The Gilbert parameter alpha describing the damping of magnetization dynamics is commonly taken to be an isotropic scalar. We argue that it is a tensor, that is anisotropic, leading to a dependence of the damping on both the instantaneous direction of the magnetization M(t) (orientational anisotropy) and on the direction of rotation of the magnetization (rotational anisotropy). For small-angle precession of M around a prescribed axis in the crystal, the rotational anisotropy is averaged out and the damping is determined by an e ffective damping scalar alpha sub eff which depends on the orientation of the prescribed axis. The quantity alpha sub eff of Fe, Ni and Co is calculated for various orientations as a function of the electronic scattering rate. The calculations are performed by the ab-initio density functional electron theory within the framework of the torque-correlation model. The intraband contribution of this model (breathing Fermi surface contribution) is anisotropic for all scattering rates. In contrast, the interband contribution (bubbling Fermi surface contribution) is anisotropic only at small scattering rate ( tau sup -1), but becomes increasingly isotropic as tau sup -1 increases. Because the latter contribution dominates at high tau sup -1, each material should exhibit isotropic damping at suffciently high tau sup -1 (i.e., suffciently high temperatures).
Citation: Physical Review B
Pub Type: Journals
damping, magnetization dynamics, electronic structure, electron scattering rate, Gilbert damping, transition metals