On the Ground Level Splitting of Mn ++ and Fe +++ in Nearly Cubic Crystalline Field

Abstract

405 The gro11nd level splitting and g-f~ctor of Mn + + and Fe+++ in nearly cubic crystalline field, with a small axially symmetric field superposed on it, are studied by higher-ordet perturbation calculations. It iS-shown· that the electronic energy levels arising from the configuration half-filled with electrons are unsplit under the linear effect of crystalline potentials, but can be split by the effects of even powers of them. Various higher-order processes involving crystalline potential, spin-orbit coupling and magnetic spin-spin interaction within an ion that are supposed to be dominant in the ground level splitting ~nd the g-factor deviation, are formulated and order of magnitude discussions are given for them. § l. Introduction During the past few years the paramagnetic resonance method has been applied to-study the splitting of the ground energy level. of Mn + + and of Fe++ + in paramagnetic crystals, such as manganese Tutton salts and iron alums/> in Mg()2> and in zincblende· crystals. 3) These energy le~els can be described in a simple way by a 'spin Hamiltonian.,. which is expressed in terms of the spin operato.rs. The coefficients of a spin Hamiltonian depend in a complicated way. upon the symmetry and strength of the crystalline field. the spin-orbit coupling (W Ls) , the magnetic spin-spin interaction between pairs of-electrons within the ion (Wss) and so on. 1) The order of magnitude of their splittings is smaller than that of the other. iron-group ions, sihce both Mn++ and Fe+++ are in 3d 5 6 S state which has no orbital angular momentum. On the other hand, these ground level splittings correspond to the part of the magnetic anisotropy energy of these ions which is produced by a combined effect of the crystalline field, WLS and W 88 4). And this anisotropy energy is expected to be dominant in paramagnetic crystals and in anti-and ferrimagnetics in which the spin arrangement is. of cubic symmetry, since in this case the-ordinary magnetic dipole-dipole interaction between_ ions contributes nothing to the anisotropy energy. Recently, Yosida and Tachiki 5) suggested. that the origin of the cubic anisotropy of Mn-and Ni-ferrites might be attributed to the magnetic anisotropy of ·Fe+++ ions situated on the 16c and 8{ sites of these ferrites, and somewhat to a less extent to Mn + + ions on the 8 f site in the case of Mn-ferrite. The reason is that the observed anisotropy energies-per ion are comparable with those of Fe+++ in ferric alums and that their temperature dependence appears-to be similar to those of one•ion cubic anisotropy; In Ni-ferrite,_.the_ anisotropic .exchange interaction is small and