Short Notes K63

phys. stat. sol. (b) 175, K63 (1993)

Subject classification: 75.30; S1.1; S1.2; S1.4

Cryogenic Laboratory, Department of Physics, University of Hanoi')

Effects of the 3d-5d Hybridization on the 4f-3d Coupling in the Rare Earth-Transition Metal Compounds

BY NGUYEN Huu Duc

Znrroduction The rare earth-transition metal intermetallics are usually treated as two- sublattice magnetic materials with the R-sublattice of localized 4f moments and the T-sublattice of d (3d and 5d) electrons. The investigation of the intersublattice R-T interactions in these compounds has been the subject of many theoretical and experimental studies. Considerable work has been done in attempt to deduce the (effective) R-Fe and R-Co intersublattice exchange interactions from the systematics of the Curie temperatures [l to 41, the compensation points [4], and the high field magnetization ([5] and references therein). The result has shown that in a given rare earth, going from T-poor to T-rich compounds, both the R-Fe and R-Co interactions decrease monotonously [2 to 51. This systematic decrease of the R-T interactions has been discussed in relation with the value of the magnetic moment of the T-sublattice. A linear decrease of the R-T interactions with increasing T-magnetic moment is reported with some modification at around 1 pB/at [3]. Density functional calculations for the RFe, compounds [6] add to this picture the important role of the 3d-5d hybridization. Experimentally, it was found that the R-T compounds, which are rich in T-component, have largest T-moment, i.e. possess the largest 3d-band splitting. This leads to a reduced hybridization of the 3d spin-up states with 5d states. Therefore, the hybridized states will have more spin-down character, implying an increase of the 3d-5d interactions, and thus R-T ones, with increasing T-magnetic moment. The obtained results, however, can be understood as a consequence of depletion of the hybridized 3d-5d bands.

In this note, by combining the consideration of the R-T exchange interactions in the R-Fe and R-Co compounds with those in a number of the R-Ni compounds, a wider variation of the R-T interactions with MT is overviewed. The results are discussed in the frame of a general mechanism proposed by Brooks et al. [6] and the important role of the 3d-5d hybridization effects on the R-T interactions is confirmed.

Coupling between 4f-3d spins In the rare earth-transition metal intermetallics, it is generally accepted that there are three types of interactions, namely, the R-R interactions between the magnetic moments within the R-sublattice, the T-T interactions between the magnetic moments of the T-sublattice, and the R-T intersublattice interactions. The T-T interactions are direct exchange interactions between the 3d spins, whereas the R-R interactions are indirect, presumably proceeding via the 4f-5d-5d-4f mechanism. The R-T interactions are also indirect, being a combination of the intra-atomic 4f-5d and

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K64 physica status solidi (b) 175

inter-atomic 5d-3d exchange interactions [7]. As a general rule, the latter interactions are found to be antiferromagnetic for electrons residing in a less than half-filled d band (the 5d band) interacting with electrons in a more than half-filled d band (the 3d band). By means of this scheme, it can be understood that the magnetic ordering in the R-T intermetallic compounds is either of the ferromagnetic type, if R is a light rare earth element, or of the ferrimagnetic type, if R is a heavy rare earth. This was first suggested, on the basis of expertiment, by Campbell [7]. Recently, using band structure calculations, Brooks et al. [6] were able to show that in the rare earth-transition metal compounds the interactions between the 4f moments and the band magnetism can occur only through the local exchange interactions on the rare earth atom, that is between the 4f and 5d states. However, the 3d-5d hybridization plays a critical role in, firstly, producing significant 5d conduction electron charge and spin density at the R-sites and, secondly, being responsible for the coupling between 5d and 3d spin directions and therefore the 4f and 3d spin directions.

The simplest approximation to the interactions which couple the directions of 4f and 3d spins can be expressed as an effective exchange of the Heisenberg type,

where S , and ST are the spins at the R- and T-sites, respectively. A,, is the exchange coupling between the neighbouring R- and T-spins. However, as shown above the only possible way that the 3d spin can interact with 4f spin is indirectly through hybridization with the 5d states and the exchange interactions between 5d and 4f states. That is, the origin of the molecular field at the R-site must be the effect upon the 4f states of the 5d spin density.

The exchange interaction energy between the 4f and 5d states is the quadratic form

where the exchange integral r 4 f 5 d is given as

Here g[n] is a well-know (after [6]) function of density. r4f5d , thus, depends upon the

Finally, the effective R-T exchange parameter is given by 4f-5d overlap densities.

The strength of the interactions between the rare earth local moment and the transition metal itinerant moments is, therefore, expected to depend above all on the 5d spin induced by the hybridization with the 3d bands and the local exchange integral which is less dependent upon the rare earth environments.

Summary of experimental results and discussion In Fig. 1 a common overview is presented of the variation of A,,, reported by several authors [4, 8,9] for a number of R-(Fe, Co, Ni) systems. For a given rare earth, the variation of A,, can be focused on the relation with S5d (see (4)). However, due to the difficulties in the experimental determination of the value of the 5d magnetic moments, the results, here, are still plotted against MT (= M,, - M5J, the total T-magnetic moment contributed by the 3d and 5d electrons. Experimentally, MT is obtained from the magnetization in the compounds with non-magnetic

Short Notes K65

0.5 1 .o 1.5 2.0

MT ( PB / a t ) - Fig. 1. The variation of ART as a function of the T-magnetic moments in a number of R-T compounds (0 data from [4], A data reported from [S] for Dy,(Ni, -xCo,)17 compounds, and data from [S, 91)

rare earth elements (R = Y or Lu). It is clearly seen from this figure that A,, starts to increase monotonously with increasing M, in the compounds having small MT-values. Then it reaches a maximum at MT x 1.25 p$at and finally decreases with increasing MT in almost all of the R-Fe and R-Co compounds (with MT 2 1.25 pB/at). Within the concept of the 3d-5d hybridization, these features can be understood as follows.

(i) Before hybridization between the two sets of d bands, the pure 3d bands are almost filled and the pure 5d bands are almost empty. The pure 3d and 5d bands hybridize to form a hybridized region at the top of the 3d bands and at the bottom of the 5d bands. However, when the 3d band is not split, i.e. the magnetic moment does not develop at T-sites, the occupation of the 5d spin-up and spin-down states is the same and the 5d magnetic moment at R-sites equals zero. In this case, the 4f-5d interactions do not exist. This is the reason why the R-T interactions can usually be neglected in the RNi, compounds [l to 4, lo]. In Fig. 1, this data is not included, however, it can be shown by the tendency of ART to annul at MT = 0.

(ii) When a moment develops at the T-sites, the energy of spin-up 3d states is lowered, reducing the 3d-5d hybridization for the spin-up states. This lowers the occupation of the 5d spin-up states. The opposite effect occurs for the spin-down states and the 5d moment which is related to the 5d occupation is induced. The 4f-5d and thus the 4f-3d interactions are created. The induced 5d moment is therefore antiparallel to the 3d moment and strongly related to the 3d-band splitting.

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K66 physica status solidi (b) 175

(iii) Following one and the same line, it turns out, in general, that the 3d-5d hybridization effects and then the 4f-3d interactions increase with 3d-band splitting. For the compounds with small value of MT, i.e. in the case of the R2Ni1,, R,(Ni, Co),,, RCo,,B,, RCo,B, and RCo, compounds, the effect of the 3d-band splitting on the increase of MT seems to be most important, so that the increase of ART with MT is understandable.

(iv) For the compounds, in which the 3d magnetism is well established, the observed results suggests a decrease of the hybridization effects with increasing MT. In these compounds, the 3d-band splitting can be considered to be almost saturated to its possible limit. This is evidenced by the results calculated by Brooks et al. [6] that in GdFe, the value of M , , is equal to 2.12 p$Fe-at which is rather close to that observed in the pure Fe ion. Then, the tendency of MT to reach the value of the magnetic moment of pure Fe and Co metal with increasing T-concentration implies a slight decrease of M,, , i.e. a reduction of the 3d-5d hybridization. The observed behaviour may indicate an increase of the energy distance between the 3d and 5d bands upon a slight decrease of the R-T distance.

In concluding, we would like to point out here that, instead of the remarks in literature suggesting a polarization of the d electrons by the “exchange field” of the rare earth moments, the true mechanism of the R-T exchange interactions must be understood on the basis of the 3d-5d hybridization effects as proposed by Brooks et al. [6]. Within this model, a reasonable explanation for the variation of the 4f-3d coupling in the rare earth-transition metal compounds has been given.

The author is indebted to Prof. M.S.S.Brooks and Prof. F. R.de Boer for hepful discussions and encouragement to this work.

References

[I] E. BELORIZKY, M. E. FREMY, J . P. GAVIGAN, D. GIVORD, and H. S. LI, J . appl. Phys. 61, 3971 (1987).

[2] N. H.’Duc, phys. stat. sol. (b) 164, 545 (1991). [3] N. H. Duc, T. D. HIEN, and D. GIVORD, J. Magnetism magnetic Mater. 104/1(n, 1344 (1992). [4] N. H. Duc, T. D. HIEN, D. GIVORD, J. J. M. FRANSE, and F. R. DE BOER, J. Magnetism magnetic

[5] F. R. DE BOER and K. H. J. BUSCHOW, Proc. Conf. RHMF, Amsterdam 1991 ; published in

[6] M. S. S. BROOKS, L. NORDSTROM, and B. JOHANSSON, Physica (Utrecht) 172B, 95 (1991). [7] I. A. CAMPBELL, J. Phys. F 2, L478 (1991). [8] N. H. Duc, to be published. [9] J. J. M. FRANSE, F. E. KAYZEL, C. MARQUINA, R. J . RADWANSKI, and R. VERHOEF, Proc. 9th

Mater. (1992). in the press.

Physica B (1991).

Rare Earth Research Conf., Lexington (USA) 1991. [lo] A. CASTETS, D. GIGNOUX, B. HENNION, and R. M. NICKLOW, J. appl. Phys. 53, 1979 (1982).

(Received September I , 1992)