Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences

Relaxation effects are of primary importance in the description of magnetic excitations, leading to a myriad of methods addressing the phenomenological damping parameter. In this work [1], we compare several well-established forms of calculating the intrinsic Gilbert damping within a unified theoretical framework, mapping out their connections and approximations required to derive each formula. Most methods lead to similar results for the bulk ferromagnets Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence of the spin pumping mechanism. Starting from simulated ferromagnetic resonance spectra based on the underlying electronic structure, we unambiguously demonstrate that the damping parameter obtained within the constant broadening approximation diverges for three-dimensional bulk magnets in the clean limit, while it remains finite for monolayers. Our work puts into perspective the several methods to compute the Gilbert damping, building a solid foundation for future investigations of magnetic relaxation effects in any kind of material.

[1] F. S. M. Guimarães, arXiv:1807.11808 (2018)