# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 4 Results and Discussions
### Temperature Dependence of Coherent Optical Phonons  
The temperature dependence of phonon modes in YMnO\({}_{3}\) has intensively investigated by Raman spectroscopy [17; 19; 20] and infrared spectroscopy [18]. The temperature-dependent shift of the phonon frequency is the main concern; several phonon modes exhibit anomalies around the Neel temperature. This behaviour could be affected by the spin-lattice coupling that is relevant to the electromagnetic effect. Thus, the investigation of the coherent optical phonon as a function of temperature is extremely important. Here, we describe the characteristics of the temperature dependence of the coherent optical phonon. Figure 7 shows the \(\Delta R/R_{0}\) signals in the temperature ranges from 10 to 90 K (a) and from 100 to 300 K (b) under the fixed pump photon energy of 1.72 eV. The oscillatory signals of the coherent optical phonon are discernible at several temperatures. Moreover, the fast and slow components show a strong temperature dependence, which is discussed in Section 4.4. Figure 8a shows the time-domain oscillatory signals numerically extracted from the \(\Delta R/R_{0}\) signals in Figure 7. The amplitude of the coherent phonon strongly depends on the temperature. We performed the Fourier transform (FT) of the time-domain oscillatory signals to precisely evaluate the temperature dependence of the coherent phonon. The calculated FT power spectra are shown in Figure 8b. The peak frequency and intensity of the FT band depend on the temperature. Figure 6: (**a**) Fitted result of the oscillatory signal of Figure 5b at 1.72 eV with 20 mW using a damped harmonic oscillation curve. (**b**) Pump photon energy dependence of the oscillation amplitude, where the bar indicates FWHM of the spectrum of pump pulses. The dashed curve indicates the absorption spectrum at 10 K. (**c**) Pump power dependence of the oscillation amplitude. The solid line is the linear fitted result. First, we discuss the temperature dependence of the peak frequency. Figure 9a shows the peak frequency of the FT spectrum as a function of temperature, where the length of the bar corresponds to FWHM of the FT band. The solid curve is a guide to the eye. The peak frequency has a small temperature dependence. The frequency shift is \(\sim\)0.3 THz (\(\sim\)10 cm\({}^{-1}\)) as increasing from 10 to 300 K. The total amount of the shift almost agrees with that of the peak shift of the corresponding Raman spectrum [17]. In contrast to previous Raman studies, the anomaly of the frequency shift around the Neel temperature is unidentified in Figure 9a. The possible reason is that the accuracy of the estimated frequency is insufficient to observe the anomalous behaviour around the Neel temperature because of the anomalous behavior. Figure 8: (**a**) Temperature dependence of the time-domain oscillatory signal extracted from the data in Figure 7. (**b**) FT power spectra of the time-domain oscillatory signals in (**a**). Figure 7: (**a**) Temperature dependence of the \(\Delta R/R_{0}\) signal in the YMnO\({}_{3}\) thin film at the pump photon energy of 1.72 eV with 20 mW in the temperature ranges from 10 to 90 K (**a**) and from 100 to 300 K (**b**). the intensity drop of the oscillation as described in the next paragraph. The slight broadening of the FT band is seen with increasing temperature. It is attributed to a build-up of energy relaxation processes of the optical phonon. The FT intensity of the coherent optical phonon exhibits a complex temperature dependence. The integrated intensity of the FT band is plotted in Figure 9b as a function of temperature together with the Neel temperature (70 K) as the vertical dotted line, where the solid curve is a guide to the eye. It is indicated that the FT intensity decreases as the temperature increases to the Neel temperature from 10 K. The intensity has a minimum value at \(\sim\)100 K and then it slightly recovers in a higher temperature range.