Diffusion Constant in the Effective Bloch Equation for Ferromagnetic Resonance in Metals

A method is given for calculating the spin-diffusion constant in a ferromagnetic metal using a spin-transport equation. The result is that the diffusion constant in a ferromagnetic metal is reduced below that for a normal metal by the factor ${(1+{{\omega }_{\mathrm{ex}}}^2{T_p}^2)}^{-1\mathrm{}}$, where ${\omega }_{\mathrm{ex}}$ is the effective exchange frequency and $T_p$ is the momentum relaxation time. The physical idea for the calculation was first thought of by L. L. Hirst, who has obtained the same results using an alternative method of calculation.