# 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.

## Key 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.