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STIFFNESS CONSTANTS

IN D I S O R D E R E D

F.C.C. P d - F e ALLOYS

H. YAMAUCHI, E. SAIT(3 and H. WATANABE The Research Institute of Iron, Steel and Other Metals, Tohoku University, Sendai, Japan

The temperature dependence of the magnetization of disordered f.c.c. P d - F e alloys has been measured at low temperatures. The exchange stiffness constants D and the exchange integrals J are estimated from the analysis on the basis of the spin wave theory. The composition dependence of D is consistent with that obtained from neutron diffraction measurements.

It has received considerable attention that the ferromagnetic and the antiferromagnetic interactions are considered to coexist in f.c.c. ferromagnetic Fe°alloys such as Ni-Fe, Pd-Fe and Pt-Fe from the composition dependence of the magnetic moment and the Curie temperature. Several investigations on the exchange stiffness constant of the disordered Pd-Fe alloys and on spin-wave dispersion relation of the ordered Pd3Fe alloy and some information about the exchange interaction in Pd-Fe alloys have been reported in the literature [1-6]. The purpose of this paper is to report the results of a study of the magnetic interactions in the disordered Pd-Fe alloys. All samples are melt in alumina crucibles in argon atmosphere and are pressed to 0.1 mm thickness in order to minimize the demagnetizing field. The pressed samples are annealed for 5h at 1000°C and quenched into water after annealing in order to obtain disordered samples. We could not observe any superlattice lines in the X-ray diffraction patterns of these samples. Magnetization measurements of f.c.c. Pd-Fe alloys using a pendulum-type magnetometer have been made from liquid He temperature to room temperature. Magnetization vs. temperature curves have been analysed on the basis of the spin-wave theory. According to the spin-wave theory, the saturation magnetization M ( T ) at a low-temperature T is expanded as follows; M ( T ) = M(0){1 - C T m - E T 5t2 ...}

(2)

where g, /xs, ka, D and M(0) are the specPhysica 86-88B (1977) 347-348 © North-Holland

i

p

i

.i

,

=

,

200

150

't

•"

> I00

•

Smifh- Gardner-Budnick

x

Sfringfellow

• Megshi kov- Sidorov - Kvz'min

o AnfoninJ-Medine-Meflzinget(order) o Presell! Work 50

o Fe

' io

;o

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o

4o

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%

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Pd

Fig. 1. Variation of D with composition obtained by: A Smith et al.; x Stringfellow; • Men'shikov et al.; [] Antonini et al.; O present authors.

(1)

with gPa (3 Tg'~( k. ,~3/z -" C = -M(O) ~" 2" --~] \ ~-~-~] ,

troscopic splitting g factor, the Bohr magneton, the Boltzmann constant, the exchange stiffness constant, and magnetization at OK, respectively, ~[~. (TJT)] is the modified Riemann zetafunction, T~ = (g/zB/kQ(H + HA) with applied field H and anisotropy field HA. Experimental data of M ( T ) have been analysed by computer with best fit method using eqs. (1) and (2) with applied field H =6.7kOe by neglecting the terms higher order than the T 5/2 term and the anisotropy field below temperature of 0.2 To. The exchange stiffness constants D are estimated and shown in fig. 1 together with other authors' data.

The composition dependence of D is consistent with that obtained by Stringfellow [1] and Men'shikov et al. [2] from small angle scattering of neutrons but the values of D are rather smaller than those of Men'shikov et al. [2]. The value of D for disordered Pd3Fe is about 25% smaller than that of ordered phase obtained by

348 Table I The spatial second moments of the exchange integrals between Pd-Pd, PD-Fe and Fe-Fe pairs of atoms obtained from: O ordered Pd3Fe; × partially ordered Pd3Fe; A disordered Pd-Fe (units in meV). 12) J~d-Pd

Antonini et al. O Sterling et al. O Menzinger et al. × Men'shikov et al. A Present work A

(2) J~a-ee

j(2) IPo-F¢

1.6 3.5 1.7 47 16

(3)

and in a cubic ferromagnet having spin S, the exchange stiffness constant D is defined as;

J(2) = j~2)+

A-A A'B B'B

2

Z r

J(r)(---~-r ~ 2, A-A A-B B-B

12~ J~Fe-V~

-47

6.9 6.0 6.8

Pd using the linear composition dependence of D ranged from 70 to 8 5 a t . % P d results in Jte~_pd=16-0.4(meV), the curvature of the composition dependence of D in the region from 45 to 70 at.% Pd gives J~-Fe = 27 --+3 (meV) and J~F~-Ve=--3---+ 3 (meV) is obtained using eq. (6) in which A and B are replaced by Pd and Fe. For the values of Spa and SFe those obtained by Shirane et al. [7] from neutron diffraction measurement are used. The second spatial moment of the exchange integrals J~-Pd, J

(4)

When we consider a disordered binary alloy consisting of A and B atoms, we have three sets of second spatial moment of the exchange integral; j(2) 1 =

12~ Ji Fe-F~

- 1 -3

'

1 2 (2) D = ~ZRnJ S.

,](2) Fe-F¢

32

41 27

Antonini et al. [3], and Menzinger et al. [4] from the diffraction technique with polarized neutrons and by Stirling et al. [5] and Holden [6] from neutron inelastic scattering techniques. We consider the spatial moment j

q2~ Jeeo v~

(5)

1~./

.i2(2)+

4./3(2)+..

",

(7)

where j~2) is the second spatial moment of exchange integral between the nth nearest neighbors. From table I we can deduce an interesting conclusion for the second spatial moment of the exchange integral between F e - F e pair of atoms that r~2) (2) positive and that the ° l Fe-Fe is negative, J 2Fe-Fe contribution from the terms higher than third order in eq. (7) is large.

and g2j(2) = (casA)2j~2) +

References

2CaCBSASBj~2?~

+ ( CBSB ) 2j(B2?B

(6)

with S = CaSa+ CsSn and D = 4R~P2)S in the case of f.c.c, structure where Ca, Ca and Sa, Sn are each element's concentration and spin per atom. From composition dependence of D ranged from 45 to 85 at.% Pd the values for the second spatial moment of the exchange integral between P d - P d , P d - F e and F e - F e pairs of atoms are determined. The value of D extrapolated to

[1] M.W. Stringfellow, J. Phys. CI (1968) 1699. [2] A.Z. Men'skikov, S.K. Sidrov and N.N. Kvz'min, Sov. Phys. JETP Lett. 16 (1972) 6. [3] B. Antonini, R. Medina and F. Menzinger, Solid State Commun. 9 (1971) 257. [4] F. Menzinger, F. Sacchetti and R. Teichner, Solid State Commun. 9 (1971) 1579. [5] W.G. Stiring and R.A. Cowley, Solid State Commun. II (1972) 271. [6] T.M. Holden, AIP Conf. Proc. No. 24 (1974) 159. [7] G. Shirane, R. Nathans, S.J. Pickart and H.A. Alperin, Proc. Int. Conf. on Magnetism, Nottingham (1964) p. 222.