# Spin polarization and orbital effects in superconductor-ferromagnet structures

## TL;DR

This paper theoretically investigates how superconductor-ferromagnet bilayers generate spontaneous currents and magnetic fields due to proximity effects, revealing dependence on ferromagnet exchange energy and induced magnetization.

## Contribution

It provides a detailed theoretical analysis of spontaneous currents and magnetic fields in S-F bilayers caused by proximity effects, highlighting the roles of exchange energy and induced magnetization.

## Key findings

- Spontaneous Meissner currents occur without external magnetic fields.
- Magnetic induction penetrates the superconductor over the London length.
- The amplitude and sign of the magnetic field depend on ferromagnet exchange energy.

## Abstract

We study theoretically spontaneous currents and magnetic field induced in a superconductor-ferromagnet (S-F) bilayer due to direct and inverse proximity effects. The induced currents {are Meissner currents that appear even in the absence of an external magnetic field due to the magnetic moment in the ferromagnet }and {to the magnetization } in the superconductor . The latter is induced by the inverse proximity effect over a distance of the order of the superconducting correlation length $\xi _{S}$. On the other hand the magnetic induction $B$, caused by Meissner currents, penetrates the S film over the London length $\lambda _{S}$. Even though $\lambda _{S}$ usually exceeds considerably the correlation length, the amplitude and sign of $B$ at distances much larger than $\xi _{S}$ depends crucially on the strength of the exchange energy in the ferromagnet and on the magnetic moment induced in the in the S layer.