Modeling the fs Demagnetization: Laser-Induced Reversal in an Applied Magnetic Field
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0941-Q02-02
Modeling the fs Demagnetization: Laser-Induced Reversal in an Applied Magnetic Field Francesco Dalla Longa, Dion Boesten, Harm H.J.E. Kicken, Wim J.M. de Jonge, and Bert Koopmans Department of Applied Physics and center for NanoMaterials (cNM), Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
ABSTRACT A novel model for ultrafast laser-induced magnetization dynamics is analyzed. Equilibration of the magnetic system is described by including electron-phonon scattering events with a finite spin flip probability. Recently, we demonstrated that such a model predicts a direct relation between the demagnetization time and the Gilbert damping. Here we present numerical simulations based on the same Hamiltonian, but including the presence of an external applied field. Thereby, reversal of the magnetization after heating above the Curie temperature (TC) can be modeled. We demonstrate that magnetization reversal can be achieved even if the lattice temperature stays below TC.
INTRODUCTION All-optical techniques exploiting femtosecond laser pulses have opened the way towards the exploration of the ultimate limits of magnetization dynamics. It has been found that magnetic order in ferromagnetic transition metals can be quenched [1,2] or induced [3,4] within a time scale τM of only a few hundred femtoseconds after laser heating. However, the microscopic interpretation of the phenomena at the sub-ps level remained unclear despite interesting theoretical activities [5]. Recently, we introduced a microscopic model [6] that shows that τM can be directly related to the so-called Gilbert damping factor α that describes damping of GHz precessional motion of the magnetization vector, thereby unifying two apparently unrelated issues in applied magnetism. The crucial ingredient in our approach is the inclusion of spin-flip processes accompanying momentum scattering with impurities or phonons. A simple model Hamiltonian is used to derive analytical expressions for both the Gilbert damping and the demagnetization. Independent of the spin-scattering mechanism, an appealingly simple equation relating the two key parameters via the Curie temperature TC is derived, τM ~ c0 ħ / k TC α,
(1)
with ħ and k the Planck and Boltzmann constant, resp., and the prefactor c0 ~ 1/4. This readily reproduces a demagnetization time τM ~ 100 fs for reasonable values of Gilbert damping in ferromagnetic nickel [6]. Within the community, two presumptions about a phonon-mediated mechanism are widespread: (i) a model involving phonons would be incapable of explaining a demagnetization
that is faster than the energy equilibration time τE between the electron and the phonon system. The reason would be that if the spin system were heated by interaction with the lattice, the spin temperature Ts would always lag the lattice temperature Tl in a 3-temperature description [1], as schematically indicated in Fig. 1(a). (ii) In order to fully quench the magnetization [7], or even to switch it after laser heating in a reverse bia
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