Nonlocal Gilbert damping and magnetic interactions in noncollinear magnetic nanostructures from first principles*

Damping is essential to the magnetization dynamics underpinning the performance of any type of magnetic device. Utilizing a first-principles description of the spin dynamics of noncollinear magnetic nanostructures based on linear-response time-dependent density functional theory [1], we demonstrate that the Gilbert damping and gyromagnetic tensors can be expressed in terms of couplings, chiral or not, of the magnetic moments. We illustrate the theory considering magnetic adatoms, dimers and trimers, both within a generalized Alexander-Anderson model and using real magnetic atoms on Au(111) together with magnetic constraints [2]. These properties are related to the filling of the magnetic orbitals of the clusters, to their hybridization with the surface electrons, and to the role played by spin-orbit coupling. We put forward a generalized Landau-Lifshitz-Gilbert equation accounting for the dependence of damping on the underlying magnetic structure and address the dynamics of different magnetic ground states.
[1] M. dos Santos Dias et al., PRB 91, 075405 (2015)
[2] S. Brinker et al., New J. Phys. 21, 083015 (2019)