Zone center phonons of the orthorhombic RMnO 3 ( 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 RMnO3 perovskites (R = rare earth elements) have been the object of research mainly as parent materials of mixed valence manganites exhibiting colossal magnetoresistivity (CMR) [1-4]. 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 RMnO3 [5-10]. All RMnO3 perovskites show a distortion of MnO6 octahedra due to orbital ordering characteristic of the John-Teller effect of Mn cations [11-15]. 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 RMnO3. Martin Carron et al. [11] studied the behavior of Raman phonons through the transition from static to dynamic Jahn-Teller order in stoichiometric RMnO3 samples (R = La, Pr, Y). Also Martin Carron et al. [12] studied orthorhombic RMnO3 (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 Published: 17 March 2008 PMC Physics B 2008, 1:9 doi:10.1186/1754-0429-1-9 Received: 2 November 2007 Accepted: 17 March 2008 This article is available from: http://www.physmathcentral.com/1754-0429/1/9 © 2008 Gupta and Tripathi This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Page 1 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9 http://www.physmathcentral.com/1754-0429/1/9 bond distances, octahedral tilt angle and Jahn-Teller distortion. Further rationalization of the Raman spectra of orthorhombic RMnO3 (R = Pr, Nd, Tb, Ho, Er) and different phases of Caor Srdoped RMnO3 compounds as well as cation deficient RMnO3 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 RMnO3 (R = La, Pr, Nd, Sm) compounds and they also assigned three main Raman peaks. Recently, the polarized Raman spectra of orthorhombic RMnO3 (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 NdMnO3 has first been made by Gupta et al. [16]. In the present study, the theoretical investigations of phonons in the orthorhombic RMnO3 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 RMnO3 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 MnO6 octahedra progressively increases from Pr to Er due to simple steric factors. Additionally, all of the perovskites show a distortion of the MnO6octahedra due to orbital ordering characteristic of the Jahn-Teller of the Mn 3+ cations. Structural data of EuMnO3 is very recent because of its high neutron absorption and they are perfectly correlated with the other members of RMnO3 series [18]. The total number of irreducible representations for RMnO3 are = 7Ag + 7B1g + 5B2g + 5B3g + 8Au + 8B1u + 10B2u + 10B3u Page 2 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9 http://www.physmathcentral.com/1754-0429/1/9 There are four Raman active species, Ag, B1g, B2g and B2g, three infrared active species B1u, B2u and B3u and inactive specie Au. In the present paper, an attempt has been made to study the zone center phonons in RMnO3 (R = Pr, Eu, Tb, Dy, Ho) for the first time using SRFCM. We have used nine valence force constants K1(Mn-O2), K2(Mn-O1), K3(Mn-O2), K4(R-O1), K5(R-O2), K6(R-O1), K7(R-O2), K8(RO1), K9(R-O2); and eight bending force constants H1(O1-R-O1), H2(O1-R-O1), H3(O1-R-O1), H4(O1-R-O2), H5(O1-R-O2), H6(O1-R-O2), H7(O2-R-O2) and H8(O2-R-O2) at various interatomic distances and angles as shown in Table 1(only for PrMnO3). Table 1: Force constant, Coordination number, Inter-atomic Distances (Å) and Angles (deg) and Force constant values (N/cm) for Orthorhombic PrMnO3 Force constant K1 K2 K3 K4 K5 K6 K7 K8 K9 H1 H2 H3 H4 H5 H6 H7 H8 Coord. Number. 8 8 8 4 8 4 8 4 8 8 8 4 4 8 8 7 8 Distance/ Angle 1.91 1.95 2.21 2.36 2.40 2.48 2.62 3.17 3.52 89 67 110 90 56 66 160 120 Force constant values 0.597 0.535 0.950 0.456 0.019 0.311 0.382 0.335 0.598 0.432 0.413 0.404 0.373 0.338 0.329 0.136 0.022 The structure of Orthorhombic RMnO3 (R = Pr, Nd, Eu, Gd, Tb, Dy, Ho) compounds at room temperature, belonging to Pbnm space group Figure 1 The structure of Orthorhombic RMnO3 (R = Pr, Nd, Eu, Gd, Tb, Dy, Ho) compounds at room temperature, belonging to Pbnm space group. The structure has four formulae unit with R atoms, Mn atoms and O atoms (O1 and O2). Page 3 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9 http://www.physmathcentral.com/1754-0429/1/9 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 K1 and K3 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 MnO6 octahedra. Further, as shown in Table 1 the force constant K3 (0.950 N/cm) is quite large when compared with the similar force constant obtained in studies of NdNiO3 [19] and NdGaO3 [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 MnO6 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 MnO6 octahedra. The force constants between R and O1 atoms, K4 and K6 increase with decrease of R-O1 distance almost uniformly throughout the series. The force constant K8 (R-O1) changes by a small amount as the R-O1 distance also shows the similar behavior. The force constants K5, K7 and K9 also show a uniform increase. Although force constant K5 is very Table 2: *Observed [15] and Calculated Raman Wave Numbers (cm) for Orthorhombic RMnO3 (R = Pr, Eu, Tb, Dy, Ho) Modes *Pr Pr *Eu Eu *Tb Tb *Dy Dy *Ho Ho Ag 491 491 501 501 509 509 513 513 520 520 462 462 479 479 489 489 492 492 499 499 386 392 402 412 408 324 324 361 361 378 378 386 386 395 395 232 232 270 269 272 288 288 206 205 211 213 210 64 67 79 79 77 B1g 607 607 610 610 612 612 614 614 615 615 496 496 518 518 528 528 534 534 537 537 486 499 501 501 503 445 445 465 465 474 474 478 478 481 481 312 312 324 324 331 331 336 336 340 114 122 127 129 129 84 91 96 97 97 B2g 627 611 621 624 617 492 511 519 521 529 432 463 469 476 482 283 295 302 306 309 125 131 134 134 135 B3g 537 521 545 553 546 400 429 432 432 454 305 367 381 390 402 239 266 270 274 286 123 124 127 127 125 Page 4 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9 http://www.physmathcentral.com/1754-0429/1/9 small but K9 shows comparatively a large value. The bending force constants H1-H4 show a very small change in force constant values while H7 and H8 exhibit uniformly increasing values. The calculated Raman frequencies in Table 2 agreed satisfactorily with the observed values [15]. The assignment of infrared frequencies as shown in Table 3 has been done for the first time. Still a precise experimental analysis of infrared frequencies is needed to verify the results of present calculations. The potential energy distribution (PED) for most of the force constant is found to be almost similar throughout the series. The PED showed that high wave numbers are dominated by stretching force constants involving Mn and O atoms and bending force constants having R and O atoms. Therefore, the symmetric stretching of the basal oxygens of the octahedra, around 610 cm (B1g symmetry); the asymmetric stretching at about 490 cm -1 (Ag symmetry) associated with the Jahn-Teller distortion is expected. The Ag mode (324 cm 395 cm) showing a drastic increase in frequency is purely a stretching mode dominated by K9 (R-O2). Most of the lower wave number modes have a convincing influence by R-O bending and stretching force constants. For all the compounds of the orthorhombic RMnO3 series, we calculated the eigen vectors Table 3: Calculated Infrared Wave Numbers (cm) for Orthorhombic RMnO3 (R = Pr, Eu, Tb, Dy, Ho) Modes Pr Eu Tb Dy Ho B1u 608 611 612 614 617 569 581 581 580 582 485 492 509 514 516 303 323 328 332 338 205 213 214 214 223 141 152 158 159 161 133 135 142 144 143 0 0 0 0 0 B2u 614 612 617 620 620 571 582 582 580 580 467 494 498 500 511 389 395 406 417 410 290 304 309 312 318 223 229 232 234 235 201 206 208 208 213 177 176 180 179 178 132 142 148 148 149 0 0 0 0 0 B3u 535 538 551 558 562 484 505 515 519 522 431 458 463 465 474 343 384 398 406 419 315 320 318 316 315 244 268 272 277 289 181 181 185 184 184 131 137 143 144 143 106 115 118 120 122 0 0 0 0 0 Page 5 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9 http://www.physmathcentral.com/1754-0429/1/9 representing the displacements of various atoms. It was observed that for larger wave numbers, the displacement of O atoms is important whereas for smaller wave numbers, the displacement of R atoms dominates as given in Table 4 and Table 5 only for PrMnO3. Vibrations of several atoms are involved in some middle order modes. Table 4: Calculated Raman Wave Numbers (cm) of PrMnO3 along with their Eigen-vector Lengths representing Atomic Displacements for various Atoms Modes Wave-numbers Pr Pr O1 O1 O2 O2 O2 Ag 491 0.04 0.26 -0.08 -0.46 0.69 -0.43 0.21 462 0.05 0.16 -0.24 0.53 0.60 0.52 -0.02 386 0.05 0.05 0.96 0.05 0.20 0.15 0.01 324 0.12 -0.15 -0.06 -0.66 0.09 0.54 -0.47 232 -0.30 0.21 -0.03 -0.27 -0.18 0.47 0.74 206 0.91 -0.16 -0.04 -0.01 -0.07 0.06 0.36 64 0.24 0.90 0.00 -0.01 -0.27 0.01 -0.25 B1g 607 -0.03 0.10 -0.06 0.96 -0.05 0.09 0.24 496 0.33 0.05 0.78 0.06 -0.49 -0.13 -0.10 486 0.05 0.00 0.10 -0.08 -0.07 0.99 -0.03 445 0.07 -0.17 0.51 0.06 0.82 0.01 0.14 312 -0.27 0.34 0.15 -0.25 -0.12 0.00 0.84 114 0.28 0.90 -0.05 -0.01 0.24 0.00 -0.23 84 0.85 -0.18 -0.30 -0.07 0.01 -0.01 0.38 B2g 627 0.01 0.90 0.13 0.37 0.20 493 0.08 -0.20 0.95 0.20 -0.06 432 -0.17 -0.27 -0.25 0.88 -0.25 283 0.09 -0.28 -0.05 0.19 0.94 125 0.98 -0.01 -0.12 0.11 -0.13 B3g 537 0.06 0.59 0.41 0.68 -0.08 400 0.04 -0.23 -0.69 0.64 0.25 305 0.21 -0.73 0.41 0.32 -0.40 239 0.28 -0.18 0.39 0.00 0.86 123 0.93 0.19 -0.20 -0.14 -0.18 Page 6 of 8 (page number not for citation purposes) PMC Physics B 2008, 1:9http://www.physmathcentral.com/1754-0429/1/9 References1. 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Dabrowski B, Kolesnik S, Baszczuk A, Chmaissem O, Maxwell T, Mais J: J Solid State Chem 2005, 178:629.Table 5: Calculated Infrared Wave Numbers (cm) of PrMnO3 along with their Eigen-vector Lengths representing AtomicDisplacements for various Atoms Modes Wave-numbers Mn Mn Mn Pr Pr O1 O1 O2 O2 O2 B1u606-0.02 -0.02 0.01 -0.100.950.11 -0.06 0.255690.02 -0.53 0.03 0.01-0.100.84 -0.04 -0.024850.08 -0.05 -0.27 -0.070.090.03 0.94 -0.16303-0.19 0.01 -0.17 -0.35-0.260.02 0.12 0.862050.95 0.01 0.20 -0.20-0.05-0.01 0.00 0.15141-0.24 -0.25 0.76 -0.48-0.01-0.17 0.17 -0.12133-0.07 0.81 0.23 -0.14-0.040.50 0.08 -0.0700.00 0.00 0.47 0.760.000.00 0.26 0.36B2u614-0.01 -0.03 0.00 0.07 0.04 0.02 0.93 -0.25 0.14 0.005710.02 -0.53 0.02 0.06 -0.06 0.00 -0.14 -0.01 0.83 -0.04467-0.01 -0.01 -0.03 -0.03 -0.30 -0.22 0.21 0.88 0.03 0.18389-0.04 0.00 0.10 -0.04 -0.07 0.96 0.01 0.19 0.01 0.12290-0.27 0.01 -0.08 -0.10 0.03 -0.08 -0.24 -0.15 0.02 0.91223-0.14 0.42 0.00 0.81 -0.32 0.01 -0.08 -0.06 0.17 0.022010.93 0.10 0.19 0.06 -0.06 -0.01 -0.07 -0.05 0.03 0.28177-0.20 0.04 0.97 -0.07 -0.03 -0.12 0.00 -0.01 0.01 0.00132-0.02 0.56 -0.08 -0.56 -0.46 -0.01 0.01 -0.17 0.35 -0.1000.00 0.47 0.00 0.00 0.76 0.00 0.00 0.26 0.36 0.00B3u535-0.25 0.07 -0.04 -0.21 -0.07 0.27 0.59 -0.49 0.46 -0.094840.15 -0.05 0.10 -0.28 0.03 0.85 -0.21 -0.10 -0.33 0.09431-0.21 0.10 -0.04 -0.04 0.19 0.30 0.16 0.81 0.35 -0.04343-0.04 -0.53 -0.03 -0.20 0.22 -0.14 0.57 0.15 -0.45 0.253150.05 0.82 -0.02 -0.12 0.13 -0.09 0.25 0.01 -0.31 0.35244-0.25 -0.14 -0.01 0.21 -0.19 0.07 -0.16 -0.05 0.24 0.86181-0.26 0.03 0.95 0.14 0.05 -0.03 0.06 0.00 -0.07 -0.05131-0.06 -0.03 -0.06 0.12 0.93 0.00 -0.19 -0.24 0.15 0.061060.71 -0.06 0.29 -0.40 0.05 -0.15 0.02 0.06 0.41 0.2100.47 0.00 0.00 0.76 0.00 0.26 0.36 0.00 0.00 0.00 Page 7 of 8(page number not for citation purposes) PMC Physics B 2008, 1:9http://www.physmathcentral.com/1754-0429/1/9 19. 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