Supercurrent in Long SFFS Junctions with Antiparallel Domain Configuration

TL;DR

This paper investigates the supercurrent behavior in long SFFS Josephson junctions with antiparallel ferromagnetic domains, revealing how disorder and fluctuations influence the current-phase relation and supercurrent amplitude.

Contribution

It provides a detailed analysis of how disorder and domain size fluctuations affect supercurrent oscillations in long SFFS junctions, extending understanding beyond the clean limit.

Findings

Supercurrent oscillations are non-sinusoidal and decay algebraically with exchange field in the clean limit.

Exact cancellation of phase occurs when ferromagnetic domains are equal, making amplitude independent of exchange field.

Disorder causes the current-phase relation to become sinusoidal and suppresses supercurrent exponentially with exchange field.

Abstract

We calculate the current-phase relation of a long Josephson junction consisting of two ferromagnetic domains with equal, but opposite magnetization $h$, sandwiched between two superconductors. In the clean limit, the current-phase relation is obtained with the help of Eilenberger equation. In general, the supercurrent oscillations are non-sinusoidal and their amplitude decays algebraically when the exchange field is increased. If the two domains have the same size, the amplitude is independent of $h$, due to an exact cancellation of the phases acquired in each ferromagnetic domain. These results change drastically in the presence of disorder. We explicitly study two cases: Fluctuations of the domain size (in the framework of the Eilenberger equation) and impurity scattering (using the Usadel equation). In both cases, the current-phase relation becomes sinusoidal and the amplitude of the supercurrent oscillations is exponentially suppressed with $h$, even if the domains are identical on average.