Joji Nasu
In localized electron systems, the elementary excitations from a magnetic order are described as bosons, referred to as magnons. Recently, the topological properties of magnons, such as the thermal Hall effect and spin Nernst effect, have garnered considerable attention in localized electron systems with strong spin-orbit coupling, as well as in itinerant electron systems. Thus far, these properties have been discussed based on the free-magnon picture. However, the spin-nonconserving nature of spin-orbit coupling induces strong magnon damping due to three-magnon interactions, significantly affecting transport phenomena mediated by thermally excited magnons. Furthermore, this spin-nonconserving characteristic complicates theoretical studies of the spin Nernst effect because of the challenges in defining the spin current. To address these issues, we have newly formulated a framework for the thermal Hall conductivity under magnon damping at finite temperatures and the spin Nernst coefficient for spin-nonconserved systems. We applied our frameworks to specific quantum spin models, such as the Heisenberg model with Kitaev and Dzyaloshinskii-Moriya interactions and spin dimer models, and found that the results differ significantly from those obtained using conventional methods.