Electron cooling in diffusive normal metal - superconductor tunnel junctions with a spin-valve ferromagnetic interlayer

TL;DR

This paper studies heat and charge transport in a diffusive superconductor-ferromagnet-normal metal tunnel junction, revealing how ferromagnetic exchange fields and magnetization angles influence electron refrigeration efficiency and cooling power.

Contribution

It introduces a detailed analysis of how ferromagnetic interlayers affect electron cooling in superconductor-based tunnel junctions, highlighting non-monotonic behavior near the superconducting gap.

Findings

Refrigeration efficiency increases with ferromagnetic exchange field h when h >> Δ.

Cooling power shows a non-monotonic dependence on h, with a minimum at h ≈ Δ.

Efficiency depends on ferromagnetic layer lengths, bias voltage, temperature, and magnetization angle.

Abstract

We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle {\alpha} between the magnetizations of the two F layers. As expected, for values of h much larger than the superconducting order parameter \Delta, the proximity effect is suppressed and the efficiency of refrigeration increases with respect to a NIS junction. However, for h \sim \Delta the cooling power (i.e. the heat flow out of the normal metal reservoir) has a non-monotonic behavior as a function of h showing a minimum at h \approx \Delta. We also determine the dependence of the cooling power on the lengths of the ferromagnetic layers, the bias voltage, the temperature, the transmission of the tunneling barrier and the magnetization misalignment angle {\alpha}.