Magnetism in spin-orbit coupled oxides*

Transition metal oxides with 4d and 5d ions provide a glimpse into unusual facets of spin-orbit coupled magnetism. In this talk, I will discuss how a theoretical study of resonant inelastic X-ray scattering enables us to extract single-site effective Hamiltonian parameters relevant to ``bottom-up'' modelling of such materials, including iridates, rhenates, and osmates. Such single-site Hamiltonians are useful to extract spin-exchange interactions, study its sensitivity to lattice distortions, and to understand bulk magnetism. We illustrate this via the exploration of frustrated jeff=1/2 Mott insulators on the face-centered cubic lattice. These results are applicable to a wide class of materials called double-perovskites. Finally, we show how thin films of spin-orbit coupled metallic magnets may host tunable skyrmion crystals induced by strain and magnetic field, and potentially exhibit a phenomenon we term "topological quantum oscillations".