TWO-MAGNON-ONE-PHONON SCATTERING IN THE LATTICE THERMAL CONDUCTIVITY OF MAGNETIC INSULATORS

Abstract
A simple, but general model of magnon-phonon scattering as an extension of linear spin-wave theory is presented. Both resonant one-magnon-one-phonon and two-magnon-one-phonon scattering processes are considered. The former are included in the thermal conductivity by diagonalizing the magnon-phonon Hamiltonian to obtain coupled magneto elastic modes. The two-magnon-one-phonon processes are treated in the relaxation time approximation. This model has been used to analyze the experimental dependence of the thermal conductivity on temperature and magnetic field for several antiferromagnetic and ferromagnetic insulators. For the materials studied to date the two-magnon-one-phonon processes are found to dominate over the resonant process. This can be attributed to the greater width of the band of phonon frequencies affect by the two-magnon-one-phonon processes. In applying the model to experiment some care in the transformation of the spin-Hamiltonian of this transformation may contain important contributions to the magnetic field dependence.