Inverse proximity effect in superconductor-ferromagnet structures: From the ballistic to the diffusive limit

TL;DR

This paper provides a comprehensive theoretical analysis of the inverse proximity effect in superconductor-ferromagnet structures, revealing how disorder, interface quality, and layer thickness influence the induced magnetic moment's magnitude and sign.

Contribution

It introduces a microscopic approach combining Hamiltonian and quasiclassical theory to study the inverse proximity effect across ballistic and diffusive regimes.

Findings

In the diffusive limit, the induced magnetization opposes the ferromagnet's magnetization.

In the ballistic limit, the sign of the induced magnetization depends on interface quality and layer thickness.

The penetration length of the magnetic moment is about the superconducting coherence length.

Abstract

The inverse proximity effect, i.e. the induction of a magnetic moment in the superconductor in superconductor-ferromagnet (S/F) junctions is studied theoretically. We present a microscopic approach which combines a model Hamiltonian with elements of the well established quasiclassical theory. With its help we study systems with arbitrary degree of disorder, interface transparency and thickness of the layers. In the diffusive limit we recover the result of previous works: the direction of the induced magnetization $M$ is opposite to the one of the F layer. However, we show that in the ballistic case the sign of $M$ may be positive or negative depending on the quality of the interface and thickness of the layers. {We show that, regardless of its sign, the penetration length of the magnetic moment into the superconductor is of the order of the superconductor coherence length, which demonstrates that the effect has a superconducting origin.}