Minigap in superconductor-ferromagnet junctions with inhomogeneous magnetization

TL;DR

This paper investigates how inhomogeneous magnetization in a superconductor-ferromagnet junction affects the minigap, revealing that strong inhomogeneity can preserve the minigap up to a certain exchange field, using advanced Usadel equations.

Contribution

It introduces a detailed analysis of the minigap in disordered ferromagnets with inhomogeneous magnetization, employing the triplet Usadel equations for complex magnetic textures.

Findings

Strong inhomogeneity can preserve the minigap up to a critical exchange field.

In many cases, disordered magnetization effects can be modeled as spin-flip scattering.

Full triplet equations are necessary for low-dimensional magnetic inhomogeneities.

Abstract

We consider the minigap in a disordered ferromagnet (F) in contact with a superconductor (S) in the situation when the magnetization of the F layer is inhomogeneous in space and noncollinear. If the magnetization is strongly inhomogeneous, it effectively averages out, and the minigap survives up to the exchange field $h_c ~ (L/a) E_{Th}$, where $L$ is the thickness of the F layer, $a$ is the scale on which the magnetization varies, and $E_{Th}$ is the Thouless energy. Technically, we use the "triplet" version of the Usadel equations including both singlet and triplet components of the Green's functions. In many cases, the effect of disordered magnetization may be effectively included in the conventional Usadel equations as the spin-flip scattering term. In the case of low-dimensional magnetic inhomogeneities (we consider spiral magnetization as an example), however, the full set of "triplet" equations must be solved.