# Consistent microscopic analysis of spin pumping effects

## TL;DR

This paper provides a comprehensive microscopic analysis of spin pumping effects in both metallic and insulating ferromagnets, highlighting differences in mechanisms and results, and discussing interface interactions and experimental implications.

## Contribution

It offers a unified microscopic framework for understanding spin pumping in metals and insulators, including effects of interface spin-orbit interaction and proximity effects, extending previous theories.

## Key findings

- Reproduces known results for thick metallic ferromagnets.
- Shows modifications in spin current and damping for thin metals and insulators.
- Identifies distinct mechanisms in insulating ferromagnets driven by interface exchange.

## Abstract

We present a consistent microscopic study of spin pumping effects for both metallic and insulating ferromagnets. As for metallic case, we present a simple quantum mechanical picture of the effect as due to the electron spin flip as a result of a nonadiabatic (off-diagonal) spin gauge field. The effect of interface spin-orbit interaction is briefly discussed. We also carry out field-theoretic calculation to discuss on the equal footing the spin current generation and torque effects such as enhanced Gilbert damping constant and shift of precession frequency both in metallic and insulating cases. For thick ferromagnetic metal, our study reproduces results of previous theories such as the correspondence between the dc component of the spin current and enhancement of the damping. For thin metal and insulator, the relation turns out to be modified. For the insulating case, driven locally by interface $sd$ exchange interaction due to magnetic proximity effect, physical mechanism is distinct from the metallic case. Further study of proximity effect and interface spin-orbit interaction would be crucial to interpret experimental results in particular for insulators.