Magnetization damping in a local-density approximation

TL;DR

This paper investigates the microscopic origins of magnetization damping in itinerant ferromagnets within a local-density approximation, linking susceptibility, impurity effects, and spin dephasing to the Gilbert damping parameter.

Contribution

It provides a self-consistent microscopic calculation of the Gilbert damping in itinerant ferromagnets, including impurity effects and spin-orbit interactions, and clarifies the role of exchange splitting.

Findings

Gilbert damping inversely proportional to exchange splitting.

Neglecting gradient corrections yields incorrect results at high exchange potentials.

The susceptibility calculation justifies phenomenological models of spin dephasing.

Abstract

The linear response of itinerant transition metal ferromagnets to transverse magnetic fields is studied in a self-consistent adiabatic local-density approximation. The susceptibility is calculated from a microscopic Hamiltonian, including spin-conserving impurities, impurity induced spin-orbit interaction and magnetic impurities using the Keldysh formalism. The Gilbert damping constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by an effective transverse spin dephasing rate, and is found to be inversely proportional to the exchange splitting. Our result justify the phenomenological treatment of transverse spin dephasing in the study of current-induced magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak \textit{et al.}. We show that neglect of gradient corrections in the quasiclassical transport equations leads to incorrect results when the exchange potential becomes of the order of the Fermi energy.