Dzyaloshinskii-Moriya spin-spin interaction from mixed-parity superconductivity

Interacting impurity spins adsorbed on surfaces have been suggested as basic components for applications in quantum computation and spintronics. Such spins usually prefer a parallel or antiparallel configuration, but weakly non-collinear alignments are possible due to the Dzyaloshinskii-Moriya interaction (DMI) that arises in the presence of relativistic spin-orbit coupling. Here, we show that an effective DMI can emerge purely from superconducting correlations without any spin-orbit interaction. We give an analytical proof and provide a numerical study which shows that DMI arises in mixed-parity superconductors solely from the superconducting pairing. These results enable a way to engineer spin textures using the superconducting phase transition.