Spin currents and spin superfluidity

The present review analyses and compares various types of dissipationless spin transport: ( 1) Superfluid transport, when the spin-current state is a metastable state ( a local but not the absolute minimum in the parameter space). ( 2) Ballistic spin transport, when spin is transported without losses simply because the sources of dissipation are very weak. ( 3) Equilibrium spin currents, i.e. genuine persistent currents. ( 4) Spin currents in the spin Hall effect. Since superfluidity is frequently connected with Bose condensation, recent debates about magnon Bose condensation are also reviewed. For any type of spin currents simplest models were chosen for discussion in order to concentrate on concepts rather than the details of numerous models. The various hurdles on the way of using the concept of spin current ( absence of the spin-conservation law, ambiguity of spin current definition, etc.) were analysed. The final conclusion is that the spin-current concept can be developed in a fully consistent manner, and is a useful language for the description of various phenomena in spin dynamics.