Magnetoelastic Spin Hamiltonians: Applications to Garnets

The theory of magnetoelastic spin Hamiltonians and their relation to magnetostriction is reviewed, clarified, and expanded. We consider terms representing strain modulation of bilinear exchange, of crystal field, and of the g tensor (direct-forced magnetostriction). When the unstrained spin Hamiltonian contains anisotropic exchange and large crystal-field terms, we expect some new effects: Strain modulation of the Dzyaloshinski-Moriya interaction can be important for most site symmetries; second-degree terms in spin operators give rise to high-order magnetostriction constants, and high-degree spin terms contribute to low-order magnetostriction; the temperature and field dependences may deviate from the isotropic theory. Application is made to the much-studied ${\mathrm{Yb}}^{3+}$ ion in ytterbium iron garnet and also to a model for dysprosium iron garnet. For the latter case, we show that the novel behavior of the observed magnetostriction can be explained by the large crystal fields.