Oscillations of Induced Magnetization in Superconductor-Ferromagnet Heterostructures

TL;DR

This paper demonstrates that the induced magnetization in superconductor-ferromagnet heterostructures oscillates with the product of exchange field and ferromagnet thickness, leading to possible screening or anti-screening effects depending on system purity and interface transparency.

Contribution

It reveals the oscillatory behavior of induced magnetization in SF heterostructures and its dependence on disorder, interface transparency, and ballistic versus diffusive regimes, which was not previously understood.

Findings

Magnetization oscillates as a function of $hd$ in clean systems.

Oscillations persist even with low interface transparency and disorder.

Anti-screening can occur, increasing total magnetic moment in the superconducting state.

Abstract

We study a change in the spin magnetization of a superconductor-ferromagnet (SF) heterostructure, when temperature is lowered below the superconducting transition temperature. It is assumed that the SF interface is smooth on the atomic scale and the mean free path is not too short. Solving the Eilenberger equation we show that the spin magnetic moment induced in the superconductor is an oscillating sign-changing function of the product $hd$ of the exchange field $h$ and the thickness $d$ of the ferromagnet. Therefore the total spin magnetic moment of the system in the superconducting state can be not only smaller (screening) but also greater (anti-screening) than that in the normal state, in contrast with the case of highly disordered (diffusive) systems, where only screening is possible. This surprising effect is due to peculiar periodic properties of localized Andreev states in the system. It is most pronounced in systems with ideal ballistic transport (no bulk disorder in the samples, smooth ideally transparent interface), however these ideal conditions are not crucial for the very existence of the effect. We show that oscillations exist (although suppressed) even for arbitrary low interface transparency and in the presence of bulk disorder, provided that $h \tau \gg 1$ ($\tau$ -- mean free path). At low interface transparency we solve the problem for arbitrary strength of disorder and obtain oscillating magnetization in ballistic regime ($h \tau \gg 1$) and nonoscillating magnetization in diffusive one ($h \tau \ll 1$) as limiting cases of one formula.