Tunneling Hamiltonian description of the atomic-scale 0-pi transition in superconductor/ferromagnetic-insulator junctions

TL;DR

This paper develops an analytical tunneling Hamiltonian approach to explain the atomic-scale 0-pi transition in superconductor/ferromagnetic-insulator junctions, revealing the role of spin-dependent phase shifts in this phenomenon.

Contribution

It introduces an analytical perturbation theory for Josephson transport in FI-based junctions, elucidating the mechanism behind the atomic-scale 0-pi transition.

Findings

Spin-dependent pi-phase shift causes the 0-pi transition.

Analytical calculations match previous numerical results.

The transition occurs at atomic scale thicknesses of the FI barrier.

Abstract

We show a perturbation theory of the Josephson transport through ferromagnetic insulators (FIs). Recently we have found that the appearance of the atomic scale 0-pi transition in such junctions based on numerical calculations. In order to explore the mechanism of this anomalous transition, we have analytically calculated the Josephson current using the tunneling Hamiltonian theory and found that the spin dependent pi-phase shift in the FI barrier gives the atomic scale 0-pi transition.