# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 4 Results and Discussions
### Observation of Coherent Optical Phonons  
Hereafter, we describe the results of pump-probe experiments. The observation of a coherent optical phonon in LuMnO\({}_{3}\) was first reported by [PERSON] et al. [22]. They used reflection-type pump-probe spectroscopy with 20-fs optical pulses at room temperature. The pump photon energy was 1.55 eV, which is near the absorption peak of Mn\({}^{3+}\) d-d transitions. Figure 4a shows the \(\Delta R/R_{0}\) signal in a LuMnO\({}_{3}\) single crystal at room temperature, where the pump and probe pulses were irradiated to the (0001) face. The signal shows a V-shaped profile with an oscillatory structure. The oscillatory signal extracted from Figure 4a is shown in Figure 4b. The frequency was evaluated to be \(\sim\)3.6 THz. From measurements of the polarization dependences of pump and probe pulses on the oscillation and discussion based on related Raman tensors, the oscillatory signal was assigned to the coherent  
Figure 3: (**a**) Optical conductivity spectra at 6 K and 300 K in a hexagonal HoMnO\({}_{3}\) single crystal. The inset shows a fitted result of the spectrum at 6 K considering four components. (**b**) Peak positions of each component in the inset of (**a**) as a function of temperature. Colour of the symbol corresponds to that of the component. Open and closed symbols were estimated from different experimental data. Reprinted figures with permission from [41] Copyright (2007) by the American Physical Society. Figure 2: (**a**) Temperature dependence of the absorption spectrum in the YMnO\({}_{3}\) thin film. (**b**) Peak energy of the absorption band as a function of temperature. The vertical dashed line indicates the Néel temperature. optical phonon with \(A_{1}\) symmetry. The coherent phonon signal shows a cosine shape, which indicates that the coherent phonon is generated by the DECP mechanism. In addition, the sharp drop of the \(\Delta R/R_{0}\) signal around the time origin was discussed. They interpreted it as the change in absorption of the optical transition between e\({}_{\text{2g}}\) to a\({}_{\text{1g}}\) states. Figure 4c shows the \(\Delta R/R_{0}\) signals in the YMnO\({}_{3}\) thin film at different pump powers measured at 10 K. The pump photon energy was tuned to 1.72 eV that is sufficiently higher than the absorption edge. The \(\Delta R/R_{0}\) signal has a V-shaped curve and an oscillatory structure, which are similar to those in Figure 4a. The \(\Delta R/R_{0}\) signal can be decomposed into three components; a fast spike component, slowly-varying component and oscillating component. [PERSON] et al. comprehensively analysed the \(\Delta R/R_{0}\) signal in YMnO\({}_{3}\) epitaxial films using by the following equation [40]:  
\[ \begin{array}{ll}\frac{\Delta R}{R_{0}}(T,t)=&A_{1}(T)e^{-\frac{t}{\tau_{1}}}+ A_{s1}(T)\left[1-e^{-\frac{t}{\tau_{1}}}\right]e^{-\frac{t}{\tau_{2}}}\\ &+A_{s2}(T)\left[1-e^{-\frac{t}{\tau_{2}}}\right]e^{-\frac{t}{\tau_{3}}}+A_{o} (T)e^{-\frac{t}{\tau_{4}}}\cos(\omega_{0}t+\varphi_{0})\end{array}  \tag{1}\]  
where the first to forth terms on the right-hand side correspond to the non-thermal electronic response, incoherent electron-phonon interaction, magnetization dynamics and coherent acoustic phonon oscillation, respectively. The non-thermal electronic response is originated from dense excited states, which quickly decays within 1 ps. The fast spike component in Figure 4c corresponds to the first term. The second term is a slow positive component. The thermalization process of electron and phonon systems has a fast rise time (\(\tau_{\text{s1}}\)) of \(\sim\)1 ps while the decay time (\(\tau_{2}\)) is few hundreds of picosecond. The third term is a slow negative component associated with the perturbation of the antiferromagnetic ordering due to the optical transition [25]. The disordering time (\(\tau_{\text{s2}}\)) and reordering time (\(\tau_{3}\)) are few ps and few hundreds of picosecond, respectively. The slow component in Figure 4c shows a positive value in all the pump powers.