Electron- and phonon-mediated ultrafast magnetization dynamics of Gd(0001)

Here we report on the ultrafast magnetization dynamics of Gd(0001), which we investigated as a function of equilibrium temperature by employing the femtosecond time-resolved magneto-optical Kerr effect (MOKE) and modeling by the Landau-Lifshitz-Bloch equation in combination with the two-temperature model. Based on the observed temperature-dependent transient MOKE signals, we separate the magnetization dynamics into two regimes at delays of (i) a few picoseconds and (ii) several 100 femtoseconds. In the picosecond regime, the demagnetization time determined from the experiment increases with temperature from 0.8 ps at 50 K to 1.5 ps at 280 K. A successful description of this observation was achieved by considering the dynamics of the $4f$ spin system coupled to $5d$ conduction electrons within two coupling mechanisms: (a) through electronic scattering and (b) spin-flip scattering mediated by phonons. We conclude that at temperatures below the Debye temperature, a hot electron-mediated process describes the experimentally found demagnetization times of $\approx$$0.8$ ps well. At higher temperatures phonon-mediated processes have to be included to explain the 2 times longer demagnetization time. In the second regime at time delays of few 100 fs we find an increase in the MOKE rotation and ellipticity at 50 K at delays before demagnetization sets in. Above 50 K the transient changes in rotation and ellipticity are of opposite sign. We explain this behavior by competing magnetic and nonmagnetic contributions in the transient MOKE signals at these delays directly after optical excitation when excited phonons do not yet facilitate angular momentum transfer to the lattice.

Figure 1

Time-dependent changes of the MOKE signals after femtosecond laser excitation normalized to the respective equilibrium values for 20 nm Gd(0001)/W(110) measured at different equilibrium temperatures $T_0$. Panel (a) depicts the transient MOKE rotation and (b) the MOKE ellipticity. As emphasized by the inset, rotation and ellipticity results show a different behavior within the initial few hundred femtoseconds.

Figure 2

The variation of $k_r/k_{0r}$ and $k_e/k_{0e}$ for different temperatures $T_0$ as a function of time. The amplitude was extracted from experimental data, and the transient evolution was calculated by the electron energy density (see text). Both $k_r/k_{0r}$ and $k_e/k_{0e}$ increase for $t<300$ fs at 50 K, while at higher temperatures their respective changes are of opposite sign.

Figure 3

The main panel depicts $\Delta \tilde{M}/{\tilde{M}}_0$ extracted from $\Delta \theta /{\theta }_0$ for selected equilibrium temperatures. The curves have been normalized to $-1$ at $t=4$ ps. The inset compares the transient changes in the magnetization $\Delta \tilde{M}/{\tilde{M}}_0$ at $T_0=$ 200 K which were determined from the MOKE rotation and the ellipticity measurements. Lines represent single exponential fits.

Figure 4

The demagnetization time ${\tau }_m$ as a function of $T_0$. Symbols represent the experimental data points, while lines represent the modeling results considering only electron-mediated spin flips (dashed) and combined electron- and phonon-mediated spin flips (solid line) with ${\lambda }_{s-ph}^0=0.0002$. The gray line represents the results obtained within the M3TM model assuming an EY scattering mechanism. The inset shows $\Delta M/M_0$ at the indicated time delays.

Figure 5

Schematic diagram of the model. The multispin LLB model (center) is coupled to the 2T model via two coupling mechanisms: phonon contribution via Raman processes (left) and electron contribution via dynamical spin polarization of carriers which produces a change of chemical potential $\Delta \mu$ (Ref. 37) (right). The 2T model and the LLB model are time and layer resolved and the electron diffusion is considered. The change in the phonon population with temperature is taken into account within the Debye model. The parameters of the 2T model were taken from Refs. 27 and 29.

Figure 6

The relative magnetization decay $\Delta \tilde{M}/{\tilde{M}}_0$ for various equilibrium temperatures obtained through the integration of the Landau-Lifshitz-Bloch model (symbols). The line indicates fitting to a single exponential function.