Spin dynamics with inertia in metallic ferromagnets

The nonadiabatic contribution of environmental degrees of freedom yields an effective inertia of spin in the effective spin dynamics. In this paper, we study several aspects of the inertia of spin in metallic ferromagnets: (i) a concrete expression of the spin inertia mₛ: mₛ=Sc/(2gsd), where Sc is the spin polarization of conduction electrons and gsd is the $sd$ coupling constant; (ii) a dynamical behavior of spin with inertia, discussed from the viewpoints of a spinning top and of a particle on a sphere; (iii) the behavior of spin waves and domain walls in the presence of inertia and the behavior of spin with inertia under a time-dependent magnetic field.