Spin Nernst effect and spatiotemporal dynamic simulation of topological magnons in the antiferromagnet Cu3TeO6

The topological surface state arising from the nontrivial topology of the bulk band structure has attracted a wide range of interest. Compared with electrons, the magnon propagation in magnetic materials can be more intuitively reflected in the spin precession and generate different effects. Using molecular dynamics simulations, we study the real-space evolution of the magnon topological surface state in ${\mathrm{Cu}}_{3}{\mathrm{TeO}}_{6}$, a three-dimensional antiferromagnet with Dzyaloshinskii-Moriya interaction. We observe a coherent wave-packet propagation on the surface without attenuation into the bulk. As the intensity of the chiral Dzyaloshinskii-Moriya interaction increases, spin-dependent chirality of magnons appears on the surface. Such behavior suggests that ${\mathrm{Cu}}_{3}{\mathrm{TeO}}_{6}$ displays the magnon spin Nernst effect, i.e., the system generates a transverse net spin flow after applying a longitudinal temperature gradient. In our numerical calculations, when the intensity of the Dzyaloshinskii-Moriya interaction is about $10%$ of the nearest neighbor exchange interaction, the spin Nernst coefficient in this material is estimated to be around ${\ensuremath{\alpha}}_{yz}=1--3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{4pt}{0ex}}\mathrm{J}/\mathrm{mK}$.