Topological magnons in a non-coplanar magnetic order on the triangular lattice

Abstract

The bond-dependent Kitaev interaction K is familiar in the effective spin model of transition
metal compounds with octahedral ligands. In this work, we find a peculiar non-coplanar magnetic
order can be formed with the help of K and next-nearest neighbor Heisenberg coupling J2 on the
triangular lattice. It can be seen as a miniature version of skyrmion crystal, since it has nine spins
and an integer topological number in a magnetic unit cell. The magnon excitations in such an order
are studied by the linear spin-wave theory. Of note is that the change in the relative size of J2 and K
produces topological magnon phase transitions although the topological number remains unchanged.
We also calculated the experimentally observable thermal Hall conductivity, and found that the signs
of thermal Hall conductivity will change with topological phase transitions or temperature changes in
certain regions.