  We demonstrate theoretically that the thermal Hall effect of magnons in
collinear antiferromagnetic insulators is an indicator of magnetic and
topological phase transitions in the magnon spectrum. The transversal heat
current of magnons caused by a thermal gradient is calculated for an
antiferromagnet on a honeycomb lattice. An applied magnetic field drives the
system from the antiferromagnetic phase via a spin-flop phase into the
field-polarized phase. Besides these magnetic phase transitions we find
topological phase transitions within the spin-flop phase. Both types of
transitions manifest themselves in prominent and distinguishing features in the
thermal conductivities; depending on the temperature, the conductivity changes
by several orders of magnitude, providing a tool to discern experimentally the
two types of phase transitions. We include numerical results for the van der
Waals magnet MnPS$_3$.
