Superfluid spin transport in ferro- and antiferromagnets

The paper focuses on spin superfluid transport, observation of which was recently reported in antiferromagnet Cr$_2$O$_3$ [Yuan et al., Science Advances 4, eaat1098 (2018)]. In the experiment easy-plane topology necessary for spin superfluidity is produced not by easy-plane magnetic crystal anisotropy but by an external magnetic field confining sublattice magnetizations in the plane normal to the magnetic field. The role of dissipation at conversion of spin current of injected incoherent magnons to a superfluid spin current is analyzed. Dissipation coefficients are derived from the Landau-Lifshitz-Gilbert theory with the Gilbert damping parameter and from the Boltzmann equation for magnons scattered by defects. The healing length at which incoherent spin transport transforms to coherent (superfluid) spin transport in antiferromagnets is extremely short. The Landau criterion for an antiferromagnet put in a magnetic field is derived from the spectrum of collective spin modes. The Landau instability starts in the gapped mode earlier than in the Goldstone gapless mode, in contrast to easy-plane ferromagnets where the Goldstone mode becomes unstable. The structure of the magnetic vortex in the geometry of the experiment is determined. The vortex core has the skyrmion structure with finite magnetization component normal to the magnetic field. This magnetization creates stray magnetic fields around the exit of the vortex line from the sample, which can be used for experimental detection of vortices.