## 3 Experiments
### Experimental Results  
#### 3.3.1 General Properties of Photoinduced Spin Dynamics  
First, typical results of the photoinduced spin dynamics are presented and its microscopic mechanism will be discussed. Figure 5a shows a time evolution of the photoinduced change of the MSHG intensity normalized by the value before photoexcitation, \(\frac{\Delta\mathrm{M}\mathrm{S}\mathrm{H}\mathrm{S}\mathrm{H}}{\mathrm{S} \mathrm{H}\mathrm{S}\mathrm{H}}=\frac{\mathrm{I}^{\mathrm{M}\mathrm{S} \mathrm{H}}\mathrm{G}\mathrm{n}\mathrm{n}\mathrm{I}-\mathrm{I}^{\mathrm{M} \mathrm{S}\mathrm{H}}\mathrm{G}\mathrm{n}\mathrm{I}}{\mathrm{S}\mathrm{H} \mathrm{G}\mathrm{n}\mathrm{I}}\). The data were taken at 77 K on EuO doped with 2.65% Gd (\(T_{\mathrm{C}}\)\(\sim\)119 K). The excitation density of the linearly polarized pump pulse is \(\sim\)380 \(\upmu\)J/cm\({}^{2}\). Following the photoexcitation at \(\Delta t=0\), a continuous increase of the MSHG intensity up to \(+\)30% at 3 ps is observed. This is followed by a continuous decrease passing zero at 40 ps and \(-\)25% at 3 ns. On the basis of the results, the photoinduced increase and decrease of the MSHG intensity can be explained as follows. First, as is clear from the temperature dependence of \(\sqrt{\mathrm{I}^{\mathrm{M}\mathrm{S}\mathrm{H}}}\) in Figure 4b, which reflects that of magnetization, before photoexcitation the direction of localized 4\(f\) spins is not fully aligned at 77 K due to a relatively high temperature (left panel in Figure 5b). When this magnetic state is irradiated with pump pulse, the excited 5\(d\) electrons spread to the adjacent Eu sites, and the thermally fluctuating localized 4\(f\) spins are partly aligned ferromagnetically through the intra-atomic 4\(f\)-5\(d\) exchange interaction, which leads to the increase of macroscopic magnetization (\(\Delta M>0\)) (middle panel in Figure 5b). Considering that the energy of the intra-atomic 4_f_-5\(d\) exchange interaction is \(\sim\)0.1 eV [32], which corresponds to a time of \(\sim\)40 fs, an instantaneous increase of the MSHG intensity after the photoexcitation might be expected in contrast to the strikingly different time of \(\sim\)3 ps. We have, however, to take into account that the magnetic exchange coupling is mediated via the RKKY interaction. The time \(\tau_{0}\) required to coherently establish its enhancement in the photoexcited region can be estimated from the time it takes the electronic correlation to spread through the crystal. The relevant distance is the RKKY wavelength, and the propagation velocity is the group velocity of the magnetic exciton. The latter is reduced with respect to the conduction electron group velocity by the ratio \(m_{\mathrm{e}}^{*}/m_{\mathrm{h}}^{*}\) of the effective masses of the 5_d_/6\(s\) conduction electrons (\(m_{\mathrm{e}}^{*}\)) and of the heavy holes in the 4\(f\) band (\(m_{\mathrm{h}}^{*}\)), which together form the magnetic exciton. The ratio \(m_{\mathrm{h}}^{*}/m_{\mathrm{e}}^{*}\) was taken to be equal to the inverse ratio of the respective bandwidths and was extracted from literature data [52] to be \(\sim\)\(4\times 10^{3}\). In addition, the low excitation energy within the conduction band of \(\Delta E\sim 0.5\) eV and the small wavenumber associated to this energy allows us to assume the conduction band as parabolic. Here, \(\Delta E\) is the difference between the pump photon energy \(\hbar\omega_{\mathrm{pump}}\) and the 4_f_-5_d_/6\(s\) gap energy \(E_{\mathrm{gap}}\). With \(\tau_{0}=\frac{\hbar}{4\Delta E}\cdot\frac{m_{\mathrm{e}}^{*}}{m_{\mathrm{e} }^{*}}\) we thus obtain a build-up time \(\tau_{0}\) of \(\sim\)8 ps, which is in reasonable agreement with the measured value of \(\sim\)3 ps. The ensuing decrease of MSHG intensity on the ns timescale is associated with the demagnetization (\(\Delta M<0\)) by the heating of the spin system through the transfer of the optical excitation energy from the electron system to the lattice and the spins (right panel in Figure 5b).