Exchange-correlation torques from gauge symmetries

The problem of predicting accurate exchange-correlation (xc) 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 extraneous to SDFT. Furthermore, SDFT does not apply in the presence of vector potentials and spin-orbit couplings. Here, we propose a solution that exploits the physical implications of the U(1)xSU(2) gauge invariance of the xc energy in SpinCurrent-DFT. We derive explicit xc torque expressions based on meta-generalized-gradient approximations in the framework of the generalized Kohn-Sham (GKS) formulation. One key term represents an xc-torque involving the GKS spin-kinetic energy density; and another term resembles the phenomenological spin current of the Landau-Lifshitz equations: both are derived from first-principles. We also show that the functional form ensures that the GKS particle- and spin-currents are identical, in form, to their interacting counterparts. Non-collinear equilibrium conditions and adiabatic dynamics are thus derived that resolve longstanding issues.