Magnetoelastic Effects in Rare Earth Metals and Compounds

Abstract

<p>A theory developed by Toupin, Tiersten, Brown and Melcher employing finite strains and angular momentum invariants is applied to ferromagnets which have hexagonalclose-packed or cubic symmetry. A Hamiltonian is written down which includes Heisenberg-exchange, magnetic anisotropy, magnetoelastic terms and the Zeeman term and which is invariant under combined rotations of the magnetic and elastic systems. When the approximations of small-strain theory are subsequently carried out, there appear new terms originating in the magnetic an,isotropy that are linear in the antisymmetric strains ωμν and correspond to rotations of the elastic medium. The coupling of transverse acoustic waves to the magnetic system is studied and expressions are derived for the dependence of the measured elastic constants on an applied magnetic field in the ferromagnetic phase. Using available data on magnetic anisotropy and magneto-striction, estimates are given for the size of the effects that may be expected to be found in the rare-earth metals (Gd, Tb, Dy, Ho and Er) and in some of the rare-earth-iron compounds RFe₂ (R = Tb, Dy, Ho, Er and Tm). Fractional changes in the elastic constants as large as 10⁻² are predicted in fields of about 50 kOe. Calculations are also performed for the field-dependent changes in c₁₁ and c₃₃ for longitudinal waves in the paramagnetic region for Dy and Ho.</p>