  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.
