Theory of damping in magnetization dynamics, dispelling a myth and pointing a way forward

There is a widely-held belief amongst theoreticians that the Gilbert damping parameter {\alpha} in magnetization dynamics is infinite for a pure metal at T=0. The basic error leading to this belief is pointed out explicitly and the various methods of calculation used are viewed in a unified way based on the Lorentzian lineshape of ferromagnetic resonance spectra. A general torque formula for {\alpha} is proposed as a good starting-point for treating inhomogeneous materials such as alloys, compounds and layered structures. Local spin density functional theory provides a simple physical picture, in terms of a non-uniform precessional cone angle in ferromagnetic resonance, of how such inhomogeneity contributes to the damping. In a complementary many-body theory this contribution is given by a vertex correction to the torque-torque response function.