# Ultrafast Modulation of Magnetization Dynamics in Ferromagnetic (Ga, Mn)As Thin Films
## 3 Results
According to the LLG equation, it is the total effective magnetic field that determines the precession of magnetization. In principle, the total effective magnetic field includes the exchange field, the demagnetization field, the external magnetic field, and magnetic anisotropy fields [4]. Since the precession and relaxation of hole spins are much faster than those of Mn spin, the \(p\)-\(d\) exchange field itself cannot affect the precession frequency [19; 29]. Additionally, the signal of magnetization precession has no relationship to the nonequilibrium electron-hole pairs that could also be generated in GaAs substrate [12; 30]. Moreover, the ultrafast demagnetization is characterized by the subpicosecond time scale, so it will not influence the magnetization precession on the time scale of hundreds of picoseconds either [27; 31]. Therefore, when the external magnetic field is absent, it is the optical excitation induced by magnetic anisotropy field modulation that mainly determines the value of precession frequency. That is, the optical absorption results in a transient variation of magnetic anisotropy fields (and thus of the magnetization) in the (Ga,Mn)As layer due to transient variation of both the lattice temperature and photo-excited carrier density. Thus, the thermal effect arising from laser heating and the non-thermal effect due to photo-excitation of carriers can affect the frequency of magnetization precession by respective changes in magnetic anisotropy fields caused by these two processes [13; 14; 21; 23]. According to ferromagnetic resonance (FMR) measurements, magnetic anisotropy fields are a function of temperature and carrier density [14; 32]. For the investigated (Ga,Mn)As thin films, our previous ferromagnetic resonance (FMR) measurement has revealed that: the increase of both temperature and hole density leads to a decrease of in-plane anisotropy fields \(H_{4\mid 1}\)(T, \(p\)) and \(H_{2\mid 1}\)(T, \(p\)); The out-of-plane anisotropy field \(4\pi M_{\textit{eff}}\) is also reduced by increasing temperature, but is increased by the increase of hole concentration that results from annealing [21]. For our annealed (Ga, Mn)As thin film, we estimate that a temperature increase could induce average decreases of \(4\pi M_{\textit{eff}}\), \(H_{4\mid 1}\) and \(H_{2\mid 1}\) by about 21.51 Oe/K, 11.89 Oe/K and 0.45 Oe/K, respectively. In addition to the temperature influence, about 20% increase in carrier density (\(\sim\)20% \(\times\) 10\({}^{20}\) cm\({}^{-3}\)) caused by annealing results in an average increase of \(4\pi M_{\textit{eff}}\) (\(p\)) of about 635.61 Oe, but in decreases of \(H_{4\mid 1}\)(\(p\)) and \(H_{2\mid 1}\)(\(p\)) of about 392.3 Oe and 148.85 Oe, respectively. Figure 2: (Color online) Precession frequency and precession amplitude as a function of pump intensity for the annealed sample, obtained with linearly-polarized 1.58 eV pump beam at 10 K. No external magnetic field was applied. Pump intensity was varied from 1.8 \(\upmu\)J/cm\({}^{2}\) to 28 \(\upmu\)J/cm\({}^{2}\). The extended grey dashed line and grey dash-dotted are drawn to clearly show the nonlinear dependence of both the precession frequency and the amplitude on pump intensity. Note that the increase of pump intensity from 1.8 \(\upmu\)J/cm\({}^{2}\) to 28 \(\upmu\)J/cm\({}^{2}\) at 1.58 eV is observed to cause an increase of phototexcited carrier concentration of about 30 \(\times\) 10\({}^{17}\) cm\({}^{-3}\)-120 \(\times\) 10\({}^{17}\) cm\({}^{-3}\), based on pulse absorption of photon energy. It can then be estimated that this 3-12% increase of photoexcited carrier density due to optical absorption results in an increase of 4\(\pi\)_Meff_ of about 95.34-381.4 Oe, and in decreases of \(H_{4\mid\,\mid}\) and \(H_{2\mid\,\mid}\) of about 58.84-235.38 Oe and 22.33-89.31 Oe, respectively. It is known that the lattice constant of the zinc blende (Ga,Mn)As is larger than that of GaAs, so that the (Ga,Mn)As film is compressively strained when epitaxily grown on GaAs substrate, as sketched in Figure 3[33].