A model for random-anisotropy antiferromagnetism in amorphous rare-earth alloys

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A model for random-anisotropy antiferromagnetism in amorphous rare-earth alloys

A. Bhattacharjee, B. Coqblin

To cite this version:

A. Bhattacharjee, B. Coqblin. A model for random-anisotropy antiferromagnetism in amor- phous rare-earth alloys. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-246-C5-247.

�10.1051/jphyscol:1979590�. �jpa-00219007�

A model for random-anisotropy antiferromagnetism in amorphous rare- earth alloys

Abstract. — A model for random-anisotropy antiferromagnetism is introduced to account for the magnetization curves of amorphous rare-earth alloys such as RECu or REAg (RE = Tb, Dy, Ho). The magnetoresistivity is also computed for both a random ferromagnetic or antiferromagnetic and the results are successfully applied to respectively DyNi

or TbAg type amorphous alloys.

The random-anisotropy model was introduced by Harris, Plischke and Zuckermann (HPZ) [1] for studying the properties of amorphous rare-earth alloys. The HPZ Hamiltonian is :

The local anisotropy axes z

are distributed randomly over the unit sphere according to HPZ, who assumed originally a ferromagnetic nearest-neighbour interac- tion (J

. > 0) and carried out a molecular field calcula- tion. Here, we present firstly an extension of the HPZ model to the case of an antiferromagnetic interac- tion [2].

To compute the magnetization curves for a random antiferromagnetic ordering with a negative nearest- neighbour interaction constant #, we make here a self-consistent two-spin cluster approximation : we take a pair of spins J

and J

, treat the interaction between these two exactly and replace the remaining nearest neighbours of each by the average value of the z-component of the other. Thus, the cluster Hamil- tonian is :

with

where v is the number of nearest rare-earth neighbours for a given rare-earth ion and the bar over the thermal average denotes averaging over random anisotropy directions. The two self-consistent fields 1

and X_

design respectively the magnetization Mlgn

and the sublattice magnetization. The calculation has been performed for a total angular momentum 7 = 1 and for a fixed angle 0

between the two anisotropy axes z

and z

, which is assumed here to be 0

= 0.

Details can be found in ref. [2]. Figures la and lb give the magnetization curves for 7s = — 0.25 K, g = 2 and v = 6, either at T = 0 K for several values of a = Dl | 2 uj | or for a = 2 at different tempera- tures. The spin-flop transition is shifted to a lower critical field H

with increasing a before reaching an almost steady value, while H

decreases with increas- ing temperature. Moreover, the reduced magnetiza- tion versus temperature curve plotted at a field H = 10 kG smaller than H

is passing through a maximum at a temperature slightly lower than

^N

[2]-

The contribution p

to the resistivity due to the s-f exchange Hamiltonian has been also calculated in the

Fig. 1. — Reduced magnetization for J = — 0.25 K, g = 2, v = 6 : a) at T = 0 K for different a values; b) at different temperatures for a = 2.

JOURNAL DE PHYSIQUE Colloque C 5 , supplément au n° 5, Tome 40, Mai 1979, page C5-246

A. K. Bhattacharjee a n d B. Coqblin

Laboratoire de Physique des Solides, Bâtiment 510, Université Paris-Sud, 91405 Orsay, France

Résumé. — On introduit un modèle pour l'antiferromagnétisme avec une anisotropie aléatoire pour expliquer les courbes d'aimantation des alliages amorphes de terres rares tels que RECu ou REAg (RE = Tb, Dy, Ho).

On calcule aussi la magnétorésistivité pour à la fois un ferromagnétique ou un antiferromagnétique aléatoire et les résultats sont appliqués avec succès respectivement aux alliages amorphes de type DyNi3 ou TbAg.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979590

A MODEL FOR RANDOM-ANISOTROPY ANTIFERROMAGNETISM

framework of de Gennes and Friedel for both a random ferromagnetic or antiferromagnetic ordering of the rare-earth ions in the amorphous alloy des- cribed by the preceding model [3]. Details can be found in ref. [3] and the magnetic resistivity is finally given by

where

the spin-disorder resistivity of the corresponding rare- earth metal, while F(kF) and G(k,) are two oscillating functions of k , [ 3 ] .

Thus, to compute the resistivity, we compute the average correlation function

by the same self-consistent method as previously done for 1,.

The sign of the slope ( d p m J d T ) and that of the magne- toresistivity depend on the signs of the two functions F(k,) and G(k,), but also on

which is posi- tive for a random ferromagnetic and negative for a random antiferromagnetic.

Figures 2a and 2b give typical plots of the magne- toresistivity for D

6 K , v

6 and g

2. Figure 2a shows the plot for a random ferromagnetic with 3

+ 0.25 K and the parameters previously used for the DyNi, alloy [4], while figure 2b shows the plot for a random antiferromagnetic with 3

- 0.25 K and a larger 2 k, value in order to describe the TbAg alloy which has a larger number of electrons than DyNi,. Both figures give a rapid decrease of the zero- field resistivity around the ordering temperature and a large magnetoresistivity at 30 kG, but the magne- toresistivity is positive (figure 2a) or negative (figure 2b).

The preceding model for random antiferromagne- tism can account for the magnetic properties of some amorphous alloys such as RECu or REAg

firstly, figure l a explains the experimentally observed increase of H, with increasing x in RE,Cu,-, [5], because

Fig. 2. - Relative variation of the magnetic resistivity with pmm = c l pM, D = 6 K, g = 2, v = 6. a ) For a random ferro- magnetic with 3 =

+

k'.

decreases with increasing x, i.e. increasing

as well as the decrease of H , as one goes along RE

Tb, Dy, Ho. Then, the low temperature isothermal magnetiza- tion curves shown in figure l b are in good qualitative agreement with those reported by Boucher [6] for amorphous alloys REAg (RE

Tb, Dy, Ho).

Finally, the maximum occurring at roughly TN in the low field magnetization versus temperature curve is in excellent agreement with that observed by Boucher in amorphous TbAg [6].

Thus, the analysis of the magnetization curves supports the assumption of a random antiferromagne- tic ordering in amorphous REAg or RECu alloys, while a random ferromagnetic ordering was clearly established from the magnetization curves in alloys such as

[4]. Figures 2a and

check again these assumptions

the zero-field resistivity decreases sharply around the ordering temperature in both cases, but the magnetoresistivity is positive in the ferromagnetic case, as experimentally observed in DyNi,, and negative in the antiferromagnetic case, as in TbAg [4]. Moreover, we can perform a quanti- tative analysis of the data by taking a p , value in rough agreement with the corresponding value for the rare-earth metal.

References

[I] HARRIS, R., PLISCHKE, M. and ZUCKERMANN, M. J., Phys. [4] ASOMOZA, R., FERT, A,, CAMPBELL, I. A. and MEYER, R., J.

Rev. Lett. 31 (1973) 160. Phys. F : Met. Phys. 7 (1977) L 327 and private communi- [2] BHATTACHAWEE, A. K. and COQBLIN, B., Solid State Commun. cation.

27 (1978) 599, and references therein. [5] HEIMAN, N. and KAZAMA, N., J. Appl. Phys. 49 (1978) 1686.

[3] BHATTACHIWEE, A. K. and COQBLIN, B., J. Phys. F : Met. [6] BOUCHER, B., Phys. Status Solidi (a) 40 (1977) 197 and ZEEE Phys. 8 (1978) L-221, and references therein. Trans. Mag. 13 (1977) 1601.