# Heat generation due to spin transport in spin valves

## TL;DR

This paper presents a theoretical analysis of heat generation mechanisms in spin valves, revealing the roles of spin-flip and spin-conserving scattering, and proposing an effective resistance model for heat calculation.

## Contribution

It introduces a comprehensive macroscopic model that accounts for both spin-flip and spin-conserving scattering mechanisms in spin-dependent heat generation.

## Key findings

- Spin-dependent heat generation involves two mechanisms: spin-flip and spin-conserving scattering.
- In thin nonmagnetic layers, heat generation is dominated by different mechanisms depending on magnetic configuration.
- Heat generation cannot be simply explained by Joule heating of interface resistance; an effective resistance model is proposed.

## Abstract

Using a macroscopic approach, we studied theoretically the heat generation due to spin transport in a typical spin valve with nonmagnetic spacer layer of finite thickness. Our analysis shows that the spin-dependent heat generation can also be caused by another mechanism, the spin-conserving scattering in the presence of spin accumulation gradient, in addition to the well-known spin-flip scattering. The two mechanisms have equal contributions in semi-infinite layers, such as the ferromagnetic layers of the spin valve. However, in the nonmagnetic layer of a thickness much smaller than its spin-diffusion length, the spin-dependent heat generation is dominated by the spin-flip scattering in the antiparallel configuration, and by the spin-conserving scattering in the parallel configuration. We also proved that the spin-dependent heat generation cannot be interpreted as the Joule heating of the spin-coupled interface resistance in each individual layer. An effective resistance is proposed as an alternative so that the heat generation can still be described simply by applying Joule's law to an equivalent circuit.