Zone center phonons of the orthorhombic RMnO3 (R = Pr, Eu, Tb, Dy, Ho) perovskites
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Zone center phonons of the orthorhombic RMnO (R = Pr, Eu, Tb, Dy, Ho) perovskites HC Gupta* and Upendra Tripathi Address: Physics Department, Indian Institute of Technology, Hauz Khas, New Delhi, India and Physics Department, AmityUniversity, Noida, UttarPradesh, IndiaEmail: HC Gupta* - [email protected]; Upendra Tripathi - [email protected]* Corresponding author
Abstract
A short range force constant model (SRFCM) has been applied for the first time toinvestigate the phonons in RMnO (R = Pr, Eu, Tb, Dy, Ho) perovskites in theirorthorhombic phase. The calculations with 17 stretching and bending force constantsprovide good agreement for the observed Raman frequencies. The infrared frequencieshave been assigned for the first time. PACS Codes:
Introduction
Until recently the RMnO perovskites (R = rare earth elements) have been the object of researchmainly 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 rela-tionships among the lattice distortions, magnetism, dielectric, and transport properties ofundoped RMnO [5-10]. All RMnO perovskites show a distortion of MnO octahedra due toorbital ordering characteristic of the John-Teller effect of Mn cations [11-15]. An investigationof infrared and Raman frequencies will be quite useful in describing the details of such proper-ties. Practically, very limited information is available on the infrared and Raman scattering oforthorhombic RMnO . Martin Carron et al . [11] studied the behavior of Raman phononsthrough the transition from static to dynamic Jahn-Teller order in stoichiometric RMnO samples(R = La, Pr, Y). Also Martin Carron et al . [12] studied orthorhombic RMnO (R = Pr, Nd, Eu, Tb,Dy, Ho) manganites for their Raman phonons as a function of the rare earth ions and tempera-ture. They had assigned only some of the Raman modes. They correlated the frequencies of threemost intense modes of orthorhombic samples, with some structural parameters such as Mn-O Published: 17 March 2008
PMC Physics B MC Physics B (page number not for citation purposes) bond distances, octahedral tilt angle and Jahn-Teller distortion. Further rationalization of theRaman spectra of orthorhombic RMnO (R = Pr, Nd, Tb, Ho, Er) and different phases of Ca- orSr- doped RMnO compounds as well as cation deficient RMnO were made by Martin Carron etal . [13]. Their assignment of the peaks related to octahedral tilt were in good agreement with theother authors but the assignment of peak to an antisymmetric stretching associated with theJahn-Teller distortion was doubtful. Wang Wei-Ran et al . [14] measured Raman active phononsin orthorhombic RMnO (R = La, Pr, Nd, Sm) compounds and they also assigned three mainRaman peaks. Recently, the polarized Raman spectra of orthorhombic RMnO (R = Pr, Nd, Eu,Gd, Tb, Dy, Ho) series at room temperature were studied by Iliev et al . [15] where they hadassigned the observed frequencies to nine Raman modes. Their study shows that the variationsof lattice distortions with radius of rare earth atoms affect significantly both the phonon frequen-cies and the shape of some of Raman modes. To our knowledge, the theoretical investigations ofphonons, using the normal coordinate analysis in the orthorhombic NdMnO has first beenmade by Gupta et al . [16].In the present study, the theoretical investigations of phonons in the orthorhombic RMnO have been made using the normal coordinate analysis. It has been observed that a total of 17inter-atomic force constants, which include 8 bending force constants, are enough to obtain agood agreement between theory and experiment for the Raman frequencies. The assignments ofinfrared frequencies along with their corresponding eigen vectors observing the atomic displace-ments in the respective vectors have been made for the first time. There is always some scope ofmore precise infrared experiments to verify these theoretical values. Theory
The structure of stoichiometric RMnO shown in Fig. 1, described at room temperature by thePbnm space group (Z = 4), can be considered as orthorhombically distorted superstructure ofideal perovskites. In the Pbnm structure the atoms occupy four non equivalent atomic sites ofthem only the Mn site is a center of symmetry [17]. The distortion of the orthorhombic per-ovskites characterized by the tilting angle of the MnO octahedra progressively increases from Prto Er due to simple steric factors. Additionally, all of the perovskites show a distortion of theMnO octahedra due to orbital ordering characteristic of the Jahn-Teller of the Mn cations.Structural data of EuMnO is very recent because of its high neutron absorption and they are per-fectly correlated with the other members of RMnO series [18].The total number of irreducible representations for RMnO are= 7A g + 7B + 5B + 5B + 8A u + 8B + 10B + 10B MC Physics B (page number not for citation purposes) There are four Raman active species, A g , B , B and B , three infrared active species B , B and B and inactive specie A u .In the present paper, an attempt has been made to study the zone center phonons in RMnO (R = Pr, Eu, Tb, Dy, Ho) for the first time using SRFCM. We have used nine valence force con-stants K (Mn-O2), K (Mn-O1), K (Mn-O2), K (R-O1), K (R-O2), K (R-O1), K (R-O2), K (R-O1), K (R-O2); and eight bending force constants H (O1-R-O1), H (O1-R-O1), H (O1-R-O1),H (O1-R-O2), H (O1-R-O2), H (O1-R-O2), H (O2-R-O2) and H (O2-R-O2) at various inter-atomic distances and angles as shown in Table 1(only for PrMnO ). Table 1: Force constant, Coordination number, Inter-atomic Distances (Å) and Angles (deg) and Force constant values (N/cm) for Orthorhombic PrMnO Force constant K K K K K K K K K H H H H H H H H Coord. Number. 8 8 8 4 8 4 8 4 8 8 8 4 4 8 8 7 8Distance/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 120Force 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 RMnO (R = Pr, Nd, Eu, Gd, Tb, Dy, Ho) compounds at room temperature, belonging to Pbnm space group Figure 1
The structure of Orthorhombic RMnO (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). MC Physics B (page number not for citation purposes) Results and Discussions
A systematic variation in the most of the force constants is seen throughout the series. It was inter-esting to observe that although, the interatomic distances for K and K between Mn and O2atoms remain nearly unchanged from Pr to Ho but the force constant exhibited a uniformincrease. This behaviour can be related to the increase in distortion of MnO octahedra. Further,as shown in Table 1 the force constant K (0.950 N/cm) is quite large when compared with thesimilar force constant obtained in studies of NdNiO [19] and NdGaO [20] (0.620 N/cm). Asimilar kind of behaviour of large force constant between Mn and O2 atoms was observed inpyrochlore manganates [21]. This may be one of the possible reasons of associated CMR proper-ties of manganese compounds. To account for a drastic change in resistivity and a low criticaltemperature in such materials, it should be noted that the double exchange model must be com-bined with the effect of the Jahn-Teller distortion of MnO octahedra [22]. This effect promotescarrier localization and dresses charge carriers via cloud of phonons. It is in this respect where thelarge interatomic force between Mn and O2 atoms plays an important role, being a part of thedistortion of the MnO octahedra. The force constants between R and O1 atoms, K and K increase with decrease of R-O1 distance almost uniformly throughout the series. The force con-stant K (R-O1) changes by a small amount as the R-O1 distance also shows the similar behavior.The force constants K , K and K also show a uniform increase. Although force constant K is very Table 2: *Observed [15] and Calculated Raman Wave Numbers (cm -1 ) for Orthorhombic RMnO (R = Pr, Eu, Tb, Dy, Ho) Modes * Pr Pr * Eu Eu * Tb Tb * Dy Dy * Ho HoA g
491 491 501 501 509 509 513 513 520 520462 462 479 479 489 489 492 492 499 499386 392 402 412 408324 324 361 361 378 378 386 386 395 395232 232 270 269 272 288 288206 205 211 213 21064 67 79 79 77B
607 607 610 610 612 612 614 614 615 615496 496 518 518 528 528 534 534 537 537486 499 501 501 503445 445 465 465 474 474 478 478 481 481312 312 324 324 331 331 336 336 340114 122 127 129 12984 91 96 97 97B
627 611 621 624 617492 511 519 521 529432 463 469 476 482283 295 302 306 309125 131 134 134 135B
537 521 545 553 546400 429 432 432 454305 367 381 390 402239 266 270 274 286123 124 127 127 125
MC Physics B (page number not for citation purposes) small but K shows comparatively a large value. The bending force constants H -H show a verysmall change in force constant values while H and H 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 ofpresent calculations. The potential energy distribution (PED) for most of the force constant isfound to be almost similar throughout the series. The PED showed that high wave numbers aredominated by stretching force constants involving Mn and O atoms and bending force constantshaving R and O atoms. Therefore, the symmetric stretching of the basal oxygens of the octahedra,around 610 cm -1 (B symmetry); the asymmetric stretching at about 490 cm -1 (A g symmetry)associated with the Jahn-Teller distortion is expected. The A g mode (324 cm -1 - 395 cm -1 ) showinga drastic increase in frequency is purely a stretching mode dominated by K (R-O2). Most of thelower wave number modes have a convincing influence by R-O bending and stretching force con-stants. For all the compounds of the orthorhombic RMnO series, we calculated the eigen vectors Table 3: Calculated Infrared Wave Numbers (cm -1 ) for Orthorhombic RMnO (R = Pr, Eu, Tb, Dy, Ho) Modes Pr Eu Tb Dy HoB
608 611 612 614 617569 581 581 580 582485 492 509 514 516303 323 328 332 338205 213 214 214 223141 152 158 159 161133 135 142 144 1430 0 0 0 0B
614 612 617 620 620571 582 582 580 580467 494 498 500 511389 395 406 417 410290 304 309 312 318223 229 232 234 235201 206 208 208 213177 176 180 179 178132 142 148 148 1490 0 0 0 0B
535 538 551 558 562484 505 515 519 522431 458 463 465 474343 384 398 406 419315 320 318 316 315244 268 272 277 289181 181 185 184 184131 137 143 144 143106 115 118 120 1220 0 0 0 0
MC Physics B (page number not for citation purposes) 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 displacementof R atoms dominates as given in Table 4 and Table 5 only for PrMnO . Vibrations of severalatoms are involved in some middle order modes. Table 4: Calculated Raman Wave Numbers (cm -1 ) of PrMnO along with their Eigen-vector Lengths representing Atomic Displacements for various Atoms Modes Wave-numbers Pr Pr O1 O1 O2 O2 O2A g
491 0.04 0.26 -0.08 -0.46 0.69 -0.43 0.21462 0.05 0.16 -0.24 0.53 0.60 0.52 -0.02386 0.05 0.05 0.96 0.05 0.20 0.15 0.01324 0.12 -0.15 -0.06 -0.66 0.09 0.54 -0.47232 -0.30 0.21 -0.03 -0.27 -0.18 0.47 0.74206 0.91 -0.16 -0.04 -0.01 -0.07 0.06 0.3664 0.24 0.90 0.00 -0.01 -0.27 0.01 -0.25B
607 -0.03 0.10 -0.06 0.96 -0.05 0.09 0.24496 0.33 0.05 0.78 0.06 -0.49 -0.13 -0.10486 0.05 0.00 0.10 -0.08 -0.07 0.99 -0.03445 0.07 -0.17 0.51 0.06 0.82 0.01 0.14312 -0.27 0.34 0.15 -0.25 -0.12 0.00 0.84114 0.28 0.90 -0.05 -0.01 0.24 0.00 -0.2384 0.85 -0.18 -0.30 -0.07 0.01 -0.01 0.38B
627 0.01 0.90 0.13 0.37 0.20493 0.08 -0.20 0.95 0.20 -0.06432 -0.17 -0.27 -0.25 0.88 -0.25283 0.09 -0.28 -0.05 0.19 0.94125 0.98 -0.01 -0.12 0.11 -0.13B
537 0.06 0.59 0.41 0.68 -0.08400 0.04 -0.23 -0.69 0.64 0.25305 0.21 -0.73 0.41 0.32 -0.40239 0.28 -0.18 0.39 0.00 0.86123 0.93 0.19 -0.20 -0.14 -0.18
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Table 5: Calculated Infrared Wave Numbers (cm -1 ) of PrMnO along with their Eigen-vector Lengths representing Atomic Displacements for various Atoms Modes Wave-numbers Mn Mn Mn Pr Pr O1 O1 O2 O2 O2B
606 -0.02 -0.02 0.01 -0.10 0.95 0.11 -0.06 0.25569 0.02 -0.53 0.03 0.01 -0.10 0.84 -0.04 -0.02485 0.08 -0.05 -0.27 -0.07 0.09 0.03 0.94 -0.16303 -0.19 0.01 -0.17 -0.35 -0.26 0.02 0.12 0.86205 0.95 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 -0.04 0.50 0.08 -0.070 0.00 0.00 0.47 0.76 0.00 0.00 0.26 0.36B
614 -0.01 -0.03 0.00 0.07 0.04 0.02 0.93 -0.25 0.14 0.00571 0.02 -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 0.02201 0.93 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 -0.100 0.00 0.47 0.00 0.00 0.76 0.00 0.00 0.26 0.36 0.00 B
535 -0.25 0.07 -0.04 -0.21 -0.07 0.27 0.59 -0.49 0.46 -0.09484 0.15 -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 0.25315 0.05 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 0.06106 0.71 -0.06 0.29 -0.40 0.05 -0.15 0.02 0.06 0.41 0.210 0.47 0.00 0.00 0.76 0.00 0.26 0.36 0.00 0.00 0.00
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