Energy Equilibration Processes of Electrons, Magnons, and Phonons at the Femtosecond Time Scale

We relate the energy dissipation processes at the femtosecond (electron-spin relaxation time ${\tau }_{\mathrm{el}\mathrm{\text{−}}\mathrm{sp}}$) and nanosecond time scale (Gilbert relaxation ${\tau }_{\alpha }$) to the microscopic model proposed by Koopmans [Phys. Rev. Lett. 95, 267207 (2005)]. At both time scales, Elliot-Yafet scattering is proposed as the dominant contribution. We controllably manipulate the energy dissipation by transition metal doping (Pd) and rare earth doping (Dy) of a Permalloy film. While a change in ${\tau }_{\alpha }$ of more than a factor of 2 is observed, ${\tau }_{\mathrm{el}\mathrm{\text{−}}\mathrm{sp}}$ remains constant. We explain the discrepancies as due to relaxation channels not considered in the model.

Figure 1

(a) Schematic of the pump-probe setup. (b) Experimental data for the undoped permalloy (Py) film and with 2% Dy doping for different field values (applied 35° out-of-plane). (c) The extracted values for the Gilbert damping as a function of the applied field showing an increase with Pd and Dy doping.

Figure 2

Processes leading to spin flips in an electron-scattering event in a simplified schematic band picture. (a) The bands are not spin split and the spin-orbit coupling is neglected. (b) When spin-orbit interaction is included, the bands cannot be separated into purely spin-up and purely spin-down. By scattering at so-called hot spots where bands are strongly intermixed, there is a high probability that the electron will have its spin flipped after the scattering event. (c) Rare earth $4f$ bands are very localized and thus only weakly hybridized.

Figure 3

The ultrafast demagnetization for 12 nm thick permalloy (Py) films, undoped and with Pd (2%) and Dy (1%, 2%) doping. To extract the demagnetization time, ${\tau }_{\mathrm{el}\mathrm{\text{−}}\mathrm{sp}}$ is analyzed with an analytic solution of the three-temperature model. In the inset the demagnetization time is plotted as a function of the Gilbert damping $\alpha$ for $T_C$ and $0.9T_C$ , where $T_C$ is the Py Curie temperature. The horizontal line marks the value for the undoped Py film as a reference.