Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula

TL;DR

This paper investigates Gilbert damping in conducting ferromagnets using simplified models to test the accuracy of the torque-correlation formula, aiming to improve predictions in complex materials.

Contribution

It provides a detailed analysis of Gilbert damping using toy models, assessing the reliability of approximate formulas for practical calculations.

Findings

Vertex corrections can be summed to all orders in simple models.

Approximate expressions show good agreement with exact calculations.

Results inform the use of torque-correlation formulas in complex ferromagnetic systems.

Abstract

We report on a study of Gilbert damping due to particle-hole pair excitations in conducting ferromagnets. We focus on a toy two-band model and on a four-band spherical model which provides an approximate description of ferromagnetic (Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex corrections to the long-wavelength spin-spin response function can be summed to all orders. An important objective of this study is to assess the reliability of practical approximate expressions which can be combined with electronic structure calculations to estimate Gilbert damping in more complex systems.