We present a microscopic theory for magnetization relaxation in metallic ferromagnets of nanoscopic dimensions that is based on the dynamic spin response matrix in the presence of spin-orbit coupling. Our approach allows the calculation of the spin e
xcitation damping rate even for perfectly crystalline systems, where existing microscopic approaches fail. We demonstrate that the relaxation properties are not completely determined by the transverse susceptibility alone, and that the damping rate has a non-negligible frequency dependence in experimentally relevant situations. Our results indicate that the standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to describe spin dynamics of metallic nanostructure in the presence of strong spin-orbit coupling.
We study the low energy spin excitations of zigzag graphene nanoribbons of varying width. We find their energy dispersion at small wave vector to be dominated by antiferromagnetic correlations between the ribbons edges, in accrodance with previous ca
lculations. We point out that spin wave lifetimes are very long due to the semi-conducting nature of the electrically neutral nanoribbons. However, application of very modest gate voltages cause a discontinuous transition to a regime of finite spin wave lifetime. By further increasing doping the ferromagnetic alignments along the edge become unstable against transverse spin fluctuations. This makes the experimental detection of ferromagnetism is this class of systems very delicate, and poses a difficult challenge to the possible uses of these nanoribbons as basis for spintronic devices.
