# Ultrafast Modulation of Magnetization Dynamics in Ferromagnetic (Ga, Mn)As Thin Films
## 3 Results  
Ultrafast photon excitation of (Ga,Mn)As ferromagnetic film can strongly disturb the equilibrium between holes, localized Mn spins, and the lattice [14]. On the subpicosecond time scale, laser pulse excitation leads to a coherent phase of nonequilibrium photoexcited carriers. However, the well-defined coherent phase of carriers quickly decays due to electron-electron, hole-hole, and electron-hole scattering. In this extremely short time regime, the time evolution of the coherent phase of nonequilibrium photoexcited carriers is controlled by nonlinear optical excitation, and the carrier energy distribution function cannot be characterized by a temperature. After the carriers transfer their excess energy to the lattice (within a few picoseconds), the system acquires a quasi-equilibrium temperature. The enhancement of both the local lattice temperature and the hole concentration by photoexcitation can then modulate the magnitude of magnetic anisotropy fields, which reorients the direction of the easy axes, thus triggering the magnetization dynamics on a time scale of \(\sim\)100 ps. Magnetization precession of the coupled Mn spin system triggered by such magnetic anisotropy modulation is distinct from photomagnetic phenomena such as optical-spin-transfer-torque (OSTT). Specifically, it requires no injection of angular momentum, and can thus be triggered by a linearly-polarized laser pulse. Figure 1 shows a typical magnetization precession response to such a pulse at 10 K for the annealed (Ga,Mn)As sample excited by a linearly-polarized pump beam at 1.58 eV. As shown in Figure 1a, the temporal evolution of the photoexcited magnetization observed by time-resolved magneto-optical measurement in ferromagnetic (Ga,Mn)As can be fitted by an exponentially damped sine function superimposed on a pulse-like function [7; 21],  
\[\theta_{k}=a+be^{-t/t_{0}}+Ae^{-t/\tau_{\rm{D}}}sin(\omega t+\phi), \tag{1}\]  
where \(A\), \(\tau_{D}\), \(\omega\), and \(\phi\) represent, respectively, the oscillation amplitude, the relaxation time of magnetization, the frequency of oscillation, and the phase of the magnetization oscillation; \(a\) is the offset of background; and \(b\) and \(t_{0}\) are the amplitude and decay time parameters of the pulse-like signal, charactering the slow recovery process. Earlier studies reported that the pulse-like signal which persists above the Curie temperature is related to the recovery process of nonequilibrium electron-hole pairs in the GaAs substrate [10; 28], and only the oscillatory part is directly related to the ferromagnetic order of (Ga,Mn)As [12]. The numerical fitting result by the Landau-Lifshitz-Gilbert (LLG) equation shown in Figure 1b is focused on the precession part of the observed Kerr rotation, which reflects the uniform precession of magnetization in the annealed (Ga,Mn)As film [21]. The collective spin excitation and modulation of the dynamics of precession discussed below will mainly focus on the characteristics of the oscillatory signal modulated by laser excitation. Figure 1: (Color online) Temporal profile of Kerr rotation excited by linearly-polarized pump beam at 1.58 eV with an excitation intensity of 10.9 \(\upmu\)J/cm\({}^{2}\) for the annealed (Ga,Mn)As sample. (**a**) The solid line (red color) shows the best fit by an exponentially-damped sine function. (**b**) The solid line (blue color) shows numerical fitting result to LLG equation. The initial pulse-like-signal persists to above the Curie temperature, and is associated with non-equilibrium electron–hole pairs in the GaAs substrate. The fitting is focused on the oscillatory part of the Kerr rotation, which represents a uniform precession of magnetization in the (Ga,Mn)As film [21]. The observed dependences of the precession frequency and precession amplitude on pump intensity are shown in Figure 2. One can clearly see the nonlinear behavior of precession frequency and precession amplitude as the pump intensity increasing from 1.8 \(\upmu\)J/cm\({}^{2}\) to 28 \(\upmu\)J/cm\({}^{2}\).