Capturing spin-torque effects with a semilocal exchange-correlation functional

We cure the lack of spin torque in semilocal exchange-correlation (XC) functionals by treating XC effects in the framework of spin-current-density-functional theory (SCDFT), and present the implementation of the first kind of this novel family of XC functionals in the Vienna ab-initio simulation package (VASP): An SCDFT functional featuring a U(1)$\times$SU(2) gauge-invariant $2\times 2$ XC potential. While the framework can be applied to other XC functionals, the presented flavor of the SCDFT functional is based on Becke-Roussel exchange and Colle-Salvetti correlation. In addition to the $2\times 2$ spin density and kinetic-energy density, the XC functional depends on the $2\times 2$ spin-current density. The implementation requires the computation of the spin-current density within the projector-augmented-wave method and the variation of the XC energy with respect to it. The application to a Cr$_3$ molecule and bulk MnO reveals (i) spin torque of the same order as obtained by methods including exact exchange, (ii) a counterintuitive contribution to the energy even in collinear ferromagnetic systems without spin-orbit coupling due to the gradient of the magnetization, and (iii) a similar computational cost per electronic step as calculations that depend on, inter alia, the kinetic-energy density, but convergence within fewer electronic steps.