D. Steiauf

The Gilbert equation revisited: anisotropic and nonlocal damping of magnetization dynamics

An equation of motion for the magnetization dynamics of systems with collinear or noncollinear magnetization is derived by a combination of the breathing Fermi surface model with a variant of the ab initio density functional electron theory given by the magnetic force theorem. The equation corresponds to a Gilbert equation with the constant Gilbert damping scalar α replaced by a nonlocal damping matrix , which depends on the momentary orientation of all atomic magnetic moments in the system. For collinear situations this corresponds to an anisotropy of the damping because it depends on the orientation of the magnetization in the crystal, and for systems with atomic-scale noncollinearity such as extremely narrow domain walls or vortices the nonlocality is essential. The range of validity of the theory is discussed, and the predictions are compared with experimental observations. In particular, it is outlined how the prediction of anisotropic damping can be tested by ferromagnetic resonance experiments.

Damping of near-adiabatic magnetization dynamics by excitations of electron-hole pairs

Excitation of electron hole pairs and subsequent relaxation is the most important mechanism of intrinsic damping in near-adiabatic magnetization dynamics in metallic ferromagnets. Intraband scattering dominates in the low temperature regime and is described by the breathing Fermi surface model. A Gilbert-like equation of motion is derived within this model where the constant damping scalar is replaced by a magnetization dependent and in general nonlocal damping matrix. In collinear systems the damping term shows two types of anisotropy, and in a general noncollinear situation nonlocal damping matrices enter the equation of motion.

Demagnetization on the fs time-scale by the Elliott-Yafet mechanism

An ultrashort laser pulse can change the magnetization of ferromagnetic metals such as Ni in less than a picosecond. Thereby, angular momentum is transferred from the spin system to the lattice. One possible candidate for this transfer is the Elliott-Yafet mechanism of spin-orbit mediated spin-flip scattering of electrons at phonons. Former ab-initio calculations have shown that for Ni and Co the Elliott-Yafet spin-mixing parameter which describes the degree of mixing of the two spin states for the electronic eigenstates – averaged over all states involved in the demagnetization process – is large enough to explain the experimentally observed demagnetization rates. In the present paper we calculate in addition the spin-mixing for the individual electronic states as function of their wavevector. Furthermore, the theory is extended to the case of Gd for which experiments have revealed a slower demagnetization dynamics than for Ni.