Meta-Generalized-Gradient Approximation made Magnetic

Abstract: The Jacob's ladder of density functional theory (DFT) proposes the compelling view that by extending the form of successful approximations -- being guided by exact conditions and selected (least empirical) norms -- upper rungs will do better than the lower, thus allowing to balance accuracy and computational effort. Meta-generalized-gradient-approximations (MGGAs) belong to the last rung of the semi-local approximations before hybridization with non-local wave function theories. Among the MGGAs, the Strongly Constrained and Appropriately Normed Approximation (SCAN) greatly improves upon GGAs from the lower rung. But the over magnetized solutions of SCAN make GGAs more reliable for magnetism. Here, we provide a solution that satisfies the most pressing {\em desiderata} for density functional approximations for ferromagnetic, antiferromagnetic and non-collinear states. The approach is available in an implementation in the \textsc{Crystal} electronic structure package.