  Control of magnetic domain wall motion holds promise for efficient
manipulation and transfer of magnetically stored information. Thermal magnon
currents, generated by temperature gradients, can be used to move magnetic
textures, from domain walls, to magnetic vortices and skyrmions. In the last
years, theoretical studies have centered in ferro- and antiferromagnetic spin
structures, where domain walls always move towards the hotter end of the
thermal gradient. Here we perform numerical studies using atomistic spin
dynamics simulations and complementary analytical calculations to derive an
equation of motion for the domain wall velocity. We demonstrate that in
ferrimagnets, domain wall motion under thermal magnon currents shows a much
richer dynamics. Below the Walker breakdown, we find that the temperature
gradient always pulls the domain wall towards the hot end by minimizating its
free energy, in agreement with the observations for ferro- and antiferromagnets
in the same regime. Above Walker breakdown, the ferrimagnetic domain wall can
show the opposite, counterintuitive behavior of moving towards the cold end. We
show that in this case, the motion to the hotter or the colder ends is driven
by angular momentum transfer and therefore strongly related to the angular
momentum compensation temperature, a unique property of ferrimagnets where the
intrinsic angular momentum of the ferrimagnet is zero while the sublattice
angular momentum remains finite. In particular, we find that below the
compensation temperature the wall moves towards the cold end, whereas above it,
towards the hot end. Moreover, we find that for ferrimagnets, there is a torque
compensation temperature at which the domain wall dynamics shows similar
characteristics to antiferromagnets, that is, quasi-inertia-free motion and the
absence of Walker breakdown.
