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

TL;DR

This paper investigates how the RKKY interaction between localized spins is modified in p-wave triplet superconductors, revealing new terms like Dzyaloshinskii--Moriya interaction and potential for novel magnetic ground states.

Contribution

It introduces the form of RKKY interaction in p-wave triplet superconductors, highlighting the emergence of new terms and their dependence on order parameter symmetries.

Findings

Non-unitary states induce a Dzyaloshinskii--Moriya term.

Spin-polarized Cooper pairs modulate spin--spin coupling.

Possible non-collinear magnetic ground states in triplet superconductors.

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 non-unitary 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 non-unitary superconductors in concert with the conventional RKKY interaction can lead to non-collinear 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.