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Thermal Hall responses in frustrated honeycomb spin systems

We study geometrical responses of magnons driven by a temperature gradient in frustrated spin systems. While Dzyaloshinskii-Moriya (DM) interactions are usually incorporated to obtain geometrically nontrivial magnon bands, here we investigate thermal Hall responses of magnons that do no rely on the DM interactions. Specifically, we focus on frustrated spin systems with sublattice degrees of freedom and show that a nonzero Berry curvature requires breaking of an effective $PT$ symmetry. According to this symmetry consideration, we study the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models on a honeycomb lattice as a representative example, and demonstrate that magnons in the spiral phase support the thermal Hall effect once we introduce a magnetic field and asymmetry between the two sublattices. We also show that driving the magnons by a temperature gradient induces spin current generation (i.e., magnon spin Nernst effect) in the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models.