Spirals and skyrmions in two dimensional oxide heterostructures*

A symmetry-based general free energy governing long-wavelength magnetism in two-dimensional oxide heterostructures will be presented. This leads, in the relevant regime of weak but non-negligible spin-orbit coupling, to a rich phase diagram containing in-plane ferromagnetic, spiral, cone, and skyrmion lattice phases, as well as a nematic state stabilized by thermal fluctuations. The general conclusions are vetted by a microscopic derivation for a simple model with Rashba spin-orbit coupling.