Microscopic theory of spin friction and dissipative spin dynamics

TL;DR

This paper derives a microscopic theory of spin friction and nonlocal Gilbert damping in metallic systems, revealing complex dependencies on geometry, distance, and electronic correlations, with implications for spin dynamics modeling.

Contribution

It introduces a microscopic derivation of nonlocal, time-dependent Gilbert damping using linear and adiabatic response theories for a generic electronic structure model.

Findings

Nonlocal Gilbert damping can extend relaxation times.

Directional dependence significantly affects spin relaxation.

Electronic correlations enhance nonlocal spin friction.

Abstract

The real-time dynamics of local magnetic moments exchange coupled to a metallic system of conduction electrons is subject to dissipative friction even in the absence of spin-orbit coupling. Phenomenologically, this is usually described by a local Gilbert damping constant. Here, we use both linear response theory and adiabatic response theory to derive the spin friction microscopically for a generic single-band tight-binding model of the electronic structure. The resulting Gilbert damping is time-dependent and nonlocal. For a one-dimensional model, we compare the emergent relaxation dynamics as obtained from LRT and ART against each other and against the full solution of the microscopic equations of motion and demonstrate the importance of nonlocality, while the time dependence turns out to be irrelevant. In two dimensions and for a few magnetic moments in different geometries, it is found that the inclusion of nonlocal Gilbert damping can counterintuitively lead to longer relaxation times. Besides the distance dependence, the directional dependence of the nonlocal Gilbert damping turns out as very important. Our results are based on an expression relating the nonlocal Gilbert damping to the nonlocal tight-binding density of states close to the Fermi energy. This is exact in case of noninteracting electrons. Effects due to electronic correlations are studied within the random-phase approximation. For the Hubbard model at half filling and with increasing interaction strength, we find a strong enhancement of the nonlocality of spin friction.