Sublattice Magnetization of Yttrium Iron Garnet at Low Temperatures

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 Sαz(T)=S−δα−cT−AαT3/2−BαT5/2−CαT7/2⋯. Here α labels the sublattice a or d, δα expresses the effect of zero-point motion, and cT is the Holstein-Primakoff correction for dipolar interactions. Expressions in terms of the exchange integrals Jaa, Jdd, Jad, and Jad′, where Jad′ describes interactions between next-nearest-neighbor a and d sites, are given for Aα, Bα, and, when Jad′=0, for Cα. The spin-wave spectrum of some substituted garnets and the effect of spin-wave interactions on the zero-point disordering are treated in appendices.