# $\theta_0$ thermal Josephson junction

## TL;DR

This paper predicts a phase-sensitive thermal Josephson effect in superconductor/ferromagnet/superconductor junctions with non-coplanar magnetic textures, linking heat flow to spin chirality and triplet Cooper pairs.

## Contribution

It introduces the concept of a phase shift in thermal Josephson effect caused by magnetic texture and spin chirality, extending understanding of energy transport in magnetic superconducting systems.

## Key findings

- Thermal heat current exhibits phase-sensitive interference proportional to cos(θ - θ_0).
- The phase shift θ_0 depends on magnetic spin chirality and is robust against spin relaxation.
- Potential applications include coupling heat flow with magnetic precession.

## Abstract

We predict the thermal counterpart of the anomalous Josephson effect in superconductor/ferromagnet/superconductor junctions with non-coplanar magnetic texture. The heat current through the junction is shown to have the phase-sensitive interference component proportional to $\cos(\theta - \theta_0)$, where $\theta$ is the Josephson phase difference and $\theta_0$ is the texture-dependent phase shift. In the generic tri-layer magnetic structure with the spin-filtering tunnel barrier $\theta_0$ is determined by the spin chirality of magnetic configuration and can be considered as the direct manifestation of the energy transport with participation of spin-triplet Cooper pairs. In case of the ideal spin filter the phase shift is shown to be robust against spin relaxation caused by the spin-orbital scattering. Possible applications of the coupling between heat flow and magnetic precession are discussed.