Heat Conductivity in a Two-Dimensional Finite-Size Spin System with Dzyaloshinskii--Moriya Interactions

Heat conductivity is studied by direct numerical simulations in a two-dimensional model with chiral Dzyaloshinskii--Moriya (DM) spin superexchange interactions for various DM strengths and finite sizes. We find that when temperature is not too low, the thermal conductivity can be well described in the semi classical spin wave picture, and connections of thermal conductivity with the specific heat and the dynamic relaxation time are verified to be suitable. In particular, the transition arising in Sr_14-xCa_xCu₂₄O₄₁ is related to a magnetic spin glass and qualitatively understood as a kind of Kosterlitz--Thouless transitions. It is shown that the critical temperature is linearly dependent on the spin--spin interactions for the relevant strong DM strength.