FIELD DEPENDENCE OF ELASTIC CONSTANTS OF RARE EARTH METALS AND COMPOUNDS.

A review is presented of recent theoretical work on the effect of magnetoelastic interactions on the elastic constants of the rare earth metals of hcp structure and the rare earth-iron cubic Laves phase compounds, RFe//2. Attention is directed mainly to the ferromagnetic phases of these materials. An expression is constructed for the energy density of a simple uniaxial ferromagnet which satisfies the requirement that it be invariant under arbitrary rotations of the crystal. From this the equations of motion of the components of the elastic displacement and the components of the magnetization are obtained. With the assumption that a magnetic field H is applied along the easy direction of magnetization, the coupled equations are solved for transverse acoustic waves either propagating along the direction of H or linearly polarized along this direction. The requirement of rotational invariance leads to different results for these two types of transverse wave, the difference originating in the magnetic anisotropy energy. Expressions for the field dependence of the elastic constants are presented for both hexagonal and cubic crystals and for various orientations of the magnetization and applied field.