The energies and eigenvectors for long-wavelength acoustic spin waves in yttrium iron garnet are calculated neglecting spin-wave interactions, but including the effects of anisotropy and dipolar interactions. The sublattice magnetization is found to be $S_{\alpha }^{}{}_{}{}^z\mathrm{}\left(T\right)=S-{\delta }_{\alpha }-cT-A_{\alpha }{T}^{\frac{3}{2}}-B_{\alpha }{T}^{\frac{5}{2}}-C_{\alpha }{T}^{\frac{7}{2}}\cdots$. Here $\alpha$ labels the sublattice $a$ or $d$, ${\delta }_{\alpha }$ expresses the effect of zero-point motion, and $\mathrm{cT}$ is the Holstein-Primakoff correction for dipolar interactions. Expressions in terms of the exchange integrals $J_{\mathrm{aa}}$, $J_{\mathrm{dd}}$, $J_{\mathrm{ad}}$, and $J_{\mathrm{ad}}^{}{}_{}{}^{\prime }$, where $J_{\mathrm{ad}}^{}{}_{}{}^{\prime }$ describes interactions between next-nearest-neighbor $a$ and $d$ sites, are given for $A_{\alpha }$, $B_{\alpha }$, and, when $J_{\mathrm{ad}}^{}{}_{}{}^{\prime }=0\mathrm{}$, for $C_{\alpha }$. The spin-wave spectrum of some substituted garnets and the effect of spin-wave interactions on the zero-point disordering are treated in appendices.

• Received 24 October 1966

DOI:https://doi.org/10.1103/PhysRev.155.499