Effect of magnetic anisotropy relaxation on laser-induced magnetization precession in thin galfenol films

The rate and pathways of relaxation of a magnetic medium to its equilibrium following excitation with intense and short laser pulses are the key ingredients of ultrafast optical control of spins. Here we study experimentally the evolution of the magnetization and magnetic anisotropy of thin films of a ferromagnetic metal galfenol (${\mathrm{Fe}}_{0.81}{\mathrm{Ga}}_{0.19}$) resulting from excitation with a femtosecond laser pulse. From the temporal evolution of the hysteresis loops we deduce that the magnetization $M_S$ and magnetic anisotropy parameters $K$ recover within a nanosecond, and the ratio between $K$ and $M_S$ satisfies the thermal equilibrium's power law in the whole time range spanning from a few picoseconds to 3 nanoseconds. We further use the experimentally obtained relaxation times of $M_S$ and $K$ to analyze the laser-induced precession and demonstrate how they contribute to its frequency evolution at the nanosecond timescale.

Figure 1

The geometries of (a) TR-LMOKE, (b) TR-PMOKE experiments, and (c) definitions of angles used in the calculations.

Figure 2

Field dependences (symbols) of the LMOKE rotation ${\beta }_L$ as measured in the 5- and 10-nm-thick galfenol films without pump pulse excitation [(a), (d)] and under the excitation for two pump-probe delays $\mathrm{\Delta }t$: (b), (e) before the excitation ($-50$ ps) and (c), (f) at 250 ps after the arrival of the pump pulse. The external field $H_{\mathrm{ext}}$ is parallel to $\left[1\overline{1}0\right]$. Solid lines show the fits with Eq. (1). The arrows show the corresponding values of the anisotropy field $H_A$ obtained from the fits.

Figure 3

(a)–(e) Time dependences of the magnetic parameters vs pump-probe delay time $\mathrm{\Delta }t$ obtained from the LMOKE field dependences (Fig. 2) using Eqs. (3). The lines show the fit according to Eq. (4). Shaded areas show 95% confidence levels for the fit. (f) Laser-induced demagnetization as measured using the conventional pump-probe technique in the 5-nm-thick film.

Figure 4

(a), (b) Logarithmic plot of the cubic anisotropy parameter $K_C$ vs saturation magnetization $M_S$. Power-law fit is shown by the solid line. The best fit corresponds to $a=4.7$ and 8.7 for film thickness $d=5$ and 10 nm, respectively. (c) Illustration of the applicability of the power law for the case of temporal evolution at a pump fluence 7 $\mathrm{mJ}/{\mathrm{cm}}^2$. Film thickness $d=5$ nm, ${\mu }_0{H}_{\mathrm{ext}}=100\mathrm{mT}$. Red stars at panels (a) and (b) are $K_C$ and $M_S$ obtained from the analysis of precession (Table 2) with $K_{C0}=K_C^c$ and $M_{S0}=M_S^c$.

Figure 5

(a) Experimental TR-PMOKE signal (red line). Lines I and II show the applied Hann time windows. (b) Whole-time FFT (red squares) and short-time FFT (green circles and blue diamonds) of data from (a). Lines show Gaussian fits of data.

Figure 6

(a), (b) Azimuthal dependences of whole-time FFTs of the detected magnetization precession signals. Lines show the results of approximations of the azimuthal dependences of the frequencies using Eq. (B1) for the short-time FFTs in the windows I and II (see Fig. 5). (c), (d) Azimuthal dependences of the precession amplitudes.

Figure 7

(a), (b) Ellipticity of magnetization precession after ultrafast heating for 5- and 10-nm-thick galfenol films. (c), (d) Difference between equilibrium magnetization directions for heated and cooled 5- and 10-nm-thick galfenol films.