The Effect of Magnetoelastic Interactions on the Elastic Constants of the Heavy Rare Earth Metals

A theory employing finite strains and angular momentum invariants is applied to the rare earth metals of hcp structure. A Hamiltonian is written down which is invariant under combined rotations of the magnetic and elastic systems. When the usual small strain approximations are subsequently made there appear new terms linear in the antisymmetric strains. The coupling of transverse acoustic waves to the magnetic system has been studied and expressions obtained for the dependence of the elastic constants c44 and c66 on an applied magnetic field in the ferromagnetic phase. Estimates of the effects to be expected for Gd, Tb, Dy, Ho and Er indicate that it should be possible to obtain in a direct manner the values of certain magnetoelastic constants and anisotropy constants. Calculations have also been performed for the field‐dependent changes in c11 and c33 for longitudinal waves in the paramagnetic region. These changes result from the fact that the finite strains Eμμ include terms of the form eμμ2.