Magnetocrystalline Anisotropy of 3d6 and 3d4 Ions at Triclinic. Symmetry Sites Application to Fe2+ Ions in YIG: Me4+ (Me = Si, Ge)

Abstract

The earlier suggested energy-level model based on an orbital singlet ground state for 3d6 and 3d4 ions at trigonal sites with large triclinic distortion is adopted to develop the single-ion theory of magnetic anisotropy. The Hamiltonian consisting of eight spin Hamiltonian terms and the molecular field is solved by perturbation theory. The resulting energies EMs with MS = 0, ± 1, ± 2 are applied to calculate the free energy for Fe2+ ions in Si- or Ge-substituted yttrium iron garnets where a uniform distribution of Fe2+ ions over the 12 inequivalent sites is assumed. It turns out that the first two cubic anisotropy constants K1, and K2 are insufficient to describe the anisotropy at high temperatures in the present model. By a least-squares method it is established that the anisotropy expansion series can be terminated at the fourth-order term for the present model. Thus K1, K2, K3 and K4 are derived analytically in terms of the free energy for some choosen directions of magnetization. The analytical results agree very well with the correspond­ing ones obtained by the least-squares method. The temperature dependence of Ki, i = 1. 2, 3, and 4, is calculated for a wide range of the spin Hamiltonian parameters (Bq (k)) and the molecular field (h). The theoretical K1, and K2 are fitted to the experimental values of K1, and K2 at low temperatures obtained by neglecting the higher-order anisotropy terms, to get the values of Bq (h) and for YIG:Si and YIG:Ge. A comparison of the present results with The corresponding ones of the previous doublet model, is also discussed. The theoretical account of the experimentally observed temperature dependence of the ratio K2/K1 for Fe2+ in YIG:Ge speak in favour of the present model rather than the doublet model. The change in sign of K1 observed for Fe2+ in YIG:Si, which could not be explained by the doublet model with uniform distribu­tion of Fe2+ ions, is well accounted for by the present model. The recently observed spin reorientation in YIG:Si can also be explained by the present model without resorting to a nonuniform distribution of Fe2+ ions required by the previous model. This study indicates that the higher-order constants K3 and K4 are significant at high temperatures according to the present model, whereas at low temperatures according to the doublet model. Hence an experimental determination of K3 and K4 over a wide temperature range may provide a test of the applicability of the two models.