The Current-Phase Relation of Ferromagnetic Josephson Junction Between Triplet Superconductors

TL;DR

This paper investigates the current-phase relationship in a triplet superconductor-ferromagnet junction, revealing how magnetic orientations influence the Josephson effect and identifying conditions for anomalous behavior.

Contribution

It introduces a generalized formalism to analyze the Josephson effect in triplet superconductor-ferromagnet junctions, considering interference effects and magnetic orientations.

Findings

Current-phase relation depends on d-vector and magnetization orientations.

Conditions for the anomalous Josephson effect are derived.

Interference effects significantly influence the Josephson current.

Abstract

We study the Josephson effect of a $\rm{T_1 F T_2}$ junction, consisting of spin-triplet superconductors (T), a weak ferromagnetic metal (F), and ferromagnetic insulating interfaces. Two types of the triplet order parameters are considered; $(k_x +ik_y)\hat{z}$ and $k_x \hat{x}+k_y\hat{y}$. We compute the current density in the ballistic limit by using the generalized quasiclassical formalism developed to take into account the interference effect of the multilayered ferromagnetic junction. We discuss in detail how the current-phase relation is affected by orientations of the d-vectors of superconductor and the magnetizations of the ferromagnetic tunneling barrier. General condition for the anomalous Josephson effect is also derived.