SURFACE MAGNETISM OF NEARLY MAGNETIC SYSTEMS AND RELATED PROPERTIES

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SURFACE MAGNETISM OF NEARLY MAGNETIC SYSTEMS AND RELATED PROPERTIES

M. Beal-Monod

To cite this version:

M. Beal-Monod. SURFACE MAGNETISM OF NEARLY MAGNETIC SYSTEMS AND RE- LATED PROPERTIES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-339-C5-347.

�10.1051/jphyscol:1984551�. �jpa-00224169�

JOURNAL DE PHYSIQUE

Colloque C5, suppl6rnent au _n04, Tome 45, avrii 1984 page C5-339

SURFACE MAGNETISM OF NEARLY MAGNETIC SYSTEMS AND RELATED PROPERTIES

M.T. Beal-Monod

Laboratoire de Physique d e s ~ o l i d e s * , B 6 t . 510, U n i v e r s i t k Paris-Sud, Centre d f O r s a y , 91405 &say, France

Resume - Nous presentons, p o u r quelques modeles s i m p l e s , l e s m o d i f i c a t i o n s attendues theoriquement dans l e s p r o p r i 6tGs pararnagnetiques d ' u n systeme i t i n e r a n t presque magnetique, p r e s d'une s u r f a c e ou en geometric c o n f in e e .

Quelques e x p e r i e n c e s r e c e n t e s , p r e l i m i n a i r e s , s o n t passees en revue, q u i p o u r r a i e n t correspondre aux m o d i f i c a t i o n s t h g o r i q u e s a t t e n d u e s .

A b s t r a c t - We p r e s e n t , i n s i m p l e model cases, t h e t h e o r e t i c a l l y e x p e c t e d m o d i f i c a t i o n s i n t h e paramagnetic p r o p e r t i e s o f a n e a r l y magnetic i t i n e r a n t system, n e a r a s u r f a c e o r i n c o n f i n e d geometry. A few r e c e n t , p r e l i m i n a r y , experiments , p o s s i b l e l i n k e d t o these e x p e c t a t i o n s ,are reviewed.

We must b r i e f l y r e c a l l f i r s t , t h e main f e a t u r e s o f an i t i n e r a n t n e a r l y m a g n e t i c f e r - mion system /l/, i n t h e b u l k case, ( i n f i n i t e medium), b e f o r e s w i t c h i n g t o t h e s u r - f a c e b e h a v i o r . Such systems remain paramagnetic down t o OK b u t w i t h a u n i f o r m , s t a - t i c s u s c e p t i b i l i t y c o n s i d e r a b l y l a r g e r t h a n t h e P a u l i one f o r f r e e p a r t i c l e s , a l t h o u g h s t i l l f i n i t e :

A number o f systems behave t h a t way, l i k e Landau Fermi l i q u i d s / 2 / , s t a r t i n g f r o m t h e a r c h e t y p e s : Pd(SB ^% 10), l i q u i d He3 i n normal phase (SB 10 t o 20 depending on p r e s s u r e ) , e t c . . . ^, t o t h e l a t e s t most p r o m i s i n g one, TiBe2 (SB 65).

The e x p l a n a t i o n f o r such an enhancement was g i v e n l o n g ago by t h e S l a t e r - S t o n e r i d e a /l/ t h a t a s t r o n g r e p u l s i o n I, among o p p o s i t e s p i n s , f a v o r s ferromagnetism. When I i s o f t h e o r d e r o f ( a l t o u g h s m a l l e r t h a n ) t h e c h a r a c t e r i s t i c energy EF o f t h e f r e e s p i n s (IN(EF) = 7 'I. I/EF % 1, say f o r a p a r a b o l i c band o f f e r m i o n s , w i t h N(EF) t h e d e n s i t y o f s t a t e s a t t h e Fermi l e v e l ) , t h e n i n t h e mean f i e l d p i c t u r e , t h e ( S t o n e r ) s u s c e p t i b i l i t y a l m o s t d i v e r g e s a t OK, w i t h SB i n ( 1 ) g i v e n by :

i .e. t h e system ir c l o s e t o a magnetic i n s t a b i l i t y and i s t h u s " n e a r l y m a g n e t i c " a t OK ( O r course i f I is s t r o n g enough t o exceed 1, t h e n t h e system o r d e r s a t a f i n i t e

temperature below which i t s w i t c h e s f r o m an enhanced i t i n e r a n t paramagnet t o an i t i n e r a n t f e r r o m a g n e t ) . The c r i t i c a l v a l u e o f T f o r t h e o n s e t o f magnetism i n t h e i n f i n i t e b u l k system i s t h u s :

(Tcc)B = 1 ( 3 )

As a c o r o l l a y of what was mentionned above f o r t h e u n i f o r m , s t a t i c s u s c e p t i b i l i t y when I 4 1, t h e momentum ( q ) and frequency (U) dependent dynamic s u s c e p t i b i l i t y x(q,w), computed i n t h e random phase approximation, i s t h e s o l u t i o n o f t h e homoge- neous a l g e b r a i c , B e t h e - S a l p e t e r e q u a t i o n :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984551

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( q , ~ ) i s t h e c o r r e l a t i o n f u n c t i o n i n absence o f i n t e r a c t i o n ,

I i s approximated, t o s i m p l i f y , t o be o f a c o n t a c t type xO(O,O) = N(EF) ^a x p a U l i ⁹

and i n s t a n t a n e o u s , i n r e a l space. x(q,w) e x h i b i t s "pseudo" modes, t h e so c a l l e d

"paramagnons" / 3 / , o r l o n g wave l e n g t h ( q << 2kF), t i m e p e r s i s t e n t ( T > > ( T ~ = ~ ~ - 1 ) i n a.u.) e x c i t a t i o n s i n t h e paramagnetic s t a t e , w i t h a c h a r a c t e r i s t i c s p i n f l u c - t u a t i o n energy :

kg T s f = S-I EF EF ( 5 )

Pdramagnons l i k e o t h e r f l u c t u a t i o n s (phonons e t c . . . ) r e n o r m a l i z e , i n a r t i c u l a r , a l l t h e low t e m p e r a t u r e p r o p e r t i e s o f t h e f e r m i o n system /3/ : enhanced T dependence

g

of X , enhanced e f f e c t i v e mass and t h u s enhanced c o e f f i c i e n t o f t h e l i n e a r T depen- dence o f t h e s p e c i f i c h e a t e t c . . . B u t t h e paramagnons do n o t , however, a t T = 0, m o d i f y t h e mean f i e l d forme o f X , due t o quantum e f f e c t s : t h e c r i t i c a l exponents a t T = 0 K a r e t h e mean f i e l d one /4/ ( T h i s i s i m p o r t a n t t o s t r e s s , i n o r d e r t o e x p l a i n why, i n t h e f o l l o w i n g , we f i r s t c o n c e n t r a t e on a mean f i e l d t y p e Bethe S a l p e t e r e q u a t i o n a t T = 0 K ) .

Then t h e q u e s t i o n a r i s e s : what happens near t h e s u r f a c e of such a system ? The q u e s t i o n becomes c r u c i a l f o r t h e p r o p e r t i e s of t h e i n t e r f a c e between such a n e a r l y magnetic system and a n o t h e r medium, o r f o r t h e p r o p e r t i e s of t h a t n e a r l y magnetic system i n c o n f i n e d geometry, when t h e s u r f a c e t o volume r a t i o of s p i n s i s no l o n g e r n e g l i g i b l e ( f i l m s , powders, e t c . . . ). T h a t problem was f i r s t approached a decade ago / 5 / and e x t e n s i v e l y s t u d i e d l a t e r on / 5 / / 6 / / 7 / / 8 / . T y p i c a l a p p l i c a t i o n s thus appear w o r t h w h i l e t o c o n s i d e r :

- c h e m i s o r p t i o n and c a t a l y s i s o f h y d r o g e n a t i o n r e a c t i o n s , p o s s i b l e due t o i n t e r a c - t i o n s between adsorbed atoms and t h e paramagnons o f t h e n e a r l y magnetic system, depending whether t h e y s u r v i v e o r n o t near t h e s u r f a c e /g/,

- i n c r y o g e n i c s , i n t h e c o o l i n g process of l i q u i d ~ e ~ by h e a t t r a n s f e r t o a c o o l e r s a l t ( m a g n e t i c c o n t r i b u t i o n t o t h e K a p i t z a r e s i s t a n c e a t t h e i n t e r f a c e /10/, s p i n r e l a x a t i o n n e a r a w a l l /11/, i n o r d e r t o s t u d y condensed m a t t e r a t v e r y l o w tem- p e r a t u r e , e t c . . .

The s u b j e c t o f s u r f a c e i t i n e r a n t magnetism i s a wide one. A complete s u r v e y would be i m p o s s i b l e i n these few pages, where we w i l l c o n f i n e t o some t y p i c a l aspects f o r some s i m p l e (a1 though q u i t e d i f f i c u l t t o h a n d l e ) model cases. A complete l i s t o f references i s a s w e l l i m p o s s i b l e t o p r e s e n t . F o r t h e same reason, we w i l l g i v e v e r y few f o r m u l a s : t h e d e t a i l s can be found i n t h e r e f e r e n c e s quoted a t t h e end o f t h e paper. We o n l y w i s h t o e x t r a c t some p h y s i c a l l y i m p o r t a n t f e a t u r e s and e x h i b i t t h e m a i n d i f f e r e n c e s a r i s i n g i n t h e magnetism between a f i n i t e and an i n f i n i t e i t i n e - r a n t f e r m i o n system / 1 2 / .

I - MODIFIED MAGNETISM OF NEARLY MAGNETIC ITINERANT SYSTEMS I N PRESENCE OF WALLS The problem o f t h e b e h a v i o r of X , near a surface, i s e x t r e m e l y d i f f i c u l t , compared t o t h e s i m p l e b e h a v i o r i n t h e i n f i n i t e medium, even i n mean f i e l d and even a t T = 0;

why ? The i n f i n i t e b u l k fermion system can be c h a r a c t e r i z e d as a u n i f o r m , i s o t r o p i c , t r a n s l a t i o n a l l y i n v a r i a n t system. A s u r f a c e i n t r o d u c e s a p e r t u r b a t i o n i n t o t h a t system, q u a l i t a t i v e l y analogous t o t h e one due t o i m p u r i t i e s , d e f e c t s , e t c . .. : t r a n s l a t i o n a l i n v a r i a n c e i s broken, a t l e a s t , i n t h e d i r e c t i o n ( s a y z ) p e r p e n d i c u l a r t o t h e s u r f a c e ; t h i s y i e l s t h e p r o p e r t i e s o f t h e system t o be non u n i f o r m and a n i s o - t r o p i c , even i f t r a n s l a t i o n a l i n v a r i a n c e may be supposed p r e s e r v e d i n d i r e c t i o n s p a r a l l e l t o t h e s u r f a c e s . Consequently, t h e homogeneous, a l g e b r a i c Bethe-Sal p e t e r e q u a t i o n ( 4 ) v a l i d f o r t h e i n f i n i t e medium, s w i t c h e s , i n presence o f w a l l s , t o a n i g t 2 g r a l e q u a t i o n (Fredholm e q u a t i o n o f t h e second k i n d ) w i t h a non u n i f o r m k e r n e l

(q,,

..

I n ( 6 ) ,

1

I t i s c r u c i a l , a1 though very f r u s t r a t i n g , t o note t h a t any s l i g h t m o d i f i c a t i o n o f the r e a l kernel i n ( 6 ) t o g e t a separable t r i a l f u n c t i o n , m m l d t o very d i f f e r e n t answers f o r the r e s u l t i n g X. The a c t u a l s t r u c t u r e o f the k e r n e l , t h e f r e e p a r t i c l e - f r e e h o l e c o r r e l a t i o n f u n c t i o n i n (G), i s i n s t r u c t i v e ; i t depends, o f course, on the model chosen. I t can be computed a n a l y t i c a l l y r i g o r o u s l y , f o r i n s t a n c e f o r the j e l l i u m model, w i t h an i n f i n i t e b a r r i e r p o t e n t i a l a t the surface (V(z=O) = -,

V(z

+

F i g . 1 - The f o u r processes i n v o l v e d i n x0

When none o f them i s r e f l e c t e d o r when b o t h are ( F i g . l ( a ) and ( b ) ) , one gets a u n i f o r m c o n t r i b u t i o n t o x O ( b u l k type x;(z-z') o r "image" b u l k type x;(z+z8); b u t when o n l y one i s r e f l e c t e d , ( F i g . l ( c ) and ( d ) ) one gets u n t r a c t a b l e non u n i f o r m

c o n t r i b u t i o n s ( ~ ; - ~ ( z , z ' ) ) i n r e a l space, w i t h z and z ' F o u r i e r conjugates of qZ and q;.xO o s c i l i i t e s as a f u n c t i o n o f z ( f o r f i x e d z ' ) away from the surface, t h e magnitude o f the o s c i l l a t i o n s decreasing f o r i n c r e a s i n g z.

These o s c i l l a t i o n s , o f t y p i c a l wavelength equal t o the Fermi one kF-', are induced by the surface, l i k e F r i e d e l type o s c i l l a t i o n s a r e induced by an impuri t y i n the i n f i n i t e medium. Consequently, w h i l e , i n the b u l k , o n l y long wavelengths ( q << 2kF) p l a y a r o l e i n the approach o f magnetism ( i n f r a r e d divergencies a t c r i t i c a l i t y ) , i n presence o f w a l l s , s h o r t wavelengths ( q a 2kF) a r e e q u a l l y important. Therefore Thomas-Fermi type expansions i n powers o f q f o r xo , which p l a y the e s s e n t i a l r o l e near c r i t i c a l i t y i n the bulk, y i e l d t o o n l y p a r t o f the f i n a l answer f o r X(as noted

C5-342 JOURNAL DE PHYSIQUE

concerning the 1 s t o f r e f s . 151) ; i n p a r t i c u l a r the F r i e d e l o s c i l l a t i o n s e x h i b i t e d i n an e x a c t numerical computation (see the 2nd o f r e f s . / 5 / ) and responsiblk f o r a p o s s i b l e surface i n s t a b i l i t y /7/ would be missed.

The mean r e s u l t s concerning t h e s o l u t i o n o f ( 6 ) are t h e f o l l o w i n g :

- x ( z , z l ) e x h i b i t s o s c i l l a t i o n s i n the z d i r e c t i o n , f o r f i x e d z ' , l i k e X0(a, z ' ) , b u t s t r o n g l y enhanced by the i n t e r a c t i o n compared t o those o f xO; they vanish l i k e those o f xO, deep i n the b u l k , where X recovers i t s b u l k behavior ;

- no a n a l y t i c a l formula being a v a i l a b l e f o r ~(q,,, q,, q;, ^U = 0), i t cannot be w r i t t e n under a form comparable t o the b u l k one x O ( q , O ) / ( l - ~ x O ( q , O ) ) which was p a r t i c u l a r l y convenient t o study the c r i t i c a l behavior when ( 1 - Ixo(O,O)) = 0

- f i n a l l y the uniform, s t a t i c " s u s c e p t i b i l i t y a t 0 K may be so s t r o n g l y enhanced near the surface t h a t i t diverges and the surface r e g i o n undergoes a magnetic i n s - t a b i l i t y w h i l e the b u l k p a r t o f the system remains paramagnetic.

I 1 - ONSET OF MAGNETISM I N CONFINED GEOMETRIES

The fundamental r e s u l t s can be summarized as f o l l o w s /7/ /12/

a/ the c r i t i c a l value (?ic)s f o r the onset o f magnetism near a surface i s i n general d i f f e r e n t from the i n f i n i t e medium one ( T C I m = 1

W i t h i n the hypothesis of the previous s e c t i o n ( p e r f e c t surface, specular r e f l e x i o n , i n f i n i t e b a r r i e r , constant I, e t c . . . ) one gets i n the surface r e g i o n :

( i C l S < 1 ( 8 )

An analytical v a r i a t i o n a l method / 7 / proved t h a t the above i n e q u a l i t y found numeri- c a l l y , i s indeed c o r r e c t .

- Case 1 : - I ^c ( T C I s ^c ( i C I m , the whole sample remains paramagnetic w i t h a P a u l i

type s u s c e p t i b i l i t y down t o 0 K, b u t w i t h an o v e r a l l enhancement g r e a t e r than i n the i n f i n i t e medium case : the system i s c l o s e r t o become magnetic i n confined geometry, the fermions are h e a v i e r (more enhanced e f f e c t i v e mass) e t c . . .

- Case 2 : - Ic _< (Tc), , the deep i n t e r i o r o f the system remains paramagnetic b u t

the surface r e g i o n undergoes a magnetic t r a n s i t i o n ( I t i s amusing t o r e c a l l here the existence o f the H f i e l d , i n superconductors i n presence o f s u r f a c e s / l 4 / : f o r

C3

instance, i n type 2 superconductors, when H H H the b u l k o f the sample i s

C2 ^C 3

normal b u t t h e r e i s a superconducting sheath-in some p a r t s o f the surface r e g i o n ) . Here the surface r e g i o n switches t o an i t i n e r a n t ferromagnetic phase i n p r i n c i p l e a t f i n i t e T. However s i n c e the surface r e g i o n has a 2 dimensional c h a r a c t e r and that, i n 2d, the magnetic ordered phase should o n l y be reached a t 0 K /15/, the paramagnetism o f the surface r e g i o n i s expected t o remain down t o 0 K o f a (modified) Curie-Weiss type as w i l l be e x p l a i n e d l a t e r on.

b / the p r e c i s e value o f (f ) depends on the p a r t i c u l a r model chosen. I f some o f the very simple b a s i c hypotheses used so f a r a r e released, the previous r e s u l t s are m o d i f i e d . For i n s t a n c e :

- i f i n s t e a d o f a zero range f o r I, one takes i n t o account a f i n i t e range, b u t s t i l l no z dependence, the surface i n s t a b i l i t y ,found i n case 2 abovepay disappear f o r

l a r g e enough values of t h e range / 6 / : however,

- i f , i n s t e a d of a zero range, and a c o n s t a n t magnitude f o r I , one takes i n t o account a f i n i t e range and allow f o r a z dependence t o o , a d e n s i t y functional formalism of Kohn-Hohenberg-Sham type, / 8 / , with t h e usual l o c a l d e n s i t y approxi- mation, shows t h a t I ( z ) i n c r e a s e s near the s u r f a c e ( z -t 0 ) and may e a s i l y exceed

( I c ) , ; then the s u r f a c e , magnetic i n s t a b i l i t y may p e r s i s t and would be suppressed only f o r a much l a r g e r value of the I range than above.

- i f , back t o a c o n s t a n t and z independent I , one takes i n t o account, added t o the i n f i n i t e b a r r i e r p o t e n t i a l a t the s u r f a c e , a Van der Waals type a t t r a c t i o n t o the medium possibly p r e s e n t on the o t h e r s i d e of the wall /16/, the o s c i l l a t i o n s i n the response f u n c t i o n a r e more enhanced and more c l o s e l y confined i n t h e a t t r a c t i v e well region near t h e s u r f a c e ; moreover, 1 s . d e c r e a s e d a l l the more t h a t the a t t r a c - t i v e p a r t of t h e p o t e n t i a l i s deep; thus I i s more l i k e l y t o exceed (I,)< than i n the preceding cases and t h e s u r f a c e magnetic i n s t a b i l i t y i s more e a s i l y reached. In t h i s case too, bound s t a t e s appear i n the a t t r a c t i v e well region : p a r t i c l e s i n t h e bound s t a t e s a r e , however, f r e e t o move p a r a l l e l t o t h e surface b u t they form a f l u i d of high d e n s i t y / 1 7 / , (weakly) bound t o t h e s u r f a c e .

- i f the s p e c u l a r r e f l e c t i o n s on the s u r f a c e by the p a r t i c l e and t h e hole,involved i n and x,are suppressed f o r some reason, one recovers the bulk type forms f o r x0

and X , I c = 1 and the magnetism of the system does not d i f f e r from t h e i n f i n i t e medium one. Random roughness of the s u r f a c e could possibly y i e l d such a r e s u l t through highly d e s t r u c t i v e i n t e r f e r e n c e s of the various r e f l e c t i o n s of d i f f e r e n t kinds; however a p e r i o d i c s t r u c t u r e of the s u r f a c e could, i n c o n t r a s t , y i e l d cons- t r u c t i v e i n t e r f e r e n c e s . Such . e f f e c t s on t h e magnetism would be worthwhile t o study i n d e t a i l .

F i n a l l y one cannot d i s c a r d cases where (Tc)s > (TC), , y i e l d i n g an o v e r a l l enhan- cement of t h e Pauli s u s c e p t i b i l i t y , i n the confined geometry system, smaller than i n the i n f i n i t e medium one : the s u r f a c e i s l e s s c l o s e t o become magnetic than t h e bulk. I f I-< ( I C ) , the s u r f a c e i n ~ t a b i l i t y i s never reached (nor t h e bulk o n e ) ; (of course i f I may exceed not only ( I C ) , but a l s o ( I c ) s t h e whole sample switches t o an i t i n e r a n t ferromagnet. These cases a r e obviously l e s s - i n t e r e s t i n g than t h e various ones studied above,for a l l of which one always f i n d s ( I c ) s (Ic),.

Why i s (TCIs d i f f e r e n t from

(T)=

-

-

Analogously f o r l o c a l i z e d spin systems /18/ one g e t s a ferromagnetic t r a n s i t i o n i n the s u r f a c e region of a paramagnetic bulk when the i n t e r a c t i o n between n e a r e s t neighbour Heisenberg s p i n s i s g r e a t e r a t t h e s u r f a c e than i n t h e bulk.

I11 - EXPECTED CONSEQUENCES AND POSSIBLY RELATED EXPERIMENTS

We now examine what a r e t h e p o s s i b l e i m p l i c a t i o n s of t h e above t h e o r e t i c a l r e s u l t s . on the physical p r o p e r t i e s of t h e system / V / . Let us pursue our q u a l i t a t i v e p i c t u r e

C5-344 JOURNAL DE PHYSIQUE

o f a l o c a l l y v a r y i n g enhancement S(=) = ( 1 - I g(z))-l i n the d i f f e r e n t "onion"

l a y e r s h e l l s , p a r a l l e l t o the surfaces, w i t h consequent z dependent s p i n f l u c t u a t i o n temperatures such t h a t :

S ( z ) increases

when z decreases

Tsf ( z ) decreases (10)

Case 1 corresponds t o S(z) f i n i t e f o r a l l z, w h i l e i n case 2, S ( z ) becomes i n f i n i t e i n a range z < z

0 '

- I n case 1, as a l r e a d y mentionned, average over z values y i e l d x(T = 0 ) >> xBulk and Tsf << (Tsf)Bulk. Then s c a l i n g arguments (see 2" o f / U / ) s t r a i g h f o r w a r d y y i e l d t o expect t h e "low T" (T < Tsf) behavior o f X, and any p r o p e r t y depending on X, t o be r e s t r i c t e d t o a narrower temperature range than i n the b u l k , w h i l e the "high T"

(T > T s f ) behaviors w i l l a r i s e a l r e a d y f o r temperatures where the b u l k s t i l l assume i t s "low T" behavior, when : Tsf < T (Tsf)Bulk. Therefore the " h i g h t T" type Curie- Weiss law (T + e ) - l r e c e n t l y observed /19/ f o r x(T) o f Pd i n some Au-Pd-Au sandwichs i n a low T range where b u l k Pd e x h i b i t s i t s "low T" temperature independent

enhanced P a u l i s u s c e p t i b i l i t y , m i g h t be r e l a t e d t o t h a t case.

I n t h a t case 1 too,the e f f e c t i v e mass, already increased i n the b u l k (2nd o f r e f . / 3 / ) i s even more enhanced i n t h i s confined geometry. Such an e f f e c t may correspond t o the observation made on l i q u i d ~ e 3 d r o p l e t s d i s s o l v e d i n s o l i d He4 /20/.

I n b u l k systems, s t r o n g s p i n f l u c t u a t i o n s prevent s i n g l e t p a i r i n g BCS type super- c o n d u c t i v i t y ( 3 r d of r e f . / 3 / ) , b u t , a l t o g e t h e r , f a v o r t r i p l e t p a i r i n g one /21/

as proved b y the observed s u p e r f l u i d i t y /22/ i n l i q u i d He3 a t very low T. Therefore.

since i n case 1, s p i n f l u c t u a t i o n s are even s t r o n g e r than i n t h e bulk, t r i p l e t p a i r i n g s u p e r c o n d u c t i v i t y m i g h t be more e a s i l y observed i n confined geometry /23/

(under s u i t a b l e s c o n d i t i o n s ) than i n the b u l k . Recent r e s i s t i v i t y measurements i n some Ag-Pd-Ag sanswichs e x h i b i t s /24/ s u p e r c o n d u c t i v i t y , p o s s i b l e l i n k e d t o t h a t proposal; however corresponding s u s c e p t i b i l i t y data would be needed t o check whether a "low T" temperature independent P a u l i s u s c e p t i b i l i t y , much l a r g e r than the b u l k one, i s observed i n the same T range where s u p e r c o n d u c t i v i t y appears. If so, then the p r e v i o u s l y c i t e d Au-Pd-Au sandwichs would be worthwhile t o study a t lower temperature than i n /19/, i n o r d e r t h a t the "low T" regime would be reached, and t o check then whether s u p e r c o n d u c t i v i t y appears o r n o t (although s p i n - o r b i t p a i r breaking, p o s s i b l y s t r o n g e r i n Au-Pd-Au sandwichs than i n Ag-Pd-Ag ones, may prevent i t s observation)

- I n case 2, on the o t h e r hand, one must consider, separately, the b u l k p a r t o f the sample where the v a r y i n g p i c t u r e o f S(z) holds, and the surface r e g i o n where S ( z < zn) = m i n mean f i e l d . To t h e enhanced, P a u l i type, temperature independent o v e r a l l s u s c e p t i b i l i t y o f the i n t e r i o r , one expects ( i n mean f i e l d ) , superimposed ,

a s t r o n g T dependence o f Curie-Weiss type (T - T ~ ) - I a r i s i n g from the surface region. However as a1 ready p o i n t e d out, s t r o n g 2 dimensional f l u c t u a t i o n s w i l l prevent the mean f i e l d i n s t a b i l i t y t o occur a t f i n i t e To : one expects the suscep- t i b i l i t y t o smoothly d e v i a t e from the mean f i e l d law ( T - - T ~ ) - ' , when To i s approa- ched from above, so t h a t X diverges o n l y when T = 0 K i s reached. However the sur- face r e g i o n i s n o t s t r i c t l y 2 dimensional b u t b e t t e r corresponds t o a cross over between 2 and 3 dimensions ; under such c o n d i t i o n s Tn could be found f i n i t e (Tn

+

although very small, much s m a l l e r than the mean f i e l i value. Below To+ 0 one c o u l d then have an ordered phase i n the surface r e g i o n /25/. Experimentally d i f f e r e n t groups /26/ have observed an anomalous T dependence o f the s t a t i c s u s c e p t i b i l i t y o f l i q u i d He3 i n v a r i o u s confined geometries (between mylar f o i l s , o r between carbon o f alumina p a r t i c l e s , i n g r a f o i l . . ) i n the mK range where the b u l k e x h i b i t s a T independent enhanced P a u l i type s u s c e p t i b i l i t y . The surface, s t r o n g l y T dependent

p a r t of X has been suggested /27/ t o r e f l e c t t h e t h e o r e t i c a l r e s u l t s o f case 2.

Simultaneously t h e s u r f a c e 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 T1 T-2 o f b u l k l i q u i d He ,

i s m o d i f i e d near the s u r f a c e , T1 T (3rd o f r e f s . / 1 1 / ) and was proposed t o be e x p l i c a b l e (2nd o f r e f . / 1 1 / ) w i t h the above p i c t u r e .

The two o r quasi two dimensional s u r f a c e r e g i o n b r i n g s i n t h e problem o f the a c t u a l magnetic b e h a v i o r i n a t r u l y 2-dimensional s t r o n g l y i n t e r a c t i n g i t i n e r a n t b u l k f e r m i o n systems /18/. We cannot e n t e r i n t o the d e t a i l s here, b u t t h i s problem i s much more d i f f i c u l t t h a n t h e b u l k 3 dimensional one : usual p e r t u r b a t i o n t h e o r y breaks down and r e n o r m a l i z a t i o n group methods f a i l s i n c e a Ginzburg-Landau-Wi l s o n expansion cannot be used. T h e r e f o r e t h e q u a l i t a t i v e b e h a v i o r o f X, d e s c r i b e d above i n t h e s u r f a c e r e g i o n o f case 2, i s f a r f r o m becoming r i g o r o u s l y proved : u n i v e r - s a l i t y arguments suggest a b e h a v i o r analogous t o t h e one o f 2 dimensional l o c a l i z e d s p i n system /29/, b u t t h e problem i s o n l y i n a p r e l i m i n a r y stage f o r t h e moment.

F i n a l l y we must n o t e t h a t s u r f a c e two dimensional band ferromagnetism i n a n o t h e r c o n f i n e d geometry f o r Pd was proposed t o e x p l a i n anomalous r e s i s t i v i t y b e h a v i o r /30/.

Spin f l u c t u a t i o n s were a l s o proposed /31/ t o e x p l a i n the s t r o n g T dependence o f the s u s c e p t i b i l i t y observed /32/ i n V f i n e p a r t i c l e s .

I V - CONCLUSION

We have shown t h a t even w i t h i n s i m p l e s t a r t i n g hypotheses, t h e s t u d y o f the i t i n e - r a n t paramagnetism n e a r a s u r f a c e i s e x t r e m e l y complicated. We have t r i e d t o present a p h y s i c a l p i c t u r e f o r each o f the two most i n t e r e s t i n g d i f f e r e n t b e h a v i o r s expected from t h e t h e o r y . A l o t more needs t o be done t h e o r e t i c a l l y , i n p a r t i c u l a r a? f a r as dynamics ( ~ $ 0 ) a r e concerned/33/,as we1 l as the f l u c t u a t i o n s i n t e r a c t i o n s 1 n t h e c r o s s o v e r between 2 and 3 dimensions . The experiments p o s s i b l y l i n k e d t o such e f f e c t s a r e v e r y few so f a r . More would be h e l p f u l , f i r s t t o p o s s i b l y c o n f i r m t h e expected e f f e c t s , second t o a1 low t h e t h e o r y t o focuse i n p r e c i s e d i r e c t i o n s .

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