Spin-orbit coupling in LaAlO₃/SrTiO₃ interfaces: Magnetism and orbital ordering

Rashba spin-orbit coupling together with electron correlations in the metallic interface between SrTiO₃ and LaAlO₃ can lead to an unusual combination of magnetic and orbital ordering. We consider such phenomena in the context of the recent observation of anisotropic magnetism. Firstly, we show that Rashba spin-orbit coupling can account for the observed magnetic anisotropy, assuming a correlation driven (Stoner type) instability toward ferromagnetism. Secondly, we investigate nematicity in the form of an orbital imbalance between d_xz/d_yz orbitals. We find an enhanced susceptibility toward nematicity due to the van Hove singularity in the low-electron-density regime. In addition, the coupling between in-plane magnetization anisotropy and nematic order provides an effective symmetry breaking field in the magnetic phase. We estimate this coupling to be substantial in the low-electron-density regime. The resulting orbital ordering can affect magneto transport.