# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 4 Results and Discussions
### Temperature Dependence of Coherent Optical Phonons
Accordingly, the change in intensity of the coherent optical phonon around the Neel temperature is considered to be originated from the spin-lattice coupling under the isostructural transition. The comparison of the temperature dependences of the coherent optical phonons in YMnO\({}_{3}\) and LuMnO\({}_{3}\) exhibits an interesting aspect. The temperature dependence of a coherent optical phonon in LuMnO\({}_{3}\) was reported by [PERSON] et al. [24]. Figure 11a shows the temperature dependence of the \(\Delta R/R_{0}\) signal in a LuMnO\({}_{3}\) film observed by reflection-type pump-probe spectroscopy with 20-fs pulses. The \(\Delta R/R_{0}\) signal shows an oscillatory structure at several temperatures. The frequency of the oscillatory structure was estimated to be \(\sim\)3.6 THz by the FT analysis. From the frequency, the oscillation was assigned to the lowest-frequency coherent optical phonon. Figure 11b shows the image map of the FT amplitude spectrum as a function of temperature. The frequency is slightly decreased with an increase in temperature, which is similar to Figure 9a. The image map shows that the amplitude has a maximum value at \(\sim\)200 K and is completely damped in a temperature range below the Neel temperature (\(\sim\)90 K). We note that this behaviour is oppositely different to Figure 9b: the intensity strongly decreases in a temperature range above the Neel temperature. The opposite behaviour could be originated from the property of the isostructural transitions; namely, the displacement direction of Mn atoms in YMnO\({}_{3}\) is opposite in comparison with that in LuMnO\({}_{3}\)[14]. We believe that the  
Figure 10: (**a**) \(\Delta R/R_{0}\) signals in the YMnO\({}_{3}\) thin film at different pump photon energies at the pump power of 20 mW at 70 K. (**b**) Time-domain oscillatory signals obtained from (**a**). The inset indicates the integrated intensities of the FT bands of the oscillatory signals. difference of the isostructural transition properties leads to the distinct temperature dependence of the coherent optical phonon. There are several reports on the temperature dependence of coherent acoustic phonons in \(R\)MnO\({}_{3}\) compounds [21; 23; 24; 25]. The generation process of observed acoustic phonons was considered to a propagating strained layer mechanism [43]. [PERSON] et al. studied the oscillation period, phase and decay time of a coherent acoustic phonon as a function of temperature in a LuMnO\({}_{3}\) film [21]. They found that the phase steeply changes near the Neel temperature. It is originated from a sudden change in complex refractive index around the d-d transition energy. [PERSON] et al. studied the temperature dependences of coherent acoustic phonons in YMnO\({}_{3}\)[23] and LuMnO\({}_{3}\) films [24]. The amplitudes of coherent acoustic phonons in both samples have a maximum value around 190 K and disappear below the Neel temperature, which is similar to that of the coherent optical phonon in Figure 11b. On the other hand, the frequency of that in LuMnO\({}_{3}\) does not show a monotonous change as a function of temperature. Moreover, when the temperature is well below the Neel temperature in both samples, another oscillatory structure with a different frequency appears. Such intriguing behaviours would lead to further studies on the phonon dynamics in a picosecond range.