Physical spin torques from exactly constrained exchange-correlation torques

The problem of capturing physical spin torques in non-collinear 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 {\em extraneous} to SDFT -- thus leading to {\em 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)$\times$SU(2)-invariance of the xc energy of SpinCurrent-DFT (SCDFT) -- an exact constraint that is not accessible to SDFT. Non-vanishing xc torques obtained on non-collinear 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 {\em only} the physical currents and physical spin-torques.