Thermal Hall responses in frustrated honeycomb spin systems

TL;DR

This paper explores how frustrated honeycomb spin systems can exhibit thermal Hall effects without relying on Dzyaloshinskii-Moriya interactions, emphasizing symmetry considerations and magnetic field effects.

Contribution

It demonstrates that nonzero Berry curvature and thermal Hall responses can arise in frustrated spin systems through symmetry breaking, independent of DM interactions.

Findings

Magnons in spiral phases support thermal Hall effect with magnetic field and sublattice asymmetry.

Driving magnons by temperature gradient induces magnon spin Nernst effect.

Thermal Hall responses depend on breaking effective PT symmetry in frustrated systems.

Abstract

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.