Zone center phonons of the orthorhombic RMnO3 (R = Pr, Eu, Tb, Dy, Ho) perovskites

A short range force constant model (SRFCM) has been applied for the first time to investigate the phonons in RMnO3 (R = Pr, Eu, Tb, Dy, Ho) perovskites in their orthorhombic phase. The calculations with 17 stretching and bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned for the first time. PACS Codes: 36.20.Ng, 33.20.Fb, 34.20.Cf


Introduction
Until recently the RMnO 3 perovskites (R = rare earth elements) have been the object of research mainly as parent materials of mixed valence manganites exhibiting colossal magnetoresistivity (CMR) [1][2][3][4]. In the past few years, however, there is an increased interest in the complex relationships among the lattice distortions, magnetism, dielectric, and transport properties of undoped RMnO 3 [5][6][7][8][9][10]. All RMnO 3 perovskites show a distortion of MnO 6 octahedra due to orbital ordering characteristic of the John-Teller effect of Mn 3+ cations [11][12][13][14][15]. An investigation of infrared and Raman frequencies will be quite useful in describing the details of such properties. Practically, very limited information is available on the infrared and Raman scattering of orthorhombic RMnO 3 . Martin Carron et al. [11] studied the behavior of Raman phonons through the transition from static to dynamic Jahn-Teller order in stoichiometric RMnO 3 samples (R = La, Pr, Y). Also Martin Carron et al. [12] studied orthorhombic RMnO 3 (R = Pr, Nd, Eu, Tb, Dy, Ho) manganites for their Raman phonons as a function of the rare earth ions and temperature. They had assigned only some of the Raman modes. They correlated the frequencies of three most intense modes of orthorhombic samples, with some structural parameters such as Mn-O bond distances, octahedral tilt angle and Jahn-Teller distortion. Further rationalization of the Raman spectra of orthorhombic RMnO 3 (R = Pr, Nd, Tb, Ho, Er) and different phases of Ca-or   Sr-doped RMnO 3 compounds as well as cation deficient RMnO 3 were made by Martin Carron et al. [13]. Their assignment of the peaks related to octahedral tilt were in good agreement with the other authors but the assignment of peak to an antisymmetric stretching associated with the Jahn-Teller distortion was doubtful. Wang Wei-Ran et al. [14] measured Raman active phonons in orthorhombic RMnO 3 (R = La, Pr, Nd, Sm) compounds and they also assigned three main Raman peaks. Recently, the polarized Raman spectra of orthorhombic RMnO 3 (R = Pr, Nd, Eu, Gd, Tb, Dy, Ho) series at room temperature were studied by Iliev et al. [15] where they had assigned the observed frequencies to nine Raman modes. Their study shows that the variations of lattice distortions with radius of rare earth atoms affect significantly both the phonon frequencies and the shape of some of Raman modes. To our knowledge, the theoretical investigations of phonons, using the normal coordinate analysis in the orthorhombic NdMnO 3 has first been made by Gupta et al. [16].
In the present study, the theoretical investigations of phonons in the orthorhombic RMnO 3 have been made using the normal coordinate analysis. It has been observed that a total of 17 inter-atomic force constants, which include 8 bending force constants, are enough to obtain a good agreement between theory and experiment for the Raman frequencies. The assignments of infrared frequencies along with their corresponding eigen vectors observing the atomic displacements in the respective vectors have been made for the first time. There is always some scope of more precise infrared experiments to verify these theoretical values.

Theory
The structure of stoichiometric RMnO 3 shown in Fig. 1, described at room temperature by the Pbnm space group (Z = 4), can be considered as orthorhombically distorted superstructure of ideal perovskites. In the Pbnm structure the atoms occupy four non equivalent atomic sites of them only the Mn site is a center of symmetry [17]. The distortion of the orthorhombic perovskites characterized by the tilting angle of the MnO 6 octahedra progressively increases from Pr to Er due to simple steric factors. Additionally, all of the perovskites show a distortion of the MnO 6 octahedra due to orbital ordering characteristic of the Jahn-Teller of the Mn 3+ cations.
Structural data of EuMnO 3 is very recent because of its high neutron absorption and they are perfectly correlated with the other members of RMnO 3 series [18].

Results and Discussions
A systematic variation in the most of the force constants is seen throughout the series. It was interesting to observe that although, the interatomic distances for K 1 and K 3 between Mn and O2 atoms remain nearly unchanged from Pr to Ho but the force constant exhibited a uniform increase. This behaviour can be related to the increase in distortion of MnO 6 octahedra. Further, as shown in Table 1 the force constant K 3 (0.950 N/cm) is quite large when compared with the similar force constant obtained in studies of NdNiO 3 [19] and NdGaO 3 [20] (0.620 N/cm). A similar kind of behaviour of large force constant between Mn and O2 atoms was observed in pyrochlore manganates [21]. This may be one of the possible reasons of associated CMR properties of manganese compounds. To account for a drastic change in resistivity and a low critical temperature in such materials, it should be noted that the double exchange model must be combined with the effect of the Jahn-Teller distortion of MnO 6 octahedra [22]. This effect promotes carrier localization and dresses charge carriers via cloud of phonons. It is in this respect where the large interatomic force between Mn and O2 atoms plays an important role, being a part of the distortion of the MnO 6 octahedra. The force constants between R and O1 atoms, K 4 and K 6 increase with decrease of R-O1 distance almost uniformly throughout the series. The force constant K 8 (R-O1) changes by a small amount as the R-O1 distance also shows the similar behavior.