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KONDO COUPLING, HYPERFINE AND EXCHANGE INTERACTIONS
J. Flouquet
To cite this version:
J. Flouquet. KONDO COUPLING, HYPERFINE AND EXCHANGE INTERACTIONS. Journal de
Physique Colloques, 1978, 39 (C6), pp.C6-1493-C6-1498. �10.1051/jphyscol:19786592�. �jpa-00218085�
JOURNAL DE PHYSIQUE
Colloque C6, suppf6ment au no 8, Tome 39, aotit 1978, page C6-1493
KONDO COUPLING, H Y P E R F I N E AND EXCHANGE I N T E R A C T I O N S
J. F l o u q u e t
Centre de Recherches sup Zes Tr're's Basses Tern graixres, C.N.R.S., B.P. 166
X,
38042 Grenoble Cedex,-
L a n c e-
Rdsum6.- Premisrement, l a p o s s i b i l i t d d ' o b s e r v e r une s t r u c t u r e h y p e r f i n e dans un a l l i a g e d i l u d e s t d i s c u t d e s u i v a n t l a f o r c e du couplage Kondo ; d ' a u t r e s exemples d e s t r u c t u r e s i n t e r n e s d u moment l o - c a l i s 6 s o n t montrds. Deuxismement, l e s p r o p r i 6 t 6 s remarquables d e s compos&s anormaux d e c6rium s o n t d d c r i t e s ; l e u r l i e n avec l e comportement Kondo d ' u n e impuretd i s o l d e e s t d i s c u t d .
A b s t r a c t . - F i r s t l y , t h e p o s s i b l e o b s e r v a t i o n of an h y p e r f i n e s t r u c t u r e i n d i l u t e a l l o y s i s d i s c u s s e d i n f u n c t i o n of t h e s t r e n g t h of t h e Kondo c o u p l i n g ; o t h e r examples of i n n e r s t r u c t u r e s of t h e l o c a l moment a r e g i v e n . Secondly, t h e s t r i k i n g p r o p e r t i e s of t h e abnormal r a r e e a r t h compounds of cerium a r e r e p o r t e d ; t h e i r r e l a t i o n s w i t h t h e Kondo behaviour of an i s o l a t e d i m p u r i t y a r e d i s c u s s e d .
The s t u d y of d i l u t e a l l o y s of magnetic impu- r i t i e s h a s e x p e r i e n c e d a b u r s t of a c t i v i t y i n r e c e n t y e a r s mainly i n c o n n e c t i o n w i t h t h e e l u c i d a t i o n of t h e Kondo problem / 1 , 2 / . C u r r e n t l y , a n a t t e m p t i s made t o o b s e r v e and u n d e r s t a n d t h e i n n e r s t r u c t u r e o f
t h e 3d and 4f i m p u r i t i e s when t h e k-d o r k-f mixing w i t h t h e c o n d u c t i o n e l e c t r o n s i s n o t weak t h a t i s t o s a y when t h e i n i t i a l i o n i c l e v e l s of t h e c o n f i g u r a - t i o n may be s t r o n g l y p e r t u r b e d by i n t e r a c t i o n s w i t h t h e Fermi Sea 131. An o t h e r open q u e s t i o n i s t h e r e l a t i o n between t h e Kondo behaviour found f o r a r a - r e e a r t h i m p u r i t y l i k e Ce and t h e abnormal proper- t i e s d i s c o v e r e d i n some c o r r e s p o n d i n g i n t e r m e t a l l i c compounds. I w i l l r e p o r t simple r e s u l t s o b t a i n e d i n e a c h d i r e c t i o n a t Orsay and Grenoble.
1 . THE HYPERFINE COUPLING AND THE KONDO COWLING.- Experiments performed a t low t e m p e r a t u r e down t o 3 mK by n u c l e a r o r i e n t a t i o n (N.0) / 5 / have c l e a r l y shown t h a t when t h e l o c a l i z e d moment o f s p i n S h a s an hy- p e r f i n e c o u p l i n g A w i t h i t s n u c l e u s of s p i n I :
+ +
H h f = A I . S
two d i f f e r e n t regimes o c c u r a c c o r d i n g a s t h e hyper- f i n e c o u p l i n g i s g r e a t e r o r lower t h a n t h e Kondo c o u p l i n g (A
3
kTK).
For kBTK > A ( t h e s t r o n g cou- p l i n g c a s e ) , t h e l o c a l moment i s s t r o n g l y coupled t o t h e c o n d u c t i o n e l e c t r o n s v i a t h e Kondo c o u p l i n g . At low t e m p e r a t u r e (T < TK), t h e p o l a r i z a t i o n of t h e s i n g l e t ground s t a t e i s d e s c r i b e d by a p u r e e l e c - t r o n i c term ; t h e h y p e r f i n e c o u p l i n g c a n be regarded a s a p e r t u r b a t i o n and can b e reduced t o :[H
-1
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 . Such s i t u - h f-a t i o n s have been observed f o r t h e
2
C r , Co,&
Co a l l o y s 141.
A t t h e o p p o s i t e extreme f o r k T < A ( t h e B K
weak c o u p l i n g c a s e ) , t h e n u c l e a r and t h e e l e c t r o n i c
+ + +
s p i n must b e coupled f i r s t : F = I + S . When a w e l l i s o l a t e d ground s t a t e F can b e d e f i n e d , t h e Kondo Hamiltonian i s o n l y a p e r t u r b i n g term. I t s i n i t i a l
form, g i v e n by t h e well-known e x p r e s s i o n :
where s i s t h e s p i n of t h e c o n d u c t i o n e l e c t r o n s , may b e reduced t o :
+ -+
H T e = a J F . s (1)
The s t r i k i n g r e s u l t i s t h a t a Kondo c o u p l i n g ( J > 0) may a p p e a r o r d i s a p p e a r due o n l y t o t h e a c t i o n of t h e h y p e r f i n e c o u p l i n g when I and S a r e a n t i f e r r o - m a g n e t i c a l l y coupled. For example f o r A > 0 , S < I l e a d s t o a r e v e r s e d s i g n of t h e exchange c o u p l i n g and S = I = - 1 t o t h e s p e c t a c u l a r c a s e of a s i n g l e t
2
e l e c t r o n n u c l e a r ground s t a t e . F i n a l l y , we p o i n t o u t t h a t g e n e r a l l y t h e change i n t h e degeneracy o f t h e m a g n e t i c l e v e l s must change i t s Kondo c o u p l i n g and
t h e o t h e r p r o p e r t i e s l i n k e d t o t h e exchange c o u p l i n g l i k e t h e o r d e r i n g s p i n g l a s s t e m p e r a t u r e , t h e depres- s i o n of t h e s u p e r c o n d u c t i v e t r a n s i t i o n . (These phe- nomena a r e b a s i c a l l y t h e same t h a t o c c u r s f o r 4f i o n s when t h e c r y s t a l f i e l d l e v e l s becomes depopu- l a t e d 1 4 1 ) . A n i c e experiment would b e t o s t u d y a t v e r y low t e m p e r a t u r e how t h e Kondo c o u p l i n g i s re-
l a t e d t o t h e p a r a m e t e r s of d i f f e r e n t i s o t o p e s .
Hhf = A <SZ> IZ For 3d i m p u r i t i e s weak c o u p l i n g c a s e s have
The n u c l e a r and e l e c t r o n i c term a r e uncou- been observed f o r &Mn, F r , EMn a l l o y s i n N.0 pled. The nuclei see an effective hyperfine f i e l d e x p e r i m e n t s , f o r a b m r m a l 4f i o n s f o r &Yb, % r ,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786592
C6-1494
JOURNAL DE PHYSIQUEa l l o y s . An e x c e l l e n t example i s provided by t h e s t u - dy of t h e &Yb a l l o y s made i n Grenoble on d i f f e r e n t i s o t o p e s of Ytterbium. From E.P.R., Miissbauer, N.O.
e x p e r i m e n t s 141, i t i s well-known t h a t &Yb f u l l f i l l s t h e c o n d i t i o n o f a weak c o u p l i n g regime (J > 0 , A > kT ). A f a v o r a b l e s i t u a t i o n i s r e a l i z e d a s t h e
K
element Yb h a s a number o f s t a b l e i s o t o p e s w i t h a Large v a r i e t y of n u c l e a r p a r a m e t e r s . As i n d i c a t e d i n t h e t a b l e ( I ) , t h e 17'Yb i s o t o p e h a s no n u c l e a r spin;
t h e 171Yb and 173 Yb i s o t o p e s have moments of oppo- s i t e s i g n and f u r t h e r m o r e t h e former i s o t o p e f u l l - f i l l s t h e c o n d i t i o n s f o r e l e c t r o n n u c l e a r s i n g l e t c o u p l i n g (A > 0, S = I = -). 1 S i n c e t h e s u s c e p t i b i -
2
l i t y
x
of 1 7 4 ~ b a l l o y s f o l l o w s a p u r e C u r i e lawdown 7 mK which c o r r e s p o n d s t o t h er7
e l e c t r o n i c d o u b l e t ground s t a t e , t h e &17' Yb s u s c e p t i b i l i t y showsstrong d e p a r t u r e s form t h i s b e h a v i o u r a t low t e m p e r a t u r e /5/. Below 100 mK, a c o n s t a n t s u s c e p t i b i l i t y law i s observed i n agreement w i t h t h e f o r m a t i o n of a s i n - g l e t e l e c t r o n n u c l e a r ground s t a t e . T h i s observa- t i o n i s no more t h a n t h e well-known Breit-Rabi e f - f e c t i n a t a m i c p h y s i c s .Table I
Nuclear s p i n and h y p e r f i n e c o u p l i n g of d i f f e r e n t Yb i s o t o p e s d i s s o l v e d i n g o l d r
Ain mK 128
-
35The c o r r e s p o n d i n g e l e c t r i c a l r e s i s t i v i t y of t h e m o n o i s o t o p i c a l l o y s have been measured down t o 18 mK 1'61. As p r e d i c t e d by t h e r e l a t i o n ( I ) , a r e - s i s t i v i t y d r o p i s observed i n t h e &I7' Yb a l l o y s below t h e h y p e r f i n e s p l i t t i n g e q u a l t o 128 mK. A s t r a i g h t forward t r a n s p o s i t i o n of t h e problem o f t h e r e s i s t i v i t y g i v e n by t h e f o r m a t i o n of p a i r s of im- p u r i t i e s i n Kondo systems / l o / l e a d s t o a good d e s - c r i p t i o n of t h e e x p e r i m e n t a l b e h a v i o u r even i n t h e c r o s s o v e r regime A % kT ( f i g u r e 1 ) .
These experiments show t h a t t h e h y p e r f i n e c o u p l i n g i s observed i n s t a t i c and t r a n s p o r t measu- r e m e n t s - p r o v i d e A > kTK
.
Here, t h e good comparison between t h e i n t r a c o n f i g u r a t i o n parameter A andthek-d o r k-f mixing i s t h e Kondo c o u p l i n g . The s i t u a t i o n i s r a t h e r s i m p l e a s t h e 4f l e v e l Yb i n &Yb and t h e 3d l e v e l s i n t h e r e p o r t e d examples a r e f a r below t h e Fermi l e v e l : t h e r a t i o o f t h e energy, Eo, oft h e v i r t u a l l e v e l r e l a t i v e t o t h e Fermi l e v e l t o i t s w i d t h A i s lower t h a n
-
1 .F i g . 1 : R e s i s t i v i t y of &171Yb and &17'yb. The so- l i d l i n e i s a s t r a i g h t forward t r a n s p o s i - t i o n of t h e p a i r s of i m p u r i t i e s
2. THE HYPERFINE COUPLING AND THE MAGNETISM' S ORIGIN.
-
The s i t u a t i o n i s more complex when t h e p o s i t i o n of t h e v i r t u a l l e v e l i s c l o s e r t o t h e Fermi l e v e l a s i t o c c u r s f o r most 3d i o n s (Eo/A>-1). The s i g n and ma- g n i t u d e of t h e h y p e r f i n e c o u p l i n g a r e r e l e v a n t t o t h e magnetism's o r i g i n a s t h e h y p e r f i n e c o n t r i b u - t i o n s of t h e s p i n and o r b i t a l magnetism have oppo- s i t e c o n t r i b u t i o n s w i t h d i f f e r e n t magnitudes : f o r a Co2* i o n , t h e o r b i t a l h y p e r f i n e term i s n e a r + 700 kOe p e r y B , t h e s p i n term n e a r
-
100 kOe p e rug.
The occurence of an o r b i t a l magnetism h a s o f t e n been understood a s a proof of t h e v a l i d i t y of a n i o n i c d e s c r i p t i o n a s f o l l o w i n g t h e F r i e d e l Anderson p i c t u r e i t was g e n e r a l l y a d m i t t e d t h a t o n l y t h e con- d i t i o n of s p i n magnetism i s f u l l f i l l e d f o r 3d i o n s : t h e k-d mixing may quench t h e o r b i t a l momentum.The o b s e r v a t i o n of o r b i t a l e f f e c t s i s now w e l l - e s t a b l i s h e d n o t a b l y f o r Co i o n s i n Au, Cu, W , Mo, Pd ( s e e r e f e r e n c e s / 4 / ) . , W e w i l l o n l y d i s c u s s
t h e s t r i k i n g c a s e of t h e g o a l l o y where an o r b i t a l c o n t r i b u t i o n i s c l e a r l y s e e n i n h y p e r f i n e and t r a n s - p o r t p r o p e r t i e s . (Notably i n t h e d i l u t e l i m i t of t h e magnetic i o n s , t h e a n i s o t r o p y of t h e m a g n e t o r e s i s -
t a n c e , d e f i n e d a s t h e d i f f e r e n c e of t h e magnetoresis- t a n c e measured p a r a l l e l and p e r p e n d i c u l a r t o t h e c u r r e n t , o c c u r s o n l y f o r a non s p h e r i c a l s t a t e ) .
The f i r s t column i n t a b l e I1 r e p r e s e n t s t h e h y p e r f i n e f i e l d measured f o r t h e t h r e e l a s t 3d ions'
show c l e a r l y t h a t a n abnormal behaviour o c c u r s , it h a s been i n t e r p r e t e d as t h e m a n i f e s t a t i o n of a Kondo
.g. 2 : At 1.5 K, a n i s o t r o p y of m a g n e t o r e s i t a n c e f o r E N i , E C o and E F e a s a f u n c t i o n of t h e i m p u r i t y c o n c e n t r a t i o n
i n palladium. The p o s i t i v e s i g n found f o r t h e Co and N i i m p u r i t y i n d i c a t e s a s t r o n g l o c a l o r b i t a l c o n t r i b u t i o n / 7 / . These c o n c l u s i o n s a r e s t r o n g l y s u p p o r t e d by t h e a n i s o t r o p y o f m a g n e t o r e s i s t a n c e r e p o r t e d i n f i g u r e 3 / 8 / . A t low c o n c e n t r a t i o n , on- l y t h e o r b i t a l magnetism can e x p l a i n such a n e f f e c t . For t h e N i i o n s , t h e l i m i t o f one i m p u r i t y i s e x t r a - p o l a t e d s i n c e i t s l o c a l moment d i s a p p e a r s a t low c o n c e n t r a t i o n . The d i f f e r e n c e between t h e Co and N i i o n s a r i s e s from t h e d i f f e r e n c e i n s i g n of t h e e l e c - t r i c quadrupole moments. T h i s p o i n t i s i n e x c e l l e n t agreement w i t h t h e a i o n i c f a c t o r f o r t h e 4~ ground s t a t e of a co2+ i o n and t h e 3~ o r 2~ ground s t a t e of a ~ io r ~~ i + +i o n / 9 / . For a ' F C O ~ + i o n and a s p l i t t i n g o f t h e normal c r y s t a l f i e l d g r e a t e r t h a n t h e s p i n o r b i t c o u p l i n g ( h % 0.025 eV)
,
t h e ground s t a t e must be t h e i s o t r o p i c d o u b l e t J =-
1 of t h eT,
2
ground s t a t e of t h e c r y s t a l f i e l d l e v e l ; i t s cor- r e s p o n d i n g h y p e r f i n e f i e l d ,
+
240 kOe, i s v e r y n e a r t h e e x p e r i m e n t a l v a l u e . The l a s t column of t h e t a - b l e I1 shows t h e t h e o r e t i c a l v a l u e s f o r t h k ~ e ~ + and ~ i ' + i o n s based on t h e same normal c r y s t a l f i e l d p o t e n t i a l .The complete disagreement shows t h a t t h e l e - v e l scheme ojf t h e i o n s cannot b e simply d e r i v e d a s
i
i n i n s u l a t o r s . E x p e r i m e n t a l l y a t v e r y low tempera- t u r e (T % 10 mK), t h e ground s t a t e of t h e s o a l - l o y s i s f a r from b e i n g d e t e r m i n e d . I f N.O. / 5 / , ma- g n e t i z a t i o n
/
l o / and Mzssbauer e x p e r i m e n t s/
l l /c o u p l i n g , a f i n e s t r u c t u r e and a r e l a x a t i o n e f f e c t on t h e i n t e r m e d i a t e Fe l e v e l . C l e a r l y experiments on s i n g l e c r y s t a l must b e performed t o r u l e o u t t h e occurence o f a c r y s t a l l i n e a n i s o t r o p y ; i t must b e p o i n t e d o u t t h a t t h e b r o a d NMR l i n e w i d t h observed f o r Co and N i i s u n e x p l a i n e d a s w e l l a s t h e d i f f e - r e n c e between t h e h y p e r f i n e f i e l d d e t e c t e d by N.O.
(+ 210 kOe) and by NMR (+ 240 kOe) / 4 / . T a b l e I1
Experimental h y p e r f i n e f i e l d of G F e , Co, N i and comparison w i t h t h e t h e o r e t i c a l v a l u e assuming t h e i o n i c l e v e l s d e s c r i b e d i n t h e t e x t
F i g . 3 : For d i f f e r e n t i n t e r m e t a l l i c compounds, a x i a l gamma r a y a n i s o t r o p y of I3'We n u c l e i a t 10 mK a s a f u n c t i o n of t h e a p p l i e d f i e l d . (The A1,Ce c u r v e h a s been drawn u s i n g t h e r e s u l t o b t a i - ned on t h e 13'ce n u c l e i )
F i n a l l y , on t h e same s p i r i t , we w i l l r e p o r t t h e u n u s u a l p r o p e r t y r e c e n t l y observed i n N.O. ex- p e r i m e n t s f o r v e r y d i l u t e a l l o y s of EMn. I n a cu- b i c l a t t i c e , f o r an S s t a t e o f a paramagnetic i o n ,
%
f + 78 + 240-
160 PdFe-
PdCo
-
PdNi
-
%f
i n kOe-
300+
240 + 175c6-1496
JOURNAL DE PHYSIQUEa z e r o gamma r a y a n i s o t r o p y must o c c u r i n z e r o f i e l d and t h e i n t e r a c t i o n w i t h t h e a p p l i e d f i e l d H must r e s p e c t i t s symmetry due t o t h e i s o t r o p i c p r o p e r t y of t h e ground s t a t e . For t h e ~t''Mn a l l o y s , Thomson e t a l . 1121 have observed a ~ o s i t i v e gamma r a y a n i - s o t r o p y i n z e r o f i e l d a l o n g t h e 1 1 1 a x i s of t h e P t l a t t i c e and have confirmed t h a t t h e l o c a l symmetry does n o t r e s p e c t t h a t d e f i n e d by H . C l e a r l y a f i n e s t r u c t u r e o c c u r s . One p o s s i b i l i t y i s t h a t t h e S = 5 s t a t e i s s p l i t by t h e c r y s t a l f i e l d i n t o a
r8
quar- t e t and ar7
d o u b l e t . Such a s p l i t t i n g i s well-known f o r t h e i o n i c M3+ s t a t e ( s e e Motta e t a l . 1131 i n t h i s c o n f e r e n c e ) . A n i n t e r e s t i n g q u e s t i o n i s t h e r o l e of t h e s p i n o r b i t c o u p l i n g of t h e m a t r i x on t h e magnitude of t h e f i n e s t r u c t u r e ; f o r Gd,+,
t h e f i n e s t r u c t u r e i n P t i s t h r e e t i m e s t h a t observed i n Pd and twelve times t h a t observed i n Ag 1141.The m i c r o s c o p i c d e s c r i p t i o n of t h e 3d i n n e r s t r u c - t u r e i s s t i l l and open q u e s t i o n . Haldane h a s r e c e n - t l y d i s c u s s e d t h e c r o s s o v e r between v a r i o u s regimes d e f i n e d by t h e r a t i o o f Eo/A 1151.
3 . THE ABNORMAL COMPOUNDS OF CERIUM.-The abnormal com- pounds l i k e A12Ce, A1,Ce and In3Ce a r e c h a r a c t e r i z e d i ) a t h i g h t e m p e r a t u r e (T > 10 K) b y a paramagnetic behaviour of independant t r i v a l e n t cerium i o n s i n i n t e r a c t i o n w i t h t h e c o n d u c t i o n e l e c t r o n s by a k-f c o u p l i n g which l e a d s t o h i g h t e m p e r a t u r e Kondo ano- m a l i e s 1161 and i i ) a t low t e m p e r a t u r e s by h i g h va-
l u e s of t h e l i n e a r t e m p e r a t u r e dependence of t h e s p e c i f i c h e a t C = ~ O Tw i t h yo
&
100 mKmole/^^.
It has been claimed t h a t a s t r o n g i n t e r p l a y o c c u r s between t h e exchange c o u p l i n g among t h e i o n s a n d t h el o c a l i n t e r a c t i o n w i t h i t i n e r a n t e l e c t r o n s which would l e a d t o a non-magnetic ground s t a t e of t h e i o n s . One p o s s i b i l i t y of t r a n s i t i o n from a l o n g ran- ge o r d e r e d m a g n e t i c l a t t i c e t o a non-magnetic l a t - t i c e h a s b e e n s t u d i e d by J u l l i e n e t a l . and i s known a s t h e Kondo l a t t i c e problem 1171.
F i g u r e 3 r e p r e s e n t s t h e N.O. r e s u l t s a t l O m K on t h e m ~ e n u c l e i d i s s o l v e d i n Al,Ce, In,Ce, A13Ce, Sn,Ce /18/.For a paramagnetic i o n i n an i s o -
t r o p i c d o u b l e t
r7
ground s t a t e , t h e a x i a l gamma r a y a n i s o t r o p y a l o n g H must be p o s i t i v e . I n low f i e l d s , t h e main p o i n t s a r e t h a t , i n t h e f i r s t two compounds t h e sign o f E(0) is n e g a t i v e whereas i n t h e l a s ttwo compounds E(0) > 0 . The f i r s t s i t u a t i o n i s well- e x p l a i n e d by an a n t i f e r r o m a g n e t i c - l i k e o r d e r e d ' ground s t a t e . In low f i e l d s , t h e l o c a l moments choose t o b e p e r p e n d i c u l a r t o t h e a p p l i e d f i e l d ;
t h e s i g n of E(0) i s r e v e r s e d s i n c e t h e e q u a t o r i a l and a x i a l a n i s o t r o ~ i e s have o p p o s i t e s i g n e s . The second s i t u a t i o n seems t o d e s c r i b e a paramagnetic behaviour. A t y p i c a l example of such a c a s e i s g i v e n i n f i g u r e 3 by t h e r e s u l t s o b t a i n e d on t h e d i l u t e a l l o y of A12GCe well-known a s a Kondo s t a t e
(TK % 400 mK). There can b e no doubt about Sn,Ce from t h e o t h e r measurements. More s i g n i f i c a n t e v i - dence of a non-magnetic ground s t a t e i n A13Ce h a s been g i v e n b e f o r e by Andres e t a l . 1191 who have r e p o r t e d t h e u n u s u a l l y h i g h v a l u e of
y o = 1620 d r n o l e l ~ ~ .
E x p e r i m e n t a l l y , A1,Ce i s t h e most s t u d i e d compound 1201. Below t h e maximum, a t T M % 3.8 K , of t h e s p e c i f i c h e a t , a l o n g r a n g e m a g n e t i c o r d e r i n g of a s i n u s o y d a l mode h a s been observed r e c e n t l y by a n e u t r o n measurement 1211. The absence of any o t h e r s p e c i f i c h e a t anomaly a t lower t e m p e r a t u r e 1201, t h e p e r s i s t e n c e of t h e s i n u s o y d a l mode down TM/10 1221 and t h e o b s e r v a t i o n by N.O. of an o r d e r i n g down t o 5 mK s t r o n g l y s u p p o r t t h e p e r s i s t e n c e of t h e same s t r u c t u r e t o OK. T h i s behaviour i s q u i t e unusual f o r l o c a l moments i n a d o u b l e t ground s t a t e : c l a s - s i c a l arguments r u l e o u t such a s t r u c t u r e a t OK s i n - c e , whatever w i l l b e t h e exchange f i e l d , i t s magni- t u d e i s s u f f i c i e n t , t o a l i g n t h e m a g n e t i c moment.
S t e g l i c h e t a l . ( s e e r e f e r e n c e /21/ and Benoit e t a l . 1221 have d e r i v e d a v e r y crude phenomenological model i n o r d e r t o e x p l a i n t h i s abnormal b e h a v i o u r .
A t OK, e a c h cerium i o n i s magnetized, u s i n g a Kondo-like s i n g l e t law, under t h e a c t i o n of t h e f l i c t i t i o u s Hm f i e l d produced by t h e o t h e r i o n s ; t h e occurence o f a s i n u s o i d a l s t r u c t u r e i s l i n k e d t o t h e p r e s e n c e of a c r y s t a l l i n e a n i s o t r o p y .
An i m p o r t a n t c o n t r i b u t i o n t o t h e u n d e r s t a n - d i n g o f t h e s e b e h a v i o u r s should b e g i v e n by p r e s s u r e measurements. I w i l l r e p o r t h e r e t h e r e c e n t s p e c i f i c h e a t e x p e r i m e n t s made by B e r t o n e t a l . 1231 onAl,Ce, In,Ce, A13Ce. F i g u r e 4 d e s c r i b e s t h e s p e c i f i c h e a t of A1 Ce w i t h a z e r o and 6 Kbar p r e s s u r e ; i n b o t h c a s e s , t h e m a g n e t i c e n t r o p y a s s o c i a t e d w i t h t h e or- d e r i n g AS i s n e a r 0.4 R Log 2. We have r e p o r t e d on
t a b l e 111 t h e z e r o p r e s s u r e r e s u l t s , t h e low tempe- r a t u r e d a t a i s analyzed u s i n g a c o n v e n i e n t law :
( I n o r d i n a r y a n t i f e r r o m a g n e t s , t h e T , law d e s c r i b e s t h e s p i n wave e x c i t a t i o n s ) . The f i r s t and second columns r e p r e s e n t t h e yo and B v a l u e s , t h e t h i r d t h e t e m p e r a t u r e of t h e s p e c i f i c h e a t maximum TM i f o b s e r v e d , t h e f o u r t h t h e s u s c e p t i b i l i t y
X
ex-Fig. 4 : S p e c i f i c h e a t of t h e CeA1, compound f o r a zero and 6 k b a r p r e s s u r e
Table 111
Low temperature r e s u l t s on A12Ce, In,Ce, A1,Ce a t z e r o p r e s s u r e
t h e p r e s s u r e dependence of y can be explained by t h e p i c t u r e of t h e molecular f i e l d Hm a p p l i e d t o t h e Kondo behaviour of one i o n . For one i o n , t h e Kondo coupling l e a d s t o an e l e c t r o n i c s p e c i f i c h e a t i n v e r - s e l y p r o p o r t i o n a l t o TK ; i t s f i e l d v a r i a t i o n c a n b e approximated by t h e r e l a t i o n :
Y QJ k T ~ f o r kBTK % g)-~ H
+ (g!JBH) 8
Here by i n c r e a s i n g t h e p r e s s u r e , t h e b a r e Kondo tem- p e r a t u r e i n c r e a s e s ( a "golden r u l e " f o r a d i l u t e a l l o y ) , t h e r e l a t i v e molecular f i e l d gu Hm/kT para-
6 K
meter h a s an almost c o n s t a n t dependance a s r e p o r t e d t h e i n c r e a s e of TM ; t h e f i n a l e l e c t r o n i c s p e c i f i c h e a t d e c r e a s e s .
Table I V
Same r e s u l t s under a 6 k b a r p r e s s u r e
t r a p o l a t e d t o OK, t h e f i f t h a n a t t e m p t t o g i v e an e v a l u a t i o n yHT of y j u s t above. TM f o r A12Ce and I n a c e and above 6 K f o r A1,Ce. According t o t h e d i f f e r e n t TM v a l u e s , t h e T , term i s c o n s i d e r a b l y
lower i n t h e In3Ce compound than i n A1,Ce (6 % T;,).
The v a r i a t i o n of t h e corresponding parameter u n d e r a p r e s s u r e of 6 Kbar i s i n d i c a t e d i n t a b l e I V a s t h e s h i f t ATM = TM(P)
-
TM(0) i n t h e t h i r d column. The v i c i n i t y of a non magnetic ground s t a t e seems t o occur f o r I n 3 & s i n c e ATM < 0 whereas ATM> 0 f o r A 1 Ce. The experimental consequence i s t h e s t r o n g i n c r e a s e of y and t h e almost z e r o v a l u e of 6 obser- ved i n In,Ce ; c l e a r l y t h e s p i n f l u c t u a t i o n of t h e magnetic moment w i t h t h e e l e c t r o n i c s e a i n c r e a s e st h e e l e c t r o n i c s p e c i f i c h e a t term. For A12Ce a de- c r e a s e of y and a weaker d e c r e a s e of 6 a r e o b s e r v e d ;
More d i f f i c u l t t o e l u c i d a t e a r e t h e AljCe p r o p e r t i e s s i n c e a t high temperatures, a r t e f f e c t may occur from t h e p a r a s i t i c A12Ce and All,Ce pha-
s e s 1241. Experimentally a t z e r o p r e s s u r e t h e main seems t o b e a n i n c r e a s e of C/T when T d e c r e a s e s . M e t a l l u r g i c a l p r e c a u t i o n s must b e taken b e f o r e claiming t h e evidence of Fermi l i q u i d s p i n f l u c t u - a t i o n .
Apart from n a i v e i n t e r p r e t a t i o n s , t h e theo- r e t i c a l s i t u a t i o n i s completely open. We u n d e r l i n e t h a t t h e s e new p r o p e r t i e s can b e found i n q u i t e o t h e r s i t u a t i o n s s i n c e t h e y belong t o a g e n e r a l c l a s s of phenomena l i n k e d t o t h e e x i s t e n c e of well- l o c a l i z e d fermions ( h e r e t h e 4f e l e c t r o n s ) i n s t r o n g i n t e r a c t i o n v i a a continuum ( h e r e t h e Fermi Sea) ( s i m i l a r p r o p e r t i e s a r e r e p o r t e d f o r a c t i n i d e Np compounds 1251).
Experimentally, t h e main p o i n t i s t o c o r r e - l a t e t h e e l e c t r o n i c and l a t t i c e p r o p e r t i e s w i t h t h e magnetic s t a t e of t h e i o n s . A t v e r y low temperature, few experiments have been performed n o t a b l y NMR and t r a n s p o r t measurements. Other problems, i n t h e s e examples where t h e i o n i s n e a r a valency i n s t a b i l i a a r e t h e r o l e of t h e d e f e c t s and of t h e e l e c t r o n
JOURNAL DE PHYSIQUE
phonon coupling. Finally for the cerium nuclei, the /23/ A. Berton, J. Chaussy, B. Cornut, J. Flouquet, J. Odin,
J.Palleau, J. Peyrard, R. Tournier, existence of a nuclear ordering is precluded as the
G. Chouteau and R. Tur, to be published.
stable nuclei have no nuclear moment such a case
mayA. Berton, J. Chaussy, G. Chouteau, B. Cornut, occur for other ions like Pr or
Tm.J. Peyrard and R. Tournier, Procedding Conf. on
Valence instabilities (Plenum Press) 471 (1976) /24/
M.B.Brodsky and R.J. Trainor, Proceedings ACKNOWLEDGMENTS.- "I wish especially to thank LT 15, J. Physique, to be published (1978) Dr. A. Benoit, Prof.
J.Friedel, Dr. F. Hartmann-
Boutron, Dr. J.M. Mignot, Mr. J. Peyrard, Dr. J. Odin, Dr. M. Ribault, Dr. S. Senoussi, and Dr. R. Tournier for stimulating discussions".
References
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/2/ H. Alloul, ICM 76 Physica 86-88B (1977) 449 /3/ See J.A. Gardner, Phys. Rev. (1976) 1395 /4/
J.Flouquet, Prog. Low Temp. Phys. Vol. VII
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R. Tournier, Phys. Rev. Lett. 3 (1976) 203 /6/ B. Hebral, K. Matho, J.M. Mignot and R. Tournier,
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