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 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.

21 pages (including 10 figures, 4 appendices, and references)

References in corpus (8)

• The Kernel Polynomial Method
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
• Tuning interactions between spins in a superconductor
• Nodal superconducting exchange coupling
• Tunneling processes between Yu-Shiba-Rusinov bound states
• Reduced-Shifted Conjugate-Gradient Method for a Green's Function: Efficient Numerical Approach in a Nano-structured Superconductor
• RKKY interaction in a spin-split superconductor

Cited by in corpus (2)

• Bodge: Python package for efficient tight-binding modeling of superconducting nanostructures
• Dzyaloshinskii-Moriya-type spin-spin interaction from mixed-parity superconductivity