# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 4 Results and Discussions
### Observation of Coherent Optical Phonons
Accordingly, the incoherent electron-phonon interaction (second term) would be dominant. The oscillation period of acoustic phonons is few tens of picosecond [21; 23; 25], which is much longer than the time window of Figure 4c. A clear oscillatory signal of acoustic phonons is observable with a longer time window. In the present \(\Delta R/R_{0}\) signal, the acoustic-phonon signal may contribute to the rise of the slow components. Figure 4: (**a**) \(\Delta R/R_{0}\) signal in a LuMnO\({}_{3}\) single crystal at room temperature. (**b**) Oscillatory component of the signal in (**a**). Reprinted figures with permission from [22] Copyright (2009) by the American Physical Society. (**c**) Pump power dependence of the \(\Delta R/R_{0}\) signal in the YMnO\({}_{3}\) thin film at the pump photon energy of 1.72 eV at 10 K.  
Figure 5a shows the \(\Delta R/R_{0}\) signals in the YMnO\({}_{3}\) thin film at different pump photon energies at 10 K. We tuned the pump photon energy to 1.63, 1.67 and 1.72 eV with the same pump power of 20 mW. We note that the optical density of the absorption band becomes lower as decreasing the pump photon energy from 1.72 to 1.63 eV. In the \(\Delta R/R_{0}\) signals at 1.67 and 1.72 eV, the contribution of the photoexcitation is obvious from the striking fast and slow components. On the other hand, both polarities of the fast and slow components at 1.67 eV are different from those of the signal at 1.72 eV. The polarity reversal of the fast component was observed in the pump photon energy dependence around the band gap [40]. Based on Equation (1), the negative slow component at 1.67 eV corresponds to the magnetization dynamics. This fact implies that the excitation of lower energy region (the low-energy weak component) in the absorption band leads to the strong perturbation of the magnetic ordering and/or the reduction of the incoherent electron-phonon interaction. Figure 5b shows the oscillatory signals with the subtraction of the fast and slow components. The amplitude of the oscillatory signal strongly depends on the pump photon energy. In order to analyse the oscillatory signals, we fitted the signals by a damped harmonic oscillation curve: \(A\text{exp}(-t/\tau_{\text{p}})\) cos(\(\omega t+\varphi\)), where \(A\), \(\omega/2\pi\), \(\varphi\) and \(\tau_{\text{p}}\) are the amplitude, frequency, phase and decay time of the oscillation, respectively. The fitted result of the oscillatory signal pumping at 1.72 eV with 20 mW is shown in Figure 6a as an example. All the oscillatory signals were well fitted by the oscillation curve. This means that the oscillatory signal is composed of a single-frequency mode. The estimated frequency is \(\sim\)5.1 THz (\(\sim\)170 cm\({}^{-1}\)), which is independent on the pump photon energy and power. This frequency almost agrees with the lowest-frequency one of optical phonon modes with \(A_{1}\) symmetry in hexagonal YMnO\({}_{3}\) crystals observed by Raman spectroscopy [17; 19; 20], where the calculated frequency of the longitudinal mode is the same frequency as the transverse mode [28]. The observed coherent optical phonons in LuMnO\({}_{3}\) are the lowest-frequency mode with A\({}_{1}\) symmetry [22; 24]. Moreover, the generation mechanism was assigned to DECP. As described in Section 2, the photoexcitation of electrons is essential to the DECP mechanism. Moreover, the amplitude of the coherent phonon generated by DECP tends to proportional to the pump power corresponding to the number of photoexcited electrons [42]. Figure 6b shows the pump photon energy dependence of \(A\), where the bar indicates FWHM of the pump pulse spectrum. The dashed curve indicates the absorption spectrum at 10 K. The amplitude clearly shows the relation to the amount of photoexcitation. Figure 6c shows the pump power dependence of \(A\). The amplitude is proportional to the pump power as indicated by the solid line. The coexistence of both properties shown in Figure 6b,c is consistent with the characteristics of the coherent phonon generated by the DECP mechanism.