Layered ferromagnet-superconductor structures: the $\pi$ state and proximity effects

TL;DR

This paper studies multilayered superconductor-ferromagnet structures, revealing a periodic transition between 0 and π states as the ferromagnetic layer thickness varies, affecting local electronic and magnetic properties.

Contribution

It provides a numerical analysis of the self-consistent Bogoliubov-de Gennes equations for SFS and SFSFS structures, identifying the periodic 0-π state transitions and their effects.

Findings

Ground state energy oscillates with ferromagnetic layer thickness.

Density of states exhibits periodic behavior.

Local magnetic moment reflects the 0-π transition.

Abstract

We investigate clean mutilayered structures of the SFS and SFSFS type, (where the S layer is intrinsically superconducting and the F layer is ferromagnetic) through numerical solution of the self-consistent Bogoliubov-de Gennes equations for these systems. We obtain results for the pair amplitude, the local density of states, and the local magnetic moment. We find that as a function of the thickness $d_F$ of the magnetic layers separating adjacent superconductors, the ground state energy varies periodically between two stable states. The first state is an ordinary "0-state", in which the order parameter has a phase difference of zero between consecutive S layers, and the second is a "$\pi$-state", where the sign alternates, corresponding to a phase difference of $\pi$ between adjacent S layers. This behavior can be understood from simple arguments. The density of states and the local magnetic moment reflect also this periodicity.