RKKY interaction in a spin-split superconductor

TL;DR

This paper theoretically investigates how spin-splitting in an s-wave superconductor influences the RKKY interaction between magnetic impurities, revealing dependence on impurity orientation and distance, with oscillating dominant interaction types.

Contribution

It introduces a detailed theoretical analysis of RKKY interactions in spin-split superconductors, highlighting orientation-dependent interaction types and oscillatory behavior with impurity separation.

Findings

Spin-splitting causes different interaction types based on impurity spin orientation.

The preferred magnetic alignment (ferromagnetic or antiferromagnetic) depends on spin-splitting magnitude.

The dominant RKKY interaction component oscillates with impurity distance.

Abstract

We determine theoretically the interaction between two magnetic impurities embedded in a spin-split $s$-wave superconductor. The spin-splitting in the superconductor gives rise to two different interaction types between the impurity spins, depending on whether their spins lie in the plane perpendicular to the spin-splitting field (Heisenberg) or not (Ising). For impurity separation distances exceeding $\xi_S$, we find that the magnitude of the spin-splitting can determine whether an antiferromagnetic or ferromagnetic alignment of the impurity spins is preferred by the RKKY interaction. Moreover, the Ising and Heisenberg terms of the RKKY interaction alternate on being the dominant term and their magnitudes oscillate as a function of distance between the impurities.