Dzyaloshinskii-Moriya-type 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 noncollinear 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 Dzyaloshinskii-Moriya-type interaction (DMTI) can emerge purely from superconducting correlations without any spin-orbit interaction. We give an analytical proof and provide a numerical study which shows that DMTI arises in mixed-parity superconductors solely from the superconducting pairing. Moreover, we show that the same effect can be realized in Josephson junctions between $s$-wave and $p$-wave superconductors, where a phase bias toggles the DMTI entirely on and off. These results enable a way to engineer spin textures using superconducting order.