Physical Spin Torques from Exactly Constrained Exchange-Correlation Torques

The problem of capturing physical spin torques in noncollinear magnetic systems has dominated the scene of spin-density functional theory (SDFT) in the last two decades. Progress has been hindered by the fact that the spin torque is directly connected to the divergence of the spin current, a quantity that is extraneous to SDFT-thus leading to spurious exchange-correlation (xc) torques in the spin dynamics. Moreover, SDFT cannot rigorously include vector potentials and spin-orbit couplings. Here, we propose a solution that exploits the U(1)×SU(2) invariance of the xc energy of Spin-current DFT-an exact constraint that is not accessible to SDFT. Nonvanishing xc torques obtained on noncollinear solutions are constrained by the aforementioned exact internal symmetry and do not enter the propagation of the spin magnetization-i.e., the spin dynamics involve only the physical currents and physical spin torques.