Open Access

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

PMC Physics B20081:9

DOI: 10.1186/1754-0429-1-9

Received: 02 November 2007

Accepted: 17 March 2008

Published: 17 March 2008

Abstract

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) [14]. 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 [510]. All RMnO3 perovskites show a distortion of MnO6 octahedra due to orbital ordering characteristic of the John-Teller effect of Mn3+ cations [1115]. 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 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 Ca- or Sr- doped 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 Mn3+ 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].
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).

The total number of irreducible representations for RMnO3 are

= 7Ag + 7B1g + 5B2g + 5B3g + 8Au + 8B1u + 10B2u + 10B3u

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(R-O1), 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 inter-atomic 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

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 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-1 (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-1- 395 cm-1) 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 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 2

*Observed [15] and Calculated Raman Wave Numbers (cm-1) 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

Table 3

Calculated Infrared Wave Numbers (cm-1) 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

Table 4

Calculated Raman Wave Numbers (cm-1) 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

Table 5

Calculated Infrared Wave Numbers (cm-1) of PrMnO3 along with their Eigen-vector Lengths representing Atomic Displacements for various Atoms

Modes

Wave-numbers

Mn

Mn

Mn

Pr

Pr

O1

O1

O2

O2

O2

B1u

606

-0.02

-0.02

0.01

-0.10

 

0.95

 

0.11

-0.06

0.25

 

569

0.02

-0.53

0.03

0.01

 

-0.10

 

0.84

-0.04

-0.02

 

485

0.08

-0.05

-0.27

-0.07

 

0.09

 

0.03

0.94

-0.16

 

303

-0.19

0.01

-0.17

-0.35

 

-0.26

 

0.02

0.12

0.86

 

205

0.95

0.01

0.20

-0.20

 

-0.05

 

-0.01

0.00

0.15

 

141

-0.24

-0.25

0.76

-0.48

 

-0.01

 

-0.17

0.17

-0.12

 

133

-0.07

0.81

0.23

-0.14

 

-0.04

 

0.50

0.08

-0.07

 

0

0.00

0.00

0.47

0.76

 

0.00

 

0.00

0.26

0.36

B2u

614

-0.01

-0.03

0.00

0.07

0.04

0.02

0.93

-0.25

0.14

0.00

 

571

0.02

-0.53

0.02

0.06

-0.06

0.00

-0.14

-0.01

0.83

-0.04

 

467

-0.01

-0.01

-0.03

-0.03

-0.30

-0.22

0.21

0.88

0.03

0.18

 

389

-0.04

0.00

0.10

-0.04

-0.07

0.96

0.01

0.19

0.01

0.12

 

290

-0.27

0.01

-0.08

-0.10

0.03

-0.08

-0.24

-0.15

0.02

0.91

 

223

-0.14

0.42

0.00

0.81

-0.32

0.01

-0.08

-0.06

0.17

0.02

 

201

0.93

0.10

0.19

0.06

-0.06

-0.01

-0.07

-0.05

0.03

0.28

 

177

-0.20

0.04

0.97

-0.07

-0.03

-0.12

0.00

-0.01

0.01

0.00

 

132

-0.02

0.56

-0.08

-0.56

-0.46

-0.01

0.01

-0.17

0.35

-0.10

 

0

0.00

0.47

0.00

0.00

0.76

0.00

0.00

0.26

0.36

0.00

B 3u

535

-0.25

0.07

-0.04

-0.21

-0.07

0.27

0.59

-0.49

0.46

-0.09

 

484

0.15

-0.05

0.10

-0.28

0.03

0.85

-0.21

-0.10

-0.33

0.09

 

431

-0.21

0.10

-0.04

-0.04

0.19

0.30

0.16

0.81

0.35

-0.04

 

343

-0.04

-0.53

-0.03

-0.20

0.22

-0.14

0.57

0.15

-0.45

0.25

 

315

0.05

0.82

-0.02

-0.12

0.13

-0.09

0.25

0.01

-0.31

0.35

 

244

-0.25

-0.14

-0.01

0.21

-0.19

0.07

-0.16

-0.05

0.24

0.86

 

181

-0.26

0.03

0.95

0.14

0.05

-0.03

0.06

0.00

-0.07

-0.05

 

131

-0.06

-0.03

-0.06

0.12

0.93

0.00

-0.19

-0.24

0.15

0.06

 

106

0.71

-0.06

0.29

-0.40

0.05

-0.15

0.02

0.06

0.41

0.21

 

0

0.47

0.00

0.00

0.76

0.00

0.26

0.36

0.00

0.00

0.00

Declarations

Authors’ Affiliations

(1)
Physics Department, Indian Institute of Technology
(2)
Physics Department, Amity University

References

  1. Kusters RM, Singleton J, Keen DA, McGreevy R, Hayes W, Physica B: 1989, 155: 362-
  2. von Helmholt R, Wecker J, Holzapfel B, Schultz L, Samwer K: Phys Rev Lett. 1993, 71: 2331-10.1103/PhysRevLett.71.2331.View ArticleADSGoogle Scholar
  3. Jin S, Tiefel TH, McCormack M, Fastnacht RA, Ramesh R, Chen LH: Science. 1994, 64: 413-10.1126/science.264.5157.413.View ArticleADSGoogle Scholar
  4. Tokura Y, Urushibara A, Moritomo Y, Arima T, Asamitshu A, Kido G, Furukawa N: Science. 1994, 63: 3931-Google Scholar
  5. Munoz A, Casais MT, Alonso JA, Martinez-Lope MJ, Martinez JL, Fernandez-Diaz MT: Inorg Chem. 2001, 40: 1020-10.1021/ic0011009.View ArticleGoogle Scholar
  6. Munoz A, Alonso JA, Casais MT, Martinez-Lope MJ, Martinez JL, Fernandez-Diaz MT: J Phys: Condensed Matter. 2002, 14: 3285-10.1088/0953-8984/14/12/315.ADSGoogle Scholar
  7. Kimura T, Goto T, Shintani H, Ishizaka K, Arima T, Tokura Y: Nature London. 2003, 426: 55-10.1038/nature02018.View ArticleADSGoogle Scholar
  8. Kimura T, Ishihara S, Shintani H, Arima T, Takahashi KT, Ishizaka K, Tokura Y: Phys Rev B. 2003, 68: 060403(R)-10.1103/PhysRevB.68.060403.View ArticleADSGoogle Scholar
  9. Goto T, Kimura T, Lawes G, Ramirez AP, Tokura Y: Phys Rev Lett. 2004, 92: 257201-10.1103/PhysRevLett.92.257201.View ArticleADSGoogle Scholar
  10. Dabrowski B, Kolesnik S, Baszczuk A, Chmaissem O, Maxwell T, Mais J: J Solid State Chem. 2005, 178: 629-10.1016/j.jssc.2004.12.006.View ArticleADSGoogle Scholar
  11. Martin Carron L, de Andres A: J Alloys and Compounds. 2001, 323: 417-10.1016/S0925-8388(01)01101-X.View ArticleGoogle Scholar
  12. Martin Carron L, de Andres A, Martinez-Lope MJ, Casais MT, Alonso JA: J Alloys and Compounds. 2001, 323: 494-10.1016/S0925-8388(01)01047-7.View ArticleGoogle Scholar
  13. Martin Carron L, de Andres A, Martinez-Lope MJ, Casais MT, Alonso JA: Phys Rev B. 2002, 66: 174303-10.1103/PhysRevB.66.174303.View ArticleADSGoogle Scholar
  14. Wang Wei-Ran , Xu Da Peng , Su Wen Hui : Chin Phys Lett. 2005, 22: 705-10.1088/0256-307X/22/3/051.View ArticleADSGoogle Scholar
  15. Iliev MN, Abrashev MV, Laverdiere J, Jandl S, Gospodinov MM, Wang YQ, Sun YY: Phys Rev B. 2006, 73: 064302-10.1103/PhysRevB.73.064302.View ArticleADSGoogle Scholar
  16. Gupta HC, Sharma V, Tripathi U, Rani N: J Phys Chem Solids. 2005, 66: 1314-10.1016/j.jpcs.2005.05.024.View ArticleADSGoogle Scholar
  17. Alonso JA, Martinez-Lope MJ, Casais MT, Fernandez-Diaz MT: Inorg Chem. 2000, 39: 917-10.1021/ic990921e.View ArticleGoogle Scholar
  18. Dabrowski B, Kolesnik S, Baszczuk A, Chmaissem O, Maxwell T, Mais J: J Solid State Chem. 2005, 178: 629-10.1016/j.jssc.2004.12.006.View ArticleADSGoogle Scholar
  19. Gupta HC, Singh MK, Tiwari LM: J Phys Chem Solids. 2003, 64: 531-10.1016/S0022-3697(02)00336-0.View ArticleADSGoogle Scholar
  20. Rani N, Gohel VB, Gupta HC, Singh MK, Tiwari LM: J Phys Chem Solids. 2001, 62: 1003-10.1016/S0022-3697(00)00253-5.View ArticleADSGoogle Scholar
  21. Brown S, Gupta HC, Alonso JA, Martinez-Lope MJ: Phys Rev B. 2004, 69: 054434-10.1103/PhysRevB.69.054434.View ArticleADSGoogle Scholar
  22. Mills AJ, Littlewood PB, Shraiman BI: Phys Rev Lett. 1995, 74: 5144-10.1103/PhysRevLett.74.5144.View ArticleADSGoogle Scholar

Copyright

© Gupta and Tripathi 2008

This article is published under license to BioMed Central Ltd. 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.

Advertisement