Effect of superconductivity on non-uniform magnetization in dirty SF junctions

TL;DR

This paper investigates how superconductivity influences magnetic order in disordered ferromagnetic layers within SF junctions, revealing a phase transition to non-uniform magnetization states driven by proximity effects.

Contribution

It derives a Landau functional for the phase transition and maps the complete phase diagram, highlighting a resonance point where uniform magnetization becomes unstable.

Findings

Identification of a second order phase transition between uniform and non-uniform magnetic states.

Discovery of a resonance point where the proximity effect energy matches the exchange field.

Characterization of strongly non-uniform magnetic states beyond the transition.

Abstract

We study proximity effect in a tunnel junction between a bulk superconductor and a thin disordered ferromagnetic layer on its surface. Cooper pairs penetrating from the superconductor into the ferromagnet tend to destabilize its uniform magnetic order. The competition of this effect and the intrinsic magnetic stiffness of the ferromagnet leads to a second order phase transition between uniform and non-uniform magnetic states. Using the quasiclassical Usadel equation, we derive the Landau functional for this transition and construct the complete phase diagram of the effect. We identify a special point of "resonance" at which the characteristic energy scale of the proximity effect equals the exchange field of the ferromagnet. At this point, the uniform magnetic state is unstable even in the limit of large stiffness. We further explore the parameter regime far beyond the transition and determine the properties of the resulting strongly non-uniform magnetic state.