A test drive for exchange-correlation functionals on noncollinear magnets: Mn${}_3$Ir, Mn${}_3$Ge, NiS${}_2$, and YMnO${}_3$

Abstract

A first-principles description of noncollinear magnets is challenging, and the practical behavior of genuinely noncollinear exchange-correlation approximations is largely untested. Spin-current density-functional theory (SCDFT) admits noncollinear approximations constrained by local U(1)$\times$SU(2) gauge invariance, an exact condition unavailable in the more restrictive framework of spin-DFT (SDFT). Using the Vienna ab initio simulation package (VASP), we compare two recently developed noncollinear SCDFT functionals, NCMSCAN and LFNCBR89-NCCS, against locally collinear SDFT extensions of four common functionals (PZ, PW92, PBE, and SCAN) for several noncollinear $d$-electron systems. The key finding is that among all tested functionals, only the SCDFT functionals recover the spin texture of the experimental ground state of NiS${}_2$, and they do so at a cost comparable to standard semi-local approximations. Yet the two SCDFT functionals differ in equilibrium volumes, band gaps, and on-site magnetic moments. Overall, this survey illustrates the usefulness of SCDFT in capturing noncollinear physics with the tested approximations.