Theory of a Weak-Link Superconductor-Ferromagnet Josephson Structure

TL;DR

This paper develops a theoretical model for a spin-polarized weak-link Josephson junction involving ferromagnetic materials, simplifying complex calculations and exploring physical properties like currents and density of states.

Contribution

It introduces an effective self-energy approach within Usadel theory for spin-dependent boundary conditions, enabling efficient numerical analysis of ferromagnetic Josephson junctions.

Findings

Calculated local density of states and minigaps.

Analyzed current-phase relationships and their temperature dependence.

Explored effects of magnetic domain walls on critical currents.

Abstract

We propose a model for the theoretical description of a weak-link Josephson junction, in which the weak link is spin-polarized due to proximity to a ferromagnetic metal (S-(F|S)-S). Employing Usadel transport theory appropriate for diffusive systems, we show that the weak link is described within the framework of Andreev circuit theory by an effective self-energy resulting from the implementation of spin-dependent boundary conditions. This leads to a considerable simplification of the model, and allows for an efficient numerical treatment. As an application of our model, we show numerical calculations of important physical observables such as the local density of states, proximity-induced minigaps, spin-magnetization, and the phase and temperature-dependence of Josephson currents of the S-(F|S)-S system. We discuss multi-valued current-phase relationships at low temperatures as well as their crossover to sinusoidal form at high temperatures. Additionally, we numerically treat (S-F-S) systems that exhibit a magnetic domain wall in the F region and calculate the temperature- dependence of the critical currents.