Theoretical determination of Gilbert damping in reduced dimensions
Phys. Rev. B 111, 214443 – Published 27 June, 2025
DOI: https://doi.org/10.1103/yjns-hy25
Abstract
An ab initio scheme based on the Kubo-Greenwood linear response theory of exchange torque correlation is presented to calculate intrinsic Gilbert damping parameters in magnets of reduced dimensions. The method implemented into the real-space Korringa-Kohn-Rostoker (RS-KKR) Greens' function framework enables to obtain diagonal elements of the atomic-site-dependent on-site and nonlocal Gilbert damping tensor. Going from the three-dimensional bulk and surfaces of iron and cobalt ferromagnets addressed in our previous work [B. Nagyfalusi et al., Phys. Rev. B 109, 094417 (2024)], in the present paper monolayers of Fe and Co on (001)- and (111)-oriented Cu, Ag, and Au substrates are studied, and particularly the substrate-dependent trends are compared. Furthermore, the Gilbert damping parameters are calculated for Fe and Co adatoms and dimers on (001)-oriented substrates. It is investigated how the damping parameter of single adatoms depends on their vertical position. This dependence is quantified in relation to the adatoms' density of states at the Fermi energy showing a nonmonotonic behavior. By rotating the spin moment of the adatoms and collinear magnetic dimers, an anisotropic behavior of the damping is revealed. Finally, a significant, three to ten times increase of the on-site Gilbert damping is found in antiferromagnetic dimers in comparison to the ferromagnetic ones, while the intersite damping is even more enhanced.
