THE EFFECT OF PRESSURE ON THE ONSET OF FERROMAGNETISM IN DISORDERED Pd Ni ALLOYS

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THE EFFECT OF PRESSURE ON THE ONSET OF

FERROMAGNETISM IN DISORDERED Pd Ni

ALLOYS

F. Acker, R. Huguenin

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-867

THE EFFECT OF PRESSURE ON THE ONSET OF FERROMAGNETISM

IN DISORDERED Pd Ni ALLOYS

F. Acker and R. Huguenin

Institut de Physique Exp6rimentale de I'University de Lausanne, CH 1015 Lausanne, Switzerland.

Résumé.- La t h é o r i e de Landau des t r a n s i t i o n s de phase e s t p r i s e comme base d'un modèle simple décrivant l ' a i m a n t a t i o n des a l l i a g e s Pd_ Ni. Nous estimons l a valeur de la concen-t r a concen-t i o n c r i concen-t i q u e , c , à 3,7 % a concen-t . environ. Une f a i b l e concenconcen-traconcen-tion de momenconcen-ts g é a n concen-t s , c e n t r é s (comme l ' a montré Chouteau) sur des groupes d'atomes contenant au moins 3 Ni p r o -ches v o i s i n s , p e r t u r b e l e comportement i d é a l de l a matrice de Pd_ Ni. En i n t r o d u i s a n t un seul paramètre supplémentaire, de / d p , nous rendons compte de façon s a t i s f a i s a n t e des e f f e t s de l a pression mesurés par B e i l l e , j u s q u ' à 10 % a t . Ni.

Abstract.- The Landau theory of phase transitions is taken as the basis for a simple model describing the magnetization of Pd_ Ni alloys. We find the critical concentration, cQ, around 3.7 at. % Ni. A small concentration of giant moments, centered (as shown by Chouteau) on groups of 3 or more Ni neighbour atoms, perturbs the ideal behaviour of the matrix. Intro-ducing dco/dp as a single additional parameter we obtain a good fit of the pressure effects measured by Beille, up to 10 at. % Ni.

Among the weakly magnetic Ni alloys, Pd_ Ni

seem to be the simplest ones because of the small

value of c , the critical Ni concentration for fer-o

romagnetism. The percolation limit is not yet

rea-ched and it is easy to number the Ni clusters of a given size. The more clear cut result of the

magne-tic measurements of Chouteau l\l is that the groups of 3 or more Ni first neighbour atoms bear giant

magnetic moments and polarize the surrounding

matrix.

We propose here a very simple model where

the matrix, considered as magnetically homogeneous,

follows the Landau theory of phase transitions. Its

interaction with the giant moments is described in

the molecular field approximation 121. This model applies equally well to VNi /3/, RhNi or PtNi (to

be published). The magnetization, M, is expressed by

M » Mj + M j , where

AM + BMi = H + XM2

1 p g J u (H + XM,) 1

M

2

= NgJUgBj

I

0

. J

The parameters A, B, X, N and J can be extracted from experiment. Our analysis of existing data, in

particular the measurements of Beille / 4 / , is in

agreement with the result of Chouteau /l/ that 3N = N c f l - O - c )1 2 ~ 1 2 c ( l - c )1 8! . We take 10u„

(i.e. J = 5) as the mean value of the giant moments,

and X = 500 mole/emu for the molecular field

pa-rameter, independently of the Ni concentration.

B can be considered as a constant; its inverse is approximately equal to the slope of the high field

Arrott plots (M2 vs. H/M). We chose B : 8xl0-1*

(emu/mole). At low concentration, A is simply the

inverse of the alloy susceptibility; the slight

curvature of A(c), already visible on figure 1 below 1,5 at % Ni, is clearly related to the

de-viation from linearity of the concentration of

single Ni impurities, c-j(c) = c(l-c)1 2 . 1.5 -i

\

\

- \

\

1 \

i- \

o " 1 i ^ ^ t y ^ ' 1 3 ^ > 0 e (at.*/. Ni) " ^ ^ s . 0 . 5

-F i g . 1 : Proposed v a r i a t i o n of the Landau parame-t e r A wiparame-th Ni c o n c e n parame-t r a parame-t i o n , aparame-t T - 0 (see parame-t e x parame-t ) .

I n t h e weakly f e r r o m a g n e t i c a l l o y s , above

-

4 a t . % N i , we have

I A ~

5

( 2 ~ ~ ~ ) - ~ , because of t h e p r e s e n c e of m a g n e t i c i n h o m o g e n e i t i e s (xo0 is t h e d i f f e r e n - t i a l s u s c e p t i b i l i t y ) . I n t h e c a l c u l a t i o n s presen- t e d h e r e , A(c) was r o u g h l y approximated by t h e s t r a i g h t l i n e o f f i g u r e I . The c o r r e s p o n d i n g c r i - t i c a l c o n c e n t r a t i o n i s t h u s t o o h i g h by a b o u t 0.5 a t . % ( s e e f i g u r e s 2 , 3 and 4 ) . Following t h e Sto- ner-Edwards-Wohlfarth model of weak ferromagnetism, we w r i t e A(T, c , p) = a ~ ~

+

6 ( c -c) w i t h

c = c

+

yp. The c a l c u l a t e d m a g n e t i z a t i o n , i n

0 00

f i e l d s up t o 150 kOe i s i n good agreement w i t h B e i l l e ' s measurements

131,

a l s o a t f i n i t e tempera- t u r e s . L e t u s c o n s i d e r h e r e , on f i g u r e s 2 , 3 and 4 , t h e e f f e c t of h y d r o s t a t i c p r e s s u r e on t h e m a g n e t i c p r o p e r t i e s . Fig. 2 : P r e s s u r e d e r i v a t i v e of t h e spontaneous m a g n e t i z a t i o n v e r s u s N i c o n c e n t r a t i o n . P o i n t s : B e i l l e ' s e x p e r i m e n t s ; s o l i d curve : c a l c u l a t e d ( m a t r i x

+

c l u s t e r s ) ; dashed c u r v e : c a l c u l a t e d ( m a t r i x a l o n e ) . Our s i n g l e a d d i t i o n a l p a r a m e t e r , d c /dp = 2x10- 4 kbar-I was chosen s o a s t o g i v e t h e r i g h t o r d e r of magnitude of t h e v a r i a t i o n of t h e spontaneous m a g n e t i z a t i o n w i t h p r e s s u r e , n e a r 3 a t . % N i ( f i - g u r e 2 ) . The e x p e r i m e n t a l minimum (4) a p p e a r s a t t h e r i g h t c o n c e n t r a t i o n . The observed v a r i a t i o n w i t h p r e s s u r e of t h e " a l l o y s u s c e p t i b i l i t y " , f i - g u r e 3 , and t h e C u r i e t e m p e r a t u r e , f i g u r e 4 , (de- f i n i t i o n s i n r e f e r e n c e / 4 / ) a r e a l s o f a i r l y w e l l reproduced i n s p i t e of t h e s i m p l i c i t y of t h e model

(no a t t e m p t was made t o r e f i n e t h e c h o i c e of t h e p a r a m e t e r s ) . It i s o b v i o u s , from t h e s e last t h r e e f i g u r e s , t h a t t h e r e s p o n s e of t h e m a t r i x i s s t r o n g - l y damped by t h e p r e s e n c e o f t h e g i a n t moments. F i g . 3 : P r e s s u r e d e r i v a t i v e o f t h e " a l l o y suscep- t i b i l i t y " v e r s u s N i c o n c e n t r a t i o n . Symbols and c u r v e s a s on f i g u r e 2 . F i g . 4 : P r e s s u r e d e r i v a t i v e of t h e C u r i e tempera- t u r e v e r s u s N i c o n c e n t r a t i o n . Symbols and c u r v e s a s on f i g u r e 2 . ( a ) H = 0 ; b ) Deduced from h i g h f i e l d A r r o t t p l o t s , f o l l o w i n g B e i l l e .

These c u r v e s can b e compared w i t h t h e r e s u l t s of t h e more e l a b o r a t e model of B e i l l e and Chouteau 1 4 ,

References

/

I/ Chouteau, G., Physica

84

((1976) 25.

/ 2 / Chalkwijk, M.S., B r o m e r ,

P.E.,

Cock, G.J. and Schinkel, C.J., J.Physique Colloq.

2

(1971) C1-997.

/ 3 / Acker, F. and Huguenin, R.,J.Phys.F : Metal Phys.

5

(1976) L147. /4/ Beille, J.,Thesis, Grenoble University (1975).