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

• Main Authors: Atousa Ghanbari, Vetle K. Risinggård, Jacob Linder
• Format: Article
• Language: English
• Published: Nature Publishing Group 2021-03-01
• Series: Scientific Reports
• Online Access: https://doi.org/10.1038/s41598-021-83620-3

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.