Magnetic and magnetoelastic properties of a ferromagnetic single crystal with cubic symmetry

Abstract

A crystal hamiltonian is written from symmetry considerations, including magnetic and elastic contributions, first-order magnetoelastic coupling (magnetostriction) and second-order magnetoelastic coupling (isotropic and morphic effects). This phenomenological expression is then explicitly derived from microscopic interactions based on a generalized pair model. This work develops partial results concerning rotational and magnetoelastic effects, but the methods proposed here are simpler than the « rotational invariance theory » so widely used in the recent literature. The number of independent coefficients in this hamiltonian is strongly reduced by two sets of relations. The first one illustrates the rotational invariance theorem: all the coefficients associated with rotational terms are linear combinations of the anisotropy and (usual) magnetoelastic coefficients. The second one is established only for a localized model. In the classical case of isotropic magnetization modulus, an analytical expression of the free energy can be written: magnetic anisotropy, magnetoelastic effects and elastic properties are then discussed. Last, the quantum case with anisotropic magnetization is treated and illustrated with some recent experimental results. For instance, the tetragonal strains observed in the cubic rare earth compounds with antimony (R — Sb) and zinc (R — Zn) are analyzed through each series. The corresponding magnetoelastic coefficient is checked by determination from ultrasonic data: quadrupolar exchange effects are then taken into account.