Scattering Theory of Gilbert Damping

The magnetization dynamics of a single domain ferromagnet in contact with a thermal bath is studied by scattering theory. We recover the Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert damping tensor in terms of the scattering matrix. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable spin-relaxation induced bulk and spin-pumping generated interface contributions. In linear response, our scattering theory for the Gilbert damping tensor is equivalent with the Kubo formalism.

Figure 1

Schematic picture of a ferromagnet (F) in contact with a thermal bath via metallic normal-metal leads (N).