BdG equations within lattice Hubbard model for the description of $\pi$-states in nanoscale S-FF-S junctions

TL;DR

This paper models the behavior of persistent currents in nanoscale superconductor-ferromagnet-superconductor junctions using Bogoliubov-de Gennes equations within a lattice Hubbard framework, revealing magnetic alignment-dependent 0 to π transitions.

Contribution

It introduces a self-consistent lattice Hubbard model approach to analyze persistent currents and 0-π transitions in S-F-F-S junctions.

Findings

Sign change in local current for parallel magnetization alignment.

No sign change in antiparallel alignment.

Demonstrates magnetic configuration dependence of 0-π transition.

Abstract

We calculate the persistent currents in $S-F_{\uparrow}F_{\uparrow[\downarrow]}-S$ structures (S denotes the superconductor in a closed ring geometry, F the ferromagnet in a two dimensional geometry, and the arrows the alignment of exchange field) as a function of the applied magnetic flux, self consistently by solving the Bogoliubov-de Gennes equations within the two dimensional Hubbard model. The local current shows a sign change i.e. a 0 to $\pi$ transition in the parallel alignment of the magnetizations and it does not change sign in antiparallel alignment.