Normal modes of tetragonal La2NiO4 and La2CuO4, isomorphs of the hight Tc superconductor La2-xSrxCuO4

~

Solid S t a t e Communications, Vol. 72, No. 2, pp. 187-190, 1989. Printed in G r e a t Britain.

0038-I098/8953.00+.00 Pergamon Press plc

NORMAL MODES OF TETRAGONAL La2NiO4 AND La2CuO4, ISOMORPHS OF THE HIGH Tc SUPERCONDUCTOR La2.xSrxCuO4 Frances E. Bates and J.E. Eldridge

Department of Physics, University of British Columbia, Vancouver, B.C. V6T 2A6 Canada (Received 33. July 1989 by G. Burns)

Normal-coordinate calculations of the frequencies and form of the zero-wavevector vibrations of tetragonal La2NiO4 and La2CuO4 are reported. The results of a recent inelastic neutron scattering study of La2NiO4 were used to refine the force field. For La2CuO4, very good agreement is obtained between the calculated and observed infrared frequencies. The calculations indicate that the Raman feature observed at about 228 cm -1 and usually assigned to an Alg mode may be a defect induced A2u mode. Calculated frequency shifts are also given for the La2Cu1804 isomorph.

There has been much interest in the phonon spectra of the high temperature superconductor La2.xSrxCuO4. Lattice-dynamical calculations can help in the assignment of the phonon spectra and the results of these calculations for La2-xSrxCuO4 have been reviewed recently1. Unfortunately, the experimental data available at the time of these calculations was limited to that from mainly ceramic materials. Recent single crystal or aligned crystal studies 2-8 have provided additional information concerning the symmetry type of the phonons. Previously, we have reported normal-coordinate calculations for orthorhombic and tetragonal YBa2Cu3Ox 9,10 and SmBa2Cu3Ox 11. Our initial intention was then to perform similar calculations for La2.xSrxCuO4. However detailed phonon dispersion curves obtained by inelastic neutron scattering have been reported for La2NiO411, a closely related isomorph of the tetragonal form of La2CuO412,13 which has the advantage of forming large, high-quality crystals. The calculations, therefore, were set up to try to reproduce the reported frequencies for the zone-centre normal modes of La2NiO4 and it was hoped that once a suitable force field was obtained, then the force constants could be transfered to the calculation for La2CuO4 • Tetragonal La2NiO4 belongs to the space group I41mmm (D4h17)13. The body-centred unit cell is shown in Figure 1. The Ni atom sits on sites of symmetry D4h, the La atoms and Oz atoms on sites of symmetry C4v while the remaining atoms, Ox and Oy sit on sites of symmetry D2h. The seven atoms of the primitive unit cell yield a total of 18 vibrational modes which form the irreducible representation :

..........~ y

X

©

o

• Ni @ La

Figure 1.

The tetragonal body-centred unit cell of La2NiO4

The normal coordinate calculations were performed as described previously9-11. The initial force field consisted of simple bond-stretching and anglebending force constants. The force constants were then adjusted to reproduce the zone-centre frequencies determined by inelastic neutron scattering12 and listed in Table 1. The major changes to our initial force field were : the initial value of the force constant for the short La-Oz bond that is parallel to the c axis was too small while those values adopted for the other La-Oz or La-Ox,y bonds and the angle-bends were too large. The final force field used for La2NiO4 is given irr Table 2 and consists of five bond-stretching, two angle-bending and two interaction force constants. The interaction constant i 1 relates collinear internal coordinates while i2 relates perpendicular internal coordinates. The calculated frequencies and potential energy distribution (P.E.D.) for the normal modes are given in Table 1"~. InFigure Z the forms of the normal modes are given. The displacement of the atoms is similar to that reported by Rauh and Geick for K2ZnF415.

F= 2Alg + 2Eg + 3A2u + B2u + 4Eu. The Raman-active modes are of type Alg and Eg and the infrared-active modes are of type A2u and Eu. The B2u mode is inactive in both the infrared and Rarnan spectra.

187

188

NORMAL MODES OF TETRAGONAL La2NiO4AND La2CuO4

Vol. 7 2 , No. 2

Table 1. Calculated and Observeda Frequencies for La2NiO4 and La2CuO4

P.E.D. b La2NiO4

La2NiO4 La2CuO4 Mode "0obs "0cal "0cal "0obs "o160/'0180

.60M1 + .48LI

Alg

450

450

431

.39L3 +.18L1

Alg

150

138

141 148/228 1.001

1.04L2 + .2313 - .36il

Eg

250

252

246

230

1.052

.57L3 + .3213+. 17il

Eg

88

83

79

89

1.009

•73M1 + .29L1

A2u

495

500

469

500

1.046

.50L3 +.4713

A2u

343

343

353

340

1.057

.46L1 + .24L3

A2u

225

220

215

240

1.007

.86L3 + .6013- .25il -.20i2

B2u

275

276

284

i.a.

1.060

.98M2

Eu

652

651

662

667

1.046

.52L3 + .36~

Eu

348

359

355

360

1.056

1.1L2+.2613 +.24L3 +.21a -.45i1 -.37i2 .4413 +.30L3 +.25ct

Eu

220

219

215

220

1.057

Eu

147

124

116

125

1.012

428

1.059

a The observed frequencies are from reference 12 for La2NiO4 and from references 28,17-19 for La2CuO4. b See Table 2 for the identification of the force constants.

Table 2.

Force Constants for La2NiO4 and La2CuO4 La2NiO4

Force Constant

Bond Type

Distance(/~)a

La2CuO4 Valueb

Distance(/~)c

Valueb

M1

M - Oz (2) d

2.24

1.17

2.412

0.985

M2

M - Ox,y (4)

1.93

1.55

1.890

1.63

L1

La - Oz (2)

2.33

0.86

2.355

0.86

L2

La - Oz (8)

2.78

0.29

2.732

0.29

L3

La - Ox,y (8)

2.61

0.34

2.642

0.34

o~

Ox- M - Oy (4)

0.45

0.45

13

Oz- M - Ox,y (8)

0.40

0.40

il

M1/L1, L2/L2, L3/L3

0.10

0.10

i2

L2/L2, L3/L3, L2/L3

0.04

0.04

M= Ni or Cu. a From reference 13 b Force constant units are: stretching: mdyne /~-1 and bending: mdyne /k rad -2 c From reference 14. d Number of internal coordinates.

NORMAL MODES OF TETRAGONAL La2NiO4AND La2CuO 4

Vol. 72, No. 2

)

.4

o

o

o-d

Zo

Alg 1

cm - 1

o-c

Do

O

(

,11

A l g 450 cm- I

Eg 252 cm - 1

Eg 83 cm-1

i

0

DO

A2u 500 cm- 1

~

O

A2u 343 cm I

O

A2u 220 cIn- I

)

(

(

)

(

(~

P(3,-

%

)

(

Eu 651 cm-1

Figure 2.

Eu359 crn I

®

B2u 276 :m 1

c Zo (*-

)

®

Eu 219 cm - 1

I

Eu 124 cm 1

Normal Modes of La2NiO4 .The calculated frequencies are given.

All force constants except for the M-O force constants were transferred to the La2CuO4 calculation. The values for M-O force constants were determined from the empirical formula used previously9,11. The frequencies calculated for this force field as well as the observed frequencies and the calculated ratio of the frequencies for La2Cu1604 to those of the 1gO isomorph are given in Table 1. As would be anticipated the calculated frequencies for La2CuO4 are close to those calculated for La2NiO4. Most of the earlier infrared and Raman work have been reviewed recently 1,16. The observed frequencies given in Table 1 are mainly from single crystal studies 2-8.

189

The more recent studies have the advantage of permitting the assignment of features to a symmetry type. Infrared studies have clearly identified three features at about 240, 340 and 500 cm -1 as A2u modes, and three features at about 120, 360 and 667 cm -1 as Eu modes 2,3,17. Possibly the forth Eu mode has been identified by Gervais et al. 2 at about 220 cm -1. The observation of this mode may be masked by the strong A2u mode at approximately the same frequency. From Table 1 it can be seen that the agreement between the observed and calculated frequencies for the infrared-active modes is very good. The analysis of the Raman features is more difficult. Polarized single-crystal Raman spectra have identified features that appear to correspond to the totally symmetric Alg modes at about 428 and 228 cm -1 4-8 and to one Eg mode at about 230 cm -1 6,8. The assignment of the 428 cm -1 Alg and 230 cm -1 Eg features clearly agree with our calculated values, but the assignment of the 228 cm -1 Alg feature does not. Inelastic neutron scattering studies have been performed and two low-frequency zone centre modes have been observed. One at 89 cm -1 was assigned Eg symmetry and the other at 148 cm -1 which has been assigned as having Alg symmetry 18,19. These frequencies clearly agree with our calculated values. Similar normal-coordinate calculations have also been performed by Maroni et al. 20, who calculated the frequency of the lowest Alg mode to be approximately 150 cm -1. The difference between our calculations and those of Maroni et al., is our inclusion of angle-bending coordinates, whereas, Maroni et al. needed to include an anomalously large Cu-La interaction constant. The assignment of the 228 cm -1 Raman feature is therefore questionable. Comparison of the Raman spectra of doped and undoped La2CuO4, clearly show that the intensity of the 228 cm -1 feature relative to that of the 430 cm -1 feature increases with doping 4,5,7. For some Raman spectra a line is also reported at about 520 cm -1 4,5,7,21,22 which is attributed to a symmetryforbidden A2u mode activated by impurity effects. However by far the strongest A2u mode is that observed at about 240 cm -1. We suggest therefore that the 228 cm -1 Raman feature is also an impurity induced infrared active A2u mode. Acknowledgements - Financial support was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada, Strategic Grant 5-82032 and Operating Grant 5-85653.

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5. 6.

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NORMAL MODES OF TETRAGONAL La2NiO4AND La2CuO 4

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