For metallic magnets we review the experimental and electron-theoretical investigations of fast magnetization dynamics (on a timescale of ns to 100 ps) and of laser-pulse-induced ultrafast dynamics (few hundred fs). It is argued that for both situations the dominant contributions to the dissipative part of the dynamics arise from the excitation of electron-hole pairs and from the subsequent relaxation of these pairs by spin-dependent scattering processes, which transfer angular momentum to the lattice. By effective field theories (generalized breathing and bubbling Fermi-surface models) it is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects. The basic assumptions of the Elliott-Yafet theory, which is often used to describe the ultrafast spin relaxation after laser-pulse irradiation, are discussed very critically. However, it is shown that for Ni this theory probably yields a value for the spin-relaxation time T(1) in good agreement with the experimental value. A relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.
Possible contributions of electron-magnon scatterings for the ultrafast demagnetization after femtosecond laser irradiation of films of Ni and Fe are investigated by the ab initio spin-density-functional electron theory. The calculations are based on Fermi's golden rule for transition rates, and the nonequilibrium after the action of the laser pulse is modeled by different chemical potentials for electrons which are in a "dominant spin-up" or in a "dominant spin-down" state. First, it is shown that the experimentally observed demagnetization cannot be described by electron-magnon spin-flip scatterings with concomitant changes of the electronic orbital moments which are immediately quenched by the crystal field, a mechanism which has been suggested by Carpene et al. Second, it is argued that the experimentally observed demagnetization possibly can be explained by a combination of individual spin-flip electron-phonon and spin-flip electron-magnon processes. A precondition for this is (among others) that the magnon emission rate is much larger than the magnon absorption rate. It is shown that this precondition is indeed fulfilled for Ni and especially for Fe.
There is a sign error in Eq. (12), it should readwhich directly follows from Eqs. (9)-(11). The sign of the inertial damping term (last term) is different from the sign of the usual damping term (second term) in agreement with Eq. (3) from the magnetostrictive damping theory of Suhl. 1 In contrast, in Ciornei et al., 2 the signs of the two damping terms are the same. This probably results from the different physics behind the inertial damping terms considered in the various papers. In Fähnle et al. and Suhl, 1 the inertial damping term is a consequence of memory effects [see Eq. (8) of Fähnle et al.], whereas, in Ciornei et al., 2 the term is related to the fact that, in analogy to a mechanical situation (where the dynamical state cannot be changed infinitely fast for a rigid body characterized by a tensor of inertia), the dynamical magnetization state also cannot be changed infinitely rapid. Perhaps measurements of the nutation loops (arising from the inertial damping) superimposed on the usual precession motion of the magnetic moments can show which physics dominates the inertial damping.We are grateful to W. Bailey, who showed us the sign error in our original Eq. (12).
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