Spin Nernst effects of linear flavor-waves in quantum paramagnets

Recent advances in spin transport research have highlighted the potential of quantum paramagnets as platforms for exploring novel phenomena and developing next-generation technologies. In this paper, we investigate the Nernst-type thermal spin transport in a quantum paramagnet with spin-orbit couplings. Even though the ground state is paramagnetic, the upper branch parts in this system can carry spin information. By invoking the dispersive crystal electric field (CEF) excitations, the upper branch parts can be described by bosonic quasi-particles with different flavors in the linear flavor-wave regime. To distinguish the magnon Nernst effects in ordered systems, we name this topological spin transport the flavor Nernst effect (FNE). As a proof of principle, we examine the quantum paramagnetic ground state in an effective spin-1 Hamiltonian with Dzyaloshinskii-Moriya interactions and a large hard-axis anisotropy. The flavor Nernst coefficients are calculated using linear response theory. We demonstrate the FNE in a 2D pyrochlore thin film with an all-in-all-out Ising axis configuration, and investigate their dependence on temperature, anisotropy, DM interaction, and external fields. Our results reveal the connection between the FNE and the Berry curvature of the CEF excitations, suggesting potential applications in manipulating thermal spin currents and exploring topological spin transport phenomena in quantum paramagnets.