Phase-controlled proximity-effect in ferromagnetic Josephson junctions: calculation of DOS and electronic specific heat

TL;DR

This paper investigates how the electronic specific heat and density of states in a ferromagnetic Josephson junction can be significantly tuned by the superconducting phase difference, revealing potential for thermodynamic control in such systems.

Contribution

It provides a detailed numerical analysis of the phase-controlled proximity effect on thermodynamic properties in ferromagnetic Josephson junctions, including realistic boundary conditions and spin-active interfaces.

Findings

Specific heat can be strongly modified by phase difference.

Enhancement occurs for exchange fields near the superconducting gap.

Large exchange fields suppress specific heat with phase variation.

Abstract

We study the thermodynamic properties of a dirty ferromagnetic S$\mid$F$\mid$S Josephson junction with s-wave superconducting leads in the low-temperature regime. We employ a full numerical solution with a set of realistic parameters and boundary conditions, considering both a uniform and non-uniform exchange field in the form of a Bloch domain wall ferromagnetic layer. The influence of spin-active interfaces is incorporated via a microscopic approach. We mainly focus on how the electronic specific heat and density of states (DOS) of such a system is affected by the \textit{proximity effect}, which may be tuned via the superconducting phase difference. Our main result is that it is possible to \textit{strongly modify the electronic specific heat} of the system by changing the phase difference between the two superconducting leads from 0 up to nearly $\pi$ at low temperatures. An enhancement of the specific heat will occur for small values $h\simeq\Delta$ of the exchange field, while for large values of $h$ the specific heat is suppressed by increasing the phase difference between the superconducting leads. These results are all explained in terms of the proximity-altered DOS in the ferromagnetic region, and we discuss possible methods for experimental detection of the predicted effect.