Abstract
The temperature dependence of magnon frequencies is studied for ferrimagnets. The magnon frequency increases for the acoustical branch and decreases for the optical branch, both in low-temperature regions. Temperature variations obey the ${T}^{\frac{5}{2}}$ law. In high-temperature regions, both acoustical- and optical-magnon frequencies decrease with increasing temperature. The sign change of the temperature variation of acoustical-magnon frequencies is due to optical-magnon population which increase with temperature. The sign change occurs at a lower temperature for a magnon with a shorter wavelength. This feature is in accordance with Riste's neutron-scattering experiments performed with magnetites. The second-order shift has proved to be small at low temperatures. In the course of its calculation, we give a simple expression for the matrix element of a magnon interaction. This bears a close relationship to Dyson's dynamical interaction in ferromagnets.
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