Proximity effects and characteristic lengths in ferromagnet-superconductor structures

TL;DR

This paper provides a detailed theoretical analysis of proximity effects in ferromagnet-superconductor structures, exploring how various parameters influence superconductivity leakage and spin splitting, with results aligning with experimental observations.

Contribution

It introduces a numerical approach to solve Bogoliubov-de Gennes equations for F/S systems, revealing how parameters affect proximity effects and characteristic lengths.

Findings

Superconductivity leakage length depends on temperature and interface quality.

Spin splitting in the superconductor varies with magnet polarization and Fermi mismatch.

Results agree with existing experimental data.

Abstract

We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scattering, sample size and Fermi wavevector mismatch, all of which turn out to have important influence on the results. These comprehensive results should help characterize and analyze future data and are shown to be in agreement with existing experiments.