RKKY interaction in triplet superconductors: Dzyaloshinskii-Moriya-type interaction mediated by spin-polarized Cooper pairs

Abstract

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction governs the coupling between localized spins and is strongly affected by the environment in which these spins reside. In superconductors, this interaction becomes long-ranged and provides information about the orbital symmetry of the superconducting order parameter. In this work, we consider the RKKY interaction between localized spins mediated by p-wave triplet superconductors. In contrast to the well-studied RKKY interaction in d-wave superconductors, we find that the spin of the Cooper pair in a triplet state also modulates the spin-spin coupling. We consider several different types of p-wave triplet states and find that the form of the RKKY interaction changes significantly with the symmetries of the order parameter. For nonunitary superconducting states, two new terms appear in the RKKY interaction: a background spin magnetization coupling to the individual spins and, more interestingly, an effective Dzyaloshinskii-Moriya term. The latter term oscillates with the separation distance between the impurity spins. Finally, we find that the finite spin expectation value in nonunitary superconductors in concert with the conventional RKKY interaction can lead to noncollinear magnetic ground states even when the Dzyaloshinskii-Moriya term is negligible. The RKKY interaction in p-wave triplet superconductors thus offers a way to achieve new ground state spin configurations of impurity spins and simultaneously provides information about the underlying superconducting state.

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