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 past several years, theoretical studies have focused on ferro- and antiferromagnetic spin structures, where domain walls always move toward 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 in ferrimagnets. 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 toward the hot end by minimizing 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 toward 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 toward the cold end, whereas above it toward 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. This finding opens the door for fast control of magnetic domains as given by the antiferromagnetic character while conserving the advantage of ferromagnets in terms of measuring and control by conventional means such as magnetic fields.
