Single-Ion Models and the Temperature Dependence of Magnetostriction and Piezomagnetism

Abstract

We have recently demonstrated that the 0°K magnetostriction and piezomagnetic constants of various magnetic insulators can be predicted approximately, using a single-ion model and a microscopic single-ion magnetoelastic tensor, Tijklσ, determined from the strain dependence of EPR spectra. The model leads to a natural classification of the magnetoelastic constants depending on whether their microscopic origin is in the strain dependence of a g tensor (Fijkl = ∂gij/∂εkl) or of a crystal-field energy (Gijkl = ∂Dij/∂εkl). The identification of microscopic origin also allows a prediction of the temperature dependence of the magnetoelastic constants since it identifies the relevant spin components and the power to which they are raised in the approximate Hamiltonian. The magnetostriction constants of most materials will vary (in the low-temperature region) as [M(T)/M(0)]3. For heterogeneous ion compounds such as the garnets, however, when the principal magnetostrictive mechanism is the strain dependence of the g tensor, the magnetostriction may vary as [MRE(T)/MRE(0)]×[MFe(T)/MFe(0)], e.g., YbIG. For most piezomagnetic materials the piezomagnetic constants will vary as [M(T)/M(0)], as in CoF2; cases exist, however, where more complicated temperature dependence is to be expected, for instance in the rare earth orthoferrites.