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Local model for magnetism in Y(Fe1−cAlc)2 alloys
85 L O C A L M O D E L F O R M A G N E T I S M IN Y(Fel_~Aic) 2 ALLOYS M.J. B E S N U S , J.M. B O U T O N , R. C L A D and A. H E R R CNRS, Institut de Physique, 67084 Strasbourg, France* The magnetic behavior of Y(Fe, _c AIc )2 alloys ( T = 4 K, 0 ~< c < 1) is described in a local model. This model accounts for the variation with c of the spontaneous magnetization related to magnetic Fe atoms (with at least 15 Fe neighbours) and the high-field susceptibility which arises from the non-magnetic Fe atoms.
The local model for magnetism has been found to describe satisfactorily the magnetic behaviour of disordered F e - A I alloys up to the limit of the solid solution at 51 at.% AI [1]. It seemed interesting to extend this study to a Fe-based system with full solid solution. The Y(Fel_¢AIc)2 ternaries appeared as the best suited; they crystallize like YFe2 and YA12 in the cubic C15 L a v e s phase structure, unless in a limited concentration range near equiatomic composition where they are hexagonal (C14). Alloys with A! contents ranging f r o m 0 to 100at.% were prepared by induction melting with a slight Y excess to avoid the formation of parasitic phases. After homogenizing annealings all samples were single phased of either cubic MgCu2 or hexagonal MgZn2 type structure (the 45.5 and 51 at.% AI alloys). The magnetization m e a s u r e m e n t s we report here were done at 4.2 K in fields up to 72 kOe. When AI is substituted for iron in YFe2 one observes a sharp non-linear decrease in the magnetic m o m e n t s and Curie temperatures, in good agreement with previous results [2, 3]. The magnetic m o m e n t s go to zero near 30 at.% AI. N o long-range magnetic order was o b s e r v e d at 4.2 K for larger AI contents, though the M(H) curves show p r o n o u n c e d curvatures even on the AI rich side. The M(H) curves were interpreted as the sum of two terms: a field dependent magnetization M and a susceptibility X supposed field and t e m p e r a t u r e independent in our experimental conditions. The first term results f r o m the local m o m e n t s carried by the magnetic Fe atoms; these m o m e n t s give rise to a spontaneous magnetization for c ~<0.3 (fig. 1). For higher AI contents, the observed magnetization is ascribed to clusters of magnetic Fe atoms, dispersed in a non-magnetic A1-Fe medium. The second term )¢ represents the n u m b e r of non-magnetic Fe atoms which also can be nearly magnetic with *E.R.A. no. 464 au CNRS.
Physica 86-88B (1977) 85-86 © North-Holland
Y(Fe-AI) 2
1.0' O
O e x p e r i m e n t a t T=K2K
,d
[]
from ref2
--
catcutated
0 ~ Mg Cuztype • • Mg Znz type
•
0.5
ge2
10
20
at X At
/,0
50
Fig. I. Ratio of the mean magnetic moment per Fe atom of the alloy and of the Fe moment Mo of YFe2 compared with theoretical curves for no = 15, 16.
high susceptibilities as c o m p a r e d to that X0 of an isolated Fe atom. The low t e m p e r a t u r e high-field susceptibility X shows a m a x i m u m at about c = 0.25 and a slower decrease when c increases, about unaffected in the hexagonal structure range (fig. 2). Taking for the a p p e a r a n c e of a local m o m e n t the simplest model in which the Fe m o m e n t is either m a x i m u m or zero [4], the mean magnetic m o m e n t per Fe atom of the alloy is given in the case of a random atomic distribution by N
1VIFe= Mo ~ P(C), •"~ = n o
where P(c) is the usual probability function, N the m a x i m u m n u m b e r of nearest Fe atoms possible, and n the actual n u m b e r of Fe nearest neighbours. The full lines in fig. 1 show the calculated curves taking: N = 18 (Fe a t o m s in the first and second coordination shells) and no = 15, 16. The best fit with the experimental values of
86 10
Y (Fe- At)2 i ,
!
(~©
/
C~ o\
o experimentat T=/,.2 -- catcutated n0=15 o Mg c0, typ, •
Mg Zn2 type
si
Oq
Y Fez
i
20
at 7oAt
60
I
80
YAt
Fig. 2. High-field specific susceptibilities compared with the theoretical curve 2 × I0 ~ emu.g '.
calculated
with
no = 15,
Xo =
~'l~JMo is obtained with no = 15, the iron moment M0 being constant and equal to that of YFe2. The specific susceptibility term which reflects the amounts of non-magnetic Fe atoms, i.e. Fe atoms surrounded by less than no nearest Fe neighbours, is given by
X = (1 - c)
P ( c ) . X,, n=O
where X,, the local susceptibility of an iron atom
with n nearest Fe neighbours, is taken as X, = x 0 ( l - n/no) -~ [5]. Good agreement with the experimental X values is again obtained with no = 15. X0 is taken as 2.0 × 10-5 emu.g -~ and the small atomic and non local matrix contribution (determined for c = 0 and 1) as 10 6emu.g 1. The severe 15/18 neighbour condition corresponds roughly to a 5/6 one in the first coordination shell of the Fe atoms. It traducts the tendency towards an unstability of the conditions for magnetism in YFe2. Thus the experimental quantities, M ( c ) and X(c) which arise, the first from the magnetic, the second from the non-magnetic atoms in a local model, are both correctly described in the full range of solid solution of Y(Fe-A1)2. It is worth remarking that the maximum in X is not related to any critical concentration range and that in this model the evolution from a state which is fully "magnetic" to a state which is fully " n o n magnetic" is entirely continuous. References [1] M.J. Besnus, A. Herr and A.J.P. Meyer, J. Phys. F: Metal Phys. 5 (1975) 2138. [2] K.H.J. Buschow, J. L e s s C o m m o n Metals 40 (1975) 361. [3] R. Gr6ssinger, W. Steiner and K. Krec, J. Magn. Magn. Mater. 2 (1976) 196. [4] V. Jaccarino and L R . Walker, Phys. Rev. Lett. 15 (1965) 258. [5] B. Cornut, J.P. Perrier and R. Tournier, J. P h y s . 32 CI (1971) 746.
The local model for magnetism has been found to describe satisfactorily the magnetic behaviour of disordered F e - A I alloys up to the limit of the solid solution at 51 at.% AI [1]. It seemed interesting to extend this study to a Fe-based system with full solid solution. The Y(Fel_¢AIc)2 ternaries appeared as the best suited; they crystallize like YFe2 and YA12 in the cubic C15 L a v e s phase structure, unless in a limited concentration range near equiatomic composition where they are hexagonal (C14). Alloys with A! contents ranging f r o m 0 to 100at.% were prepared by induction melting with a slight Y excess to avoid the formation of parasitic phases. After homogenizing annealings all samples were single phased of either cubic MgCu2 or hexagonal MgZn2 type structure (the 45.5 and 51 at.% AI alloys). The magnetization m e a s u r e m e n t s we report here were done at 4.2 K in fields up to 72 kOe. When AI is substituted for iron in YFe2 one observes a sharp non-linear decrease in the magnetic m o m e n t s and Curie temperatures, in good agreement with previous results [2, 3]. The magnetic m o m e n t s go to zero near 30 at.% AI. N o long-range magnetic order was o b s e r v e d at 4.2 K for larger AI contents, though the M(H) curves show p r o n o u n c e d curvatures even on the AI rich side. The M(H) curves were interpreted as the sum of two terms: a field dependent magnetization M and a susceptibility X supposed field and t e m p e r a t u r e independent in our experimental conditions. The first term results f r o m the local m o m e n t s carried by the magnetic Fe atoms; these m o m e n t s give rise to a spontaneous magnetization for c ~<0.3 (fig. 1). For higher AI contents, the observed magnetization is ascribed to clusters of magnetic Fe atoms, dispersed in a non-magnetic A1-Fe medium. The second term )¢ represents the n u m b e r of non-magnetic Fe atoms which also can be nearly magnetic with *E.R.A. no. 464 au CNRS.
Physica 86-88B (1977) 85-86 © North-Holland
Y(Fe-AI) 2
1.0' O
O e x p e r i m e n t a t T=K2K
,d
[]
from ref2
--
catcutated
0 ~ Mg Cuztype • • Mg Znz type
•
0.5
ge2
10
20
at X At
/,0
50
Fig. I. Ratio of the mean magnetic moment per Fe atom of the alloy and of the Fe moment Mo of YFe2 compared with theoretical curves for no = 15, 16.
high susceptibilities as c o m p a r e d to that X0 of an isolated Fe atom. The low t e m p e r a t u r e high-field susceptibility X shows a m a x i m u m at about c = 0.25 and a slower decrease when c increases, about unaffected in the hexagonal structure range (fig. 2). Taking for the a p p e a r a n c e of a local m o m e n t the simplest model in which the Fe m o m e n t is either m a x i m u m or zero [4], the mean magnetic m o m e n t per Fe atom of the alloy is given in the case of a random atomic distribution by N
1VIFe= Mo ~ P(C), •"~ = n o
where P(c) is the usual probability function, N the m a x i m u m n u m b e r of nearest Fe atoms possible, and n the actual n u m b e r of Fe nearest neighbours. The full lines in fig. 1 show the calculated curves taking: N = 18 (Fe a t o m s in the first and second coordination shells) and no = 15, 16. The best fit with the experimental values of
86 10
Y (Fe- At)2 i ,
!
(~©
/
C~ o\
o experimentat T=/,.2 -- catcutated n0=15 o Mg c0, typ, •
Mg Zn2 type
si
Oq
Y Fez
i
20
at 7oAt
60
I
80
YAt
Fig. 2. High-field specific susceptibilities compared with the theoretical curve 2 × I0 ~ emu.g '.
calculated
with
no = 15,
Xo =
~'l~JMo is obtained with no = 15, the iron moment M0 being constant and equal to that of YFe2. The specific susceptibility term which reflects the amounts of non-magnetic Fe atoms, i.e. Fe atoms surrounded by less than no nearest Fe neighbours, is given by
X = (1 - c)
P ( c ) . X,, n=O
where X,, the local susceptibility of an iron atom
with n nearest Fe neighbours, is taken as X, = x 0 ( l - n/no) -~ [5]. Good agreement with the experimental X values is again obtained with no = 15. X0 is taken as 2.0 × 10-5 emu.g -~ and the small atomic and non local matrix contribution (determined for c = 0 and 1) as 10 6emu.g 1. The severe 15/18 neighbour condition corresponds roughly to a 5/6 one in the first coordination shell of the Fe atoms. It traducts the tendency towards an unstability of the conditions for magnetism in YFe2. Thus the experimental quantities, M ( c ) and X(c) which arise, the first from the magnetic, the second from the non-magnetic atoms in a local model, are both correctly described in the full range of solid solution of Y(Fe-A1)2. It is worth remarking that the maximum in X is not related to any critical concentration range and that in this model the evolution from a state which is fully "magnetic" to a state which is fully " n o n magnetic" is entirely continuous. References [1] M.J. Besnus, A. Herr and A.J.P. Meyer, J. Phys. F: Metal Phys. 5 (1975) 2138. [2] K.H.J. Buschow, J. L e s s C o m m o n Metals 40 (1975) 361. [3] R. Gr6ssinger, W. Steiner and K. Krec, J. Magn. Magn. Mater. 2 (1976) 196. [4] V. Jaccarino and L R . Walker, Phys. Rev. Lett. 15 (1965) 258. [5] B. Cornut, J.P. Perrier and R. Tournier, J. P h y s . 32 CI (1971) 746.