Magnetic anisotropy in the cubic Laves REFe₂intermetallic compounds

Abstract

In the past, the Callen-Callen (1965 Phys. Rev. 139 A455-71; 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 REFe 2 compounds. In this paper, we show that it is possible to replicate the values of the phenomenological parameters K 1 , K 2 , and K 3 given by Atzmony and Dariel (1976 Phys. Rev. B 13 4006-14), by extending the CallenCallen model to second order in H CF . In particular, explanations are provided for (i) the unexpected changes in sign of K 1 and K 2 in HoFe 2 and DyFe 2 , respectively, and (ii) the origin and behaviour of the K 3 term. In addition, it is demonstrated that higher order terms are required,and that K 4 exceeds K 3 at low temperatures. Revised estimates of K 1 , K 2 , K 3 , K 4 , and K 5 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 (K N , N = 4, 6, 8, 10, 12) decrease monotonically with increasing temperature, withK N decreasing faster thanK N −2 etc. These observations are in accord with expectations based on the original Callen-Callen model.

Micromagnetic Modelling of the Dynamics of Exchange Springs in Multi-Layer Systems

“…1(a). The three coefficients used in the anisotropy expansion [7] are 33.9 10 J/m , 16.2 10 J/m , and 16.4 10 J/m . The iron experiences an exchange field , where 1.46 10 J/m is the exchange coupling constant, is the free space permeability, and .…”

Magnetic anisotropy terms in [110] MBE-grown REFe2films involving the strain term εxy

“…A more complete description of the basic theory used in this paper has already been given by Martin et al (2006). However, for convenience, an abbreviated account is set out below.…”

“…In practice, the βα nn N (T ) coefficients converge to zero as T → ∞, and to finite values as T → 0 K. More details concerning the properties of α nn N (T ) etc, can be found in appendix A of Martin et al (2006).…”

“…Proceeding in this fashion, explanations have been provided for (i) the change in sign of K 1 in HoFe 2 and K 2 in DyFe 2 , (ii) the origin of the K 3 and (iii) the need for even higher-order terms (Martin et al 2006). In particular, explicit expressions are given for phenomenological magnetic anisotropy constants K 1 -K 5 , in terms of the RE-ion crystal field parameters B 4 and B 6 and their products B 2 4 , B 4 B 6 and B 2 6 .…”

“…In addition, these authors found that some of the calculated K 1 and K 2 parameters changed sign as a function of temperature, a feature which could not be explained in the context of the Callen and Callen model , 1966, Callen and Shtrikman 1965. This problem has recently been re-visited by Martin et al (2006), using an extended version of the Callen and Callen model. They were able to provide (i) an explanation for the change in sign of K 1 in HoFe 2 and K 2 in DyFe 2 and (ii) elucidate the origins of the K 3 , and higher-order terms.…”