# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 4 Results and Discussions  
### Optical Transition Property  
First, we describe optical transition properties in \(R\)MnO\({}_{3}\). Figure 2a shows the absorption spectra at different sample temperatures in a hexagonal YMnO\({}_{3}\) thin film with the thickness of \(\sim\)300 nm epitaxially grown on a (111) MgO substrate by pulsed laser deposition [35; 36]. A strong absorption band is observed at each temperature. The profile is consistent with previous reports of an absorption spectrum [37] and imaginary part of a dielectric function [38]. In hexagonal RMnO\({}_{3}\), the crystal field of \(D_{\text{3h}}\) symmetry splits Mn 3d orbitals into two e\({}_{\text{1g}}\) (\(xz,yz\)) orbitals, two e\({}_{\text{2g}}\) (\(xy,x^{2}-y^{2}\)) orbitals and a\({}_{\text{1g}}\) (\(3x^{2}-r^{2}\)) orbital. The e\({}_{\text{1g}}\) and e\({}_{\text{2g}}\) are occupied states while a\({}_{\text{1g}}\) is unoccupied state. Accordingly, the optical transitions occur from the e\({}_{\text{1g}}\) and e\({}_{\text{2g}}\) states to a\({}_{\text{1g}}\) state [39]. It is widely considered that the absorption peak at \(\sim\)1.7 (2.3) eV is originated from the optical transition from the e\({}_{\text{2g}}\) to a\({}_{\text{1g}}\) (e\({}_{\text{1g}}\) to a\({}_{\text{1g}}\)) states [12; 37; 39]. The absorption band shows a lower energy shift with an increase in temperature. The peak energy of the absorption band is plotted in Figure 2b as a function of temperature, where the vertical dashed line indicates the Neel temperature: \(\sim\)70 K [20]. The amount of the lower-energy shift is \(\sim\)0.18 eV as increasing temperature from 10 to 300 K. In the pump-probe experiment with a fixed pump photon energy, we have to pay strict attention to this energy shift because the initial distribution of excited electron states can be changed by temperature; the feature of the initial distribution could affect ultrafast responses of the electron and phonon systems. [PERSON] et al. measured \(\Delta R/R_{0}\) signals as a function of temperature in various YMnO\({}_{3}\) epitaxial films and estimated the energy gaps from the signal amplitude around the time origin [40]. Similarly, the effect of the absorption band shift is emerged in our study, which is discussed in Section 4.4.  
In Figure 2b, the absorption peak shows an abrupt change around the Neel temperature. Such anomalies of absorption peak shifts were observed in hexagonal RMnO\({}_{3}\) thin films with \(R\) = Gd, Tb, Dy, Ho and Lu [12]. These anomalies are attributed to that the electronic state is modulated by the antiferromagnetic ordering. On the other hand, in order to rigorously analyse the temperature-dependent peak shift, the line-shape analysis of the absorption band considering several absorption bands would be required. Figure 3a shows the optical conductivity spectra at 6 K and 300 K in a hexagonal HoMnO\({}_{3}\) single crystal [41]. The inset shows a fitted result of the spectrum at 6 K considering four components. The four components were considered to be due to the transitions from two e\({}_{\text{2g}}\) states to a\({}_{\text{1g}}\) state and from two e\({}_{\text{1g}}\) states to a\({}_{\text{1g}}\) state. Figure 3b shows the peak positions of each component as a function of temperature. The temperature dependence of the peak energy is  
Figure 1: Schematic diagram of the setup for time-resolved reflection-type pump-probe spectroscopy.  
different from each other, which suggests the complexity of the mechanism of the absorption band shift. Moreover, the fitted result indicates that the band at \(\sim\)1.7 eV is composed of at least two components (striking one at \(\sim\)1.7 eV and weak one in a lower-energy range). The absorption spectra in Figure 2a may have similar components because it shows a similar asymmetric profile.