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.
Highlights
We theoretically determine the magnetic exchange interaction between two ferromagnets coupled by a superconductor using a tight-binding lattice model
When considering the impurity average J imp for a large number of realizations with random impurity configurations, we find that increasing the impurity concentration in the superconductor causes the exchange interaction to decrease
The main purpose of this paper is to investigate the indirect exchange coupling between two ferromagnets separated by a superconductor when solving self-consistently for the order parameter and taking into account both the proximity effect and the inverse proximity effect
Summary
We theoretically determine the magnetic exchange interaction between two ferromagnets coupled by a superconductor using a tight-binding lattice model. The Ruderman−Kittel−Kasuya−Yosida (RKKY) is an indirect exchange interaction between localized spins mediated by itinerant electrons in m etals[1] This interaction played an important role in the discovery of giant magnetoresistance (GMR)[2,3] and has been studied in numerous m aterials[4,5,6,7,8,9]. The interaction through a d-wave superconductor with an anisotropic order parameter was s tudied[25] It was shown on the basis of analytical approximations that this interaction, to the s-wave case, contains one oscillatory term and one term favoring an anti-parallel configuration. It was experimentally shown that in a d-wave SSV, the anti-parallel ground-state was favored for some specific lengths of the superconducting system and that nodal quasiparticles likely played a central role in mediating the magnetic c oupling[26].
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