The Gilbert equation revisited: anisotropic and nonlocal damping of magnetization dynamics

摘要: An equation of motion for the magnetization dynamics systems with collinear or noncollinear is derived by a combination breathing Fermi surface model variant ab initio density functional electron theory given magnetic force theorem. The corresponds to Gilbert constant damping scalar α replaced nonlocal matrix , which depends on momentary orientation all atomic moments in system. For situations this an anisotropy because it crystal, and atomic-scale noncollinearity such as extremely narrow domain walls vortices nonlocality essential. range validity discussed, predictions are compared experimental observations. In particular, outlined how prediction anisotropic can be tested ferromagnetic resonance experiments.