Self-consistent solution for the magnetic exchange interaction mediated by a superconductor

TL;DR

This paper presents a theoretical analysis of how a superconductor mediates magnetic exchange interactions between ferromagnets, revealing the suppression of oscillations and the influence of impurities on the interaction.

Contribution

It introduces a self-consistent lattice model to study the impact of superconductivity and impurities on magnetic exchange interactions between ferromagnets.

Findings

Superconducting state suppresses RKKY oscillations at large gaps.

Anti-parallel alignment becomes the ground state due to superconductivity.

Impurities reduce the exchange interaction by increasing quasiparticle localization.

Abstract

We theoretically determine the magnetic exchange interaction between two ferromagnets coupled by a superconductor using a tight-binding lattice model. The main purpose of this study is to determine how the self-consistently determined superconducting state influences the exchange interaction and the preferred ground-state of the system, including the role of impurity scattering. We find that the superconducting state eliminates RKKY-like oscillations for a sufficiently large superconducting gap, making the anti-parallel orientation the ground state of the system. Interestingly, the superconducting gap is larger in the parallel configuration than in the anti-parallel configuration, giving a larger superconducting condensation energy, even when the preferred ground state is anti-parallel. We also show that increasing the impurity concentration in the superconductor causes the exchange interaction to decrease, likely due to an increasing localization of the mediating quasiparticles in the superconductor.