Novel magnetic state in $d^4$ Mott insulators

We show that the interplay of strong Hubbard interaction $U$ and spin-orbit coupling $\lambda$ in systems with $d^4$ electronic configuration leads to several unusual magnetic phases. Most notably, we find that competition between superexchange and spin-orbit coupling leads to a phase transition from a non-magnetic state predicted by atomic physics to a novel magnetic state in the large $U$ limit. We show that the local moment changes dramatically across this phase transition, challenging the conventional wisdom that local moments are robust against small perturbations in a Mott insulator. The Hund's coupling plays an important role in determining the nature of the magnetism. We identify candidate materials and present predictions for Resonant X-ray Scattering (RXS) signatures of the unusual magnetism in $d^4$ Mott insulators.