Magnetostriction in Cubic Néel Ferrimagnets, with Application to YIG

Abstract

The magnetostriction of single-crystal yttrium iron garnet (YIG) has been measured from 100 to 450\ifmmode^\circ\else\textdegree\fi{}K by a capacitative technique in which the sample dilatation shifts the resonant frequency of an oscillator, and by standard strain gauge methods. To analyze the data, the theory of magnetostriction in cubic insulators is applied to the N\'eel model of a ferrimagnet. This theory permits evaluation of the individual magneto-elastic coupling coefficients for each type of site (or sublattice) and for each symmetry of strain mode. The values found are ${{B}_{0,2}}^{\ensuremath{\gamma}}(a)=\ensuremath{-}9.70\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ergs/${\mathrm{cm}}^{3}$, ${{B}_{0,2}}^{\ensuremath{\gamma}}(d)=8.95\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ergs/${\mathrm{cm}}^{3}$, ${{B}_{0,2}}^{\ensuremath{\epsilon}}(a)=5.67\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ergs/${\mathrm{cm}}^{3}$, ${{B}_{0,2}}^{\ensuremath{\epsilon}}(d)=\ensuremath{-}17.2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ergs/${\mathrm{cm}}^{3}$, where $a$ and $d$ refer to octahedrally and tetrahedrally coordinated sites, respectively, and $\ensuremath{\gamma}$ and $\ensuremath{\epsilon}$ refer to linear dilatations and shear modes, respectively; the subscripts on the coefficients indicate that these are the coefficients of the lowest order symmetry polynomials, the higher order terms being found experimentally to be relatively small. Appropriate averaging of the above constants give "effective" constants in good agreement with the mean values found by other investigators. The theoretical predictions of the temperature dependence of the magnetostriction constants ${h}_{1}$ and ${h}_{2}$ are in excellent agreement with the observed values of ${h}_{1}$, which has a minimum (\ensuremath{\sim}-2.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$) near room temperature, and of ${h}_{2}$ which increases monotonically toward zero with increasing temperature.