# Characteristics of Coherent Optical Phonons in a Hexagonal \(\mathbf{YMnO_{3}}\) Thin Film
## 1 Introduction  
Ultrafast phenomena in condensed matters have attracted considerable attention in ultrafast science and technology. With the development of ultrafast spectroscopy, dynamics of various elementary excitations have intensively investigated [1; 2]. Multiferroic materials in which two or more ferroic orders coexist [3; 4; 5] could bring an innovation in the ultrafast science field because the coupling nature between different degrees of freedom is expected to emerge novel dynamical properties of excited states. The discovery of the novel dynamics in the multiferroic material is one of recent frontier studies in the condensed matter physics [6]. Yttrium and rare-earth manganites \(\mathrm{RMnO_{3}}\) (\(R=\mathrm{Lu}\), Ho, Er, Tm, Yb) crystallize in a hexagonal phase with space group \(P6_{5}cm\)[7]. These are multiferroic materials where the ferroelectric and antiferromagnetic characteristics coexist [8; 9; 10; 11; 12; 13; 14]. The ferroelectric transition temperature is 500-1000 K and the antiferromagnetic transition temperature is about 100 K. The correlation behaviour between electric and magnetic properties emerged in the temperature dependences of dielectric constant and loss tangent around the Neel temperature [8; 9]. Through a lot of structural studies by neutron diffraction and X-ray diffraction experiments, the correlation is considered to arise from the strong coupling between spin and lattice degrees of freedom under the antiferromagnetic transition [13; 14; 15; 16]. In the process of magnetic ordering, Mn atoms displace from their ideal position. Moreover, this displacement induces further displacements of other atoms in the unit cell. This lattice response produces the electromagnetic effect. On the other hand, the temperature dependence of phonon modes has investigated by Raman and infrared spectroscopies [17; 18; 19; 20]. The existence of the spin-latticecoupling is suggested from anomalies of phonon frequency shifts. It is interesting that the property of the spin-lattice coupling depends on the rare-earth atom. For instance, the displacement direction of Mn atoms in YMnO\({}_{3}\) is opposite in comparison with that in LuMnO\({}_{3}\) under the process of ordering [14]. Moreover, the direction of the temperature-dependent frequency shift of an A\({}_{1}\)-symmetry optical phonon in YMnO\({}_{3}\) is opposite to that in LuMnO\({}_{3}\) below the Neel temperatures [19]. These behaviour indicates that hexagonal \(R\)MnO\({}_{3}\) compounds have distinct properties depending on the rare-earth atom. From the viewpoint of ultrafast phenomena, the lattice dynamics under the spin-lattice coupling regime is a fascinating subject. Coherently-excited phonons by ultrashort laser pulses, which are so-called coherent phonons, have intensively investigated in recent years [21; 22; 23; 24; 25; 26]. The dynamics of coherent phonons exhibit interesting properties around the Neel temperature. The most prominent property is that the oscillation amplitude of the coherent phonon decreases as the temperature approaches to the Neel temperature [23; 24; 25]. This behaviour suggests the existence of a dynamical spin-lattice coupling, while the mechanism is still unclear. In order to elucidate the mechanism, it should accumulate further study results on the coherent phonon dynamics in hexagonal \(R\)MnO\({}_{3}\) compounds. Although coherent acoustic phonons have observed in \(R\)MnO\({}_{3}\) with \(R=\) Y, Lu and Ho [21; 23; 24; 25], coherent optical phonons were reported only in LuMnO\({}_{3}\)[22; 24]. Therefore, the observation of coherent optical phonons in other hexagonal \(R\)MnO\({}_{3}\) compounds is crucially important. In this review, we present our recent study on the characteristics of a coherent optical phonon in a hexagonal YMnO\({}_{3}\) thin film [27] together with related optical studies in \(R\)MnO\({}_{3}\) compounds. In Section 2, two types of generation mechanisms of coherent phonons are briefly reviewed.