There are tantalizing hints of magnetism at various oxide interfaces (e.g., n-type LaAlO3/SrTiO3), but the experimental evidence remains controversial at this time. In this talk, I will argue that if magnetism exists at oxide interfaces, or more generally in 2D systems with broken inversion, then general symmetry considerations imply a spiral ground state in zero field [1] and a skyrmion crystal in an external magnetic field [2]. Remarkably, skyrmions are found to be stable over a much broader region of the phase diagram in 2D systems with Rashba spin-orbit coupling compared to non-centrosymmetric 3D materials. I will also present an analysis of various microscopic models for magnetic exchange, which shows that the easy-plane anisotropy responsible for stabilizing skyrmions in 2D naturally arises from the same spin-orbit coupling that is responsible for the chiral Dzyaloshinshkii-Moriya interactions.
[1] S. Banerjee, O. Erten and M. Randeria, Nature Physics 9, 626 (2013).
[2] S. Banerjee, J. Rowland, O. Erten and M. Randeria, Phys. Rev X 4, 031045 (2014).