Thermal Hall effects in quantum magnets

In the recent years, the thermal Hall transport has risen as an important diagnosis of the physical properties of the elementary excitations in various quantum materials, especially among the Mott insulating systems where the electronic transports are often featureless. Here we review the recent development of thermal Hall effects in quantum magnets where all the relevant excitations are charge-neutral. In addition to summarizing the existing experiments, we pay a special attention to the underlying mechanisms of the thermal Hall effects in various magnetic systems, and clarify the connection between the microscopic physical variables and the emergent degrees of freedom in different quantum phases. The external magnetic field is shown to modify the intrinsic Berry curvature properties of various emergent and/or exotic quasiparticle excitations in distinct fashions for different quantum systems and quantum phases, contributing to the thermal Hall transports. These include, for example, the conventional ones like the magnons in ordered magnets, the triplons in dimerized magnets, the exotic and fractionalized quasiparticles such as the spinons and the magnetic monopoles in quantum spin liquids. We review their contribution and discuss their presence in the thermal Hall conductivity in different physical contexts. We expect this review to provide a useful guidance for the physical mechanism of the thermal Hall transports in quantum magnets.