Spin and charge order in doped spin-orbit coupled Mott insulators

We study a two-dimensional single-band Hubbard Hamiltonian with antisymmetric spin-orbit coupling. We argue that this is the minimal model to understand the electronic properties of locally noncentrosymmetric transition metal (TM) oxides such as Sr2IrO4. Based on exact diagonalizations of small clusters and the random-phase approximation, we investigate the correlation effects on charge and magnetic order as a function of doping and of the TM-oxygen-TM bond angle theta. For small doping and theta less than or similar to 15 degrees we find dominant commensurate in-plane antiferromagnetic fluctuations, while ferromagnetic fluctuations dominate for theta greater than or similar to 25 degrees. Moderately strong nearest-neighbor Hubbard interactions can also stabilize a charge density wave order. Furthermore, we compare the dispersion of magnetic excitations for the hole-doped case to resonant inelastic x-ray scattering data and find good qualitative agreement.