Relativistic dynamical spin excitations of magnetic adatoms

TL;DR

This paper develops a first-principles theory for dynamical spin excitations in magnetic adatoms considering spin-orbit coupling, revealing the significant impact of relativistic effects on resonance energy and lifetime.

Contribution

It introduces a new sum rule due to broken spin rotational invariance and analyzes the interplay of magnetic anisotropy, external fields, and electron-hole excitations in spin dynamics.

Findings

Resonance energy and lifetime show complex behavior influenced by relativistic effects.

The Landau-Lifshitz-Gilbert equation remains valid at the atomic scale with modified parameters.

Relativistic effects significantly alter spin excitation properties in adatoms.

Abstract

We present a first-principles theory of dynamical spin excitations in the presence of spin-orbit coupling. The broken global spin rotational invariance leads to a new sum rule. We explore the competition between the magnetic anisotropy energy and the external magnetic field, as well as the role of electron-hole excitations, through calculations for 3$d$-metal adatoms on the Cu(111) surface. The spin excitation resonance energy and lifetime display non-trivial behavior, establishing the strong impact of relativistic effects. We legitimate the use of the Landau-Lifshitz-Gilbert equation down to the atomic limit, but with parameters that differ from a stationary theory.