for their size, of the order of 300 A.
lime ( hours
Fig. 5 : Variation with time of the intensity of the 110 antiferromagnetic neutron diffraction line in LiH. Before the end of the ADRF, the neutron count is that of the background (left)
What is measured at the various saturation steps of each run is the intensity of the 110 anti- ferromagnetic neutron line, and the first moment MI
s
of the 7 ~ i N M R signal. The intensity of the neutron line yields the proton sublattice polarization p
H' In a so-called "ideally imperfect" crystal, this intensity would be proportional to pH2 (with a cor- rection of the order of 20 % to account for the contribution of '~i). The actual intensity varies in fact more slowly than pH2, because of the pheno- menon of extinction. The extinction correction for the antiferromagnetic 110 reflexion was made on the basis of the extinction experimentally measured on the crystalline 220 reflexion. The proton sublattice polarizations determined in that way suffer from the uncertainty as to whether the extinction is actually the same for the reflexions 110 and 220.
The measurement of the first moment M I of 'Li yields S
Angle
Fig. 4 : Neutron diffraction lines in LiH. The crys- talline line 220 is observed in the unpolarized sam- ple. The antiferromagnetic line 110 is observed af- ter ADRF at T < 0 and Ho
//
'[loo]Figure 5 shows the variation with time of the neutron counting rate at the centre of the anti- ferromagnetic line observed in one run. It consists of a fast decay, completed in aboutcl h, superimpo- sed on a slow decay which lasts 5 h. Further expe- riments have shown that this is due to an inhomoge- neous relaxation rate in the sample, whose origin
an energy term :
The result of this analysis of the data is shown in figure 6. The point A corresponds to the zero temperature limit in the Weiss-field approxi- mation.
Energy term
E'
I kHz )Fig. 6 : Proton sublattice polarization in antifer- romagnetic LiH at negative temperature, as a func- tion of the energy term
E' = 13
<&is> + <a&'
>}INSas computed from thelFirst moment of the 7 ~ i NMR signal
Among the experiments under way or in prepa- ration in this system are the measurements of the temperature, the entropy, the various energy terms
<;)CiI>, < x i S > and < x i S > and the magnetic suscep- tibilities.
3. CONCLUSION.- The observation of an antiferroma- gnetic neutron reflexion on a nuclear antiferroma- gnet is an important step in the study of nuclear magnetic ordering. Its first result : the direct verification of the production of a long range or- der of nuclear spins under the effect of their tiny dipolar interactions, is a welcome confirmation of the evidence for nuclear magnetic ordering gathered for several years from magnetic measurements. In addition, the access to such a fundamental property of antiferromagnetism as the sublattice polariza- tions gives a new dimension to the study of nuclear magnetic ordering. Neutron diffraction is now ready to be used for the search of antiferromagnetism in substances for which theoretical predictions are not firmly grounded, or are difficult to perform.
The qualitative observations accumulated on nuclear magnetic ordering : magnetic measurements and neutron diffraction, demonstrate unambiguously that the steady state reached by an isolated system of nuclear spins is a true thermodynamic equilibrium, with a true temperature in a range several orders of magnitude below those achieved in any other macros- copic system.
References
/ I / Abragam, A., and Proctor, W.G., C.R. Hebd. S6an.
Acad. Sci. 246 (1958) 2253
-
/2/ Abragam, A., C.R. Hebd. Sban. Acad. Sci.
251
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/3/ Abragam, A., C.R. Hebd. S6an. Acad. Sci.
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(1962) 1267
/4/ Goldman, M., in Magnetic Resonance and Radiofre- quency Spectroscopy, P. Averbuch ed. (North- Holland,Amsterdam) 1969, p. 157
,151 Chapellier. M.. Goldman. . .
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M.. , Vu Hoang Chau andbrag am,
A., C.R. Hebd. Sban. Acad. ~ c i .268
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161 Abragam, A., Bacchella, G.L., Gliittli, H., Meriel, P., Piesvaux, J., and Pinot, M., C.R.
Hebd. Sban. Acad. Sci.
B
((1972) 423 /7/ Abragam, A., Bacchella, G.L., Glgttli, H.,Meriel, P., Pinot, M., and Piesvaux, J., Phys.
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(1973) 776181 Jacquinot, J.F., Wenckebach, W.T., Gbldman, M., and Abragam, A., Phys. Rev. Lett.
2
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Acad. Sci.
9
((1974) 93/lo/ Cox, S.F.J., Bouffard, V., and Goldman, M., J.
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/ 1 I / Roinel, Y., Bouf fard, V., and Roubeau, P., J.
Phys. (to be published)
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286 B (June 5, 1978), To these names should be added Avenel, 0. who has recently taken over the responsibility for the cryogenics.
Review articles :
1131 Goldman, M. -Nuclear Dipolar Magnetic Ordering- Physics Reports
%
(1977) 1.1141 Abragam, A. and Goldman, M.
-
Principles of Dynamic Nuclear Polarization-
Repts. Progr.Phys.
