Magnetic anisotropy in the cubic Laves REFe2 intermetallic compounds

In the past, the Callen–Callen (1965 Phys. Rev. 139 A455–71; 1966 J. Phys. Chem. Solids 27 1271–85) model has been highly successful in explaining the origin and temperature dependence of the magneto-crystalline anisotropy in many magnetic compounds. Yet, despite their high ordering temperatures of ∼650 K, the Callen–Callen model has proved insufficient for the REFe2 compounds. In this paper, we show that it is possible to replicate the values of the phenomenological parameters K1, K2, and K3 given by Atzmony and Dariel (1976 Phys. Rev. B 13 4006–14), by extending the Callen– Callen model to second order in HCF. In particular, explanations are provided for (i) the unexpected changes in sign of K1 and K2 in HoFe2 and DyFe2, respectively, and (ii) the origin and behaviour of the K3 term. In addition, it is demonstrated that higher order terms are required,and that K4 exceeds K3 at low temperatures. Revised estimates of K1, K2, K3, K4, and K5 are given. Finally, an alternative ‘multipolar’ approach to the problem of magnetic anisotropy is also provided. It is shown that the latter confers significant advantages over the older phenomenological method. In particular, all the multipolar coefficients (K̃N , N = 4, 6, 8, 10, 12) decrease monotonically with increasing temperature, with K̃N decreasing faster than K̃N−2 etc. These observations are in accord with expectations based on the original Callen–Callen model. (Some figures in this article are in colour only in the electronic version)