Effect of an inhomogeneous exchange field on the proximity effect in disordered superconductor-ferromagnet hybrid structures

TL;DR

This paper explores how an inhomogeneous exchange field in superconductor-ferromagnet structures influences the proximity effect, revealing that inhomogeneity suppresses oscillations in pair amplitudes and significantly affects the critical temperature.

Contribution

It introduces a model with in-plane spiral magnetic order to study the impact of exchange field inhomogeneity on superconducting proximity effects and critical temperature.

Findings

Inhomogeneity suppresses oscillations of pair amplitudes in the ferromagnet.

Superconducting critical temperature depends strongly on the spiral wavevector.

Triplet correlations are sensitive to the local exchange field orientation.

Abstract

We investigate the effect of an inhomogeneous exchange field on the proximity effect in superconductor-ferromagnet hybrid structures within the quasi-classical theory of superconductivity. As an example we study the proximity effect in a superconductor-ferromagnet bilayer with an in-plane spiral magnetic order in the ferromagnet. This model simulates a multiple magnetic domain structure where the domain walls of the N\'{e}el type are of equal size as the domains. Triplet correlations are induced in the bilayer by the superconducting proximity effect, which are sensitive to the local quantization axis of the exchange field in the ferromagnet. The coexistence of singlet and triplet pair correlations in the bilayer results into a sensitivity of the superconducting transition temperature on the spatial variation of the exchange field in the ferromagnetic layer. We show that the inhomogeneity tends to suppress the oscillating behavior of the pair amplitudes in the ferromagnet. As a result, the superconducting critical temperature is found to be strongly dependent on the spiral wavevector. We study the spin-dependent local density of states and the effect of an induction of a spin magnetization in the superconductor.