Fourth-order spin Hamiltonian terms for Fe2+ in rutile structure antiferromagnet FeF2

The paper deals with the spectroscopic and magnetic properties of Fe²⁺ ions in FeF₂. The microscopic spin Hamiltonian theory for Fe²⁺ in crystalline environments with second-kind orthorhombic symmetry is considered. Explicit formulas for the parameters B₀⁽²⁾(D),B₂⁽²⁾(E), g_x, g_y, g_z and, for the first time in the literature, the fourth-order parameters B₀⁽⁴⁾, B₂⁽⁴⁾ and B₄⁽⁴⁾, are derived. Using semi-empirical data for the ⁵D-term energy levels of Fe²⁺ ion in FeF₂, the pressure dependence of the parameters B_q^(k) in the region from 0 to 133 kbar is discussed. The relative role of the fourth-order parameters with respect to the second-order ones is found to increase strongly with pressure (e.g. in the region studied, D increases only by a factor of 3, whereas B₀⁽⁴⁾ increases by a factor of nearly 20). The magnetocrystalline anisotropy of FeF₂; is considered in the strong anisotropy model taking into account the fourth-order spin Hamiltonian terms. The uniaxial anisotropy constants K₁ and K₂ are derived theoretically and their pressure dependence is discussed quantitatively. The theory and numerical results of this paper are useful with regard to Fe²⁺ in other isomorphic fluorides, namely: MgF₂, ZnF₂, VF₂ and MnF₂. It is found that the fourth-order spin Hamiltonian parameters are accessible to experimental detection from spectroscopic studies on Fe²⁺ in non-magnetic fluorides and magnetic studies on Fe²⁺ : MnF₂ and FeF₂, preferably under high pressure.