Inplane anisotropy of longitudinal thermal conductivities and weak localization of magnons in a disordered spiral magnet

We demonstrate the inplane anisotropy of longitudinal thermal conductivities and the weak localization of magnons in a disordered screw-type spiral magnet on a square lattice. We consider a disordered spin system, described by a spin Hamiltonian for the antiferromagnetic Heisenberg interaction and the Dzyaloshinsky-Moriya interaction with the mean-field type potential of impurities. We derive longitudinal thermal conductivities for the disordered screw-type spiral magnet in the weak-localization regime by using the linear-response theory with the linear-spin-wave approximation and performing perturbation calculations. We show that the inplane longitudinal thermal conductivities are anisotropic due to the Dzyaloshinsky-Moriya interaction. This anisotropy may be useful for experimentally estimating the magnitude of a ratio of the Dzyaloshinsky-Moriya interaction to the Heisenberg interaction. We also show that the main correction term gives a logarithmic suppression with length scale due to the critical back scattering. This suggests that the weak localization of magnons is ubiquitous for the disordered two-dimensional magnets having global time-reversal symmetry. We finally discuss several implications for further research.