The effect of two-magnon-one-phonon scattering processes on the lattice thermal conductivity of antiferromagnets is studied. Transition matrix elements are obtained by expansion in lattice displacements of the exchange and anisotropy for an anisotropic Heisenberg Hamiltonian. Relaxation times for the phonons are determined by conventional perturbation theory and lattice thermal conductivities are then calculated in the Debye approximation. Results are obtained in all three field-induced phases for fields parallel to the easy axis for sublattice magnetization. It is found that in the spin-flop phase, the coefficients of the transformation to magnon operators make a substantial contribution to the magnetic field dependence.
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G. S. Dixon (1980) studied this question.
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