Spin currents, spin torques, and the concept of spin superfluidity

current operator contains a contribution which renormalizes an external magnetic field and hence affects only the precessional motion of the spin polarization. This term, which has been named angular spin current by Sun and Xie [Phys. Rev. B 72, 245305 (2005)], does not describe the translational motion of magnetic moments. We give a prescription for how to separate these two types of spin transport and show that the translational movement of the spin is always polarized along the direction of the local magnetization. We also show that at vanishing temperature the classical magnetic order parameter in magnetic insulators cannot carry a translational spin current and elucidate how this affects the interpretation of spin supercurrents.