We cure the lack of exchange-correlation (XC) spin torque in semilocal XC functionals by treating XC effects in the framework of spin-current-density-functional theory (SCDFT), and present the first projector-augmented-wave (PAW) implementation of this novel family of XC functionals: an U(1)$\times \mathrm{SU}\left(2\right)$ gauge-invariant SCDFT functional featuring a $2\times 2$ 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 PAW method and the variation of the XC energy with respect to it. The application to a ${\mathrm{Cr}}_3$ molecule and bulk MnO reveals (i) XC 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 semilocality 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.

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• Magnetism
• Spin torque
• Noncollinear magnets
• Density functional approximations
• Density functional theory
• First-principles calculations