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Physica B 378–380 (2006) 1072–1074 Orbital and lattice dynamics in pyroxenes Z.V. Popovic´ a, , M.J. Konstantinovic´ a,b , Z. Dohcˇevic´-Mitrovic´ a , M. Isobe c , Y. Ueda c a Institute of Physics-Belgrade, P. O. Box 68, 11080 Belgrade/Zemun, Serbia and Montenegro b Studiecentrum voor Kernenergie/Centre d’Etude de l’Energie Nucl 0 eaire, Boeretang 200, B-2400 Mol, Belgium c Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Abstract We have studied with infrared reflectivity and Raman scattering techniques the orbital and lattice dynamics, and the origin of the phase transitions in the pyroxene compounds NaMSi 2 O 6 (with M ¼ Ti, V, and Cr). In the quasi one-dimensional S ¼ 1/2 system NaTiSi 2 O 6 we observe the anomalous high-temperature phonon broadenings and large changes of the phonon energies and line-widths across the phase transition at 210 K. The phonon anomalies originate from an orbital order–disorder type of the phase transition, which we describe as an orbital analogue of the spin-Peierls phase transition. In the S ¼ 1 NaVSi 2 O 6 system orbital degrees of freedom are strongly suppressed since both of the active t 2g orbitals are occupied and the magnetic excitations are well described within the Heisenberg model, indicating that at T N ¼ 19 K this system orders antiferromagnetically. The NaCrSi 2 O 6 has a fully polarized t 2g core, no orbital degrees of freedom, and no anomalous phonon broadening in the Raman spectra. r 2006 Elsevier B.V. All rights reserved. PACS: 78.30.Hv; 63.20.Dj; 64.70.Kb Keywords: Orbital ordering; Pyroxenes; Infrared and Raman spectra Recently, the pyroxene compounds with transition metal ions M 3+ ¼ Ti, V, Cr [1–6] have drawn great attention as low-dimensional magnets. Among them, NaTiSi 2 O 6 is of particular interest because it is an S ¼ 1/2 chain system that differs from other S6¼1/2 pyroxenes due to the lack of low-temperature antiferromagnetic order, and instead shows signs of opening a spin gap [1]. The structure of pyroxenes can be described in terms of alternating tetrahedral and octahedral layers that lie parallel to the (1 0 0) plane. The octahedral layer contains isolated chains of edge-sharing MO 6 octahedra. Because of edge-sharing the octahedral chain looks like a zigzag chain formed by M 2 O 10 dimmers. The magnetic moments in pyroxenes come from the M ions, with different spins depending on the ionic states Ti 3+ corresponds to S ¼ 1/2, V 3+ to S ¼ 1, and Cr 3+ to S ¼ 3/2. At room temperature, all M ions are at the same crystal-lographic site [2] and the chains can be regarded as uniform linear chains with S ¼ 1/2, 1, and 3/2 for M ¼ Ti, V, and Cr, respectively. The magnetic susceptibility measurements of NaTiSi 2 O 6 show Curie–Weiss behavior at high temperatures, followed by sharp decrease below the critical temperature T c ¼ 210 K, which is argued to be the indication of opening a spin-gap [1]. Below T c a dimeriza- tion of Ti–Ti distances along the chain was observed using the X-ray scattering [2]. The phase transition in NaTiSi 2 O 6 is described as an orbital order–disorder type of the phase transition with concomitant magnetic and lattice changes. Moreover, Konstantinovic´ et al. [3] have shown that the t 2g orbitals of Ti 3+ ions dominate the exchange and fluctua- tions and argued that the phase transition in NaTiSi 2 O 6 can be regarded as an orbital analogue of the spin-Peierls phase transition. Fig. 1 shows room- and low-temperature Raman spectra of NaMSi 2 O 6 . At a first glance we noted that the phonon lines dramatically broaden in the Ti-pyroxene—an oxide with the smallest spin value. Because of the phonon broadening, the NaTiSi 2 O 6 Raman spectrum at 300 K contains effectively less phonon modes than expected by ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.469 Corresponding author. Tel.: +381 11 3161385; fax: +381 11 3162190. E-mail address: [email protected] (Z.V. Popovic´).

Orbital and lattice dynamics in pyroxenes

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ARTICLE IN PRESS

0921-4526/$ - see

doi:10.1016/j.ph

�CorrespondiE-mail addre

Physica B 378–380 (2006) 1072–1074

www.elsevier.com/locate/physb

Orbital and lattice dynamics in pyroxenes

Z.V. Popovica,�, M.J. Konstantinovica,b, Z. Dohcevic-Mitrovica, M. Isobec, Y. Uedac

aInstitute of Physics-Belgrade, P. O. Box 68, 11080 Belgrade/Zemun, Serbia and MontenegrobStudiecentrum voor Kernenergie/Centre d’Etude de l’Energie Nucl0eaire, Boeretang 200, B-2400 Mol, Belgium

cInstitute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

Abstract

We have studied with infrared reflectivity and Raman scattering techniques the orbital and lattice dynamics, and the origin of the

phase transitions in the pyroxene compounds NaMSi2O6 (with M ¼ Ti, V, and Cr). In the quasi one-dimensional S ¼ 1/2 system

NaTiSi2O6 we observe the anomalous high-temperature phonon broadenings and large changes of the phonon energies and line-widths

across the phase transition at 210K. The phonon anomalies originate from an orbital order–disorder type of the phase transition, which

we describe as an orbital analogue of the spin-Peierls phase transition. In the S ¼ 1 NaVSi2O6 system orbital degrees of freedom are

strongly suppressed since both of the active t2g orbitals are occupied and the magnetic excitations are well described within the

Heisenberg model, indicating that at TN ¼ 19K this system orders antiferromagnetically. The NaCrSi2O6 has a fully polarized t2g core,

no orbital degrees of freedom, and no anomalous phonon broadening in the Raman spectra.

r 2006 Elsevier B.V. All rights reserved.

PACS: 78.30.Hv; 63.20.Dj; 64.70.Kb

Keywords: Orbital ordering; Pyroxenes; Infrared and Raman spectra

Recently, the pyroxene compounds with transition metalions M3+

¼ Ti, V, Cr [1–6] have drawn great attention aslow-dimensional magnets. Among them, NaTiSi2O6 is ofparticular interest because it is an S ¼ 1/2 chain systemthat differs from other S6¼1/2 pyroxenes due to the lack oflow-temperature antiferromagnetic order, and insteadshows signs of opening a spin gap [1].

The structure of pyroxenes can be described in terms ofalternating tetrahedral and octahedral layers that lieparallel to the (1 0 0) plane. The octahedral layer containsisolated chains of edge-sharing MO6 octahedra. Because ofedge-sharing the octahedral chain looks like a zigzag chainformed by M2O10 dimmers.

The magnetic moments in pyroxenes come from the M

ions, with different spins depending on the ionic states Ti3+

corresponds to S ¼ 1/2, V3+ to S ¼ 1, and Cr3+ to S ¼

3/2. At room temperature, all M ions are at the samecrystal-lographic site [2] and the chains can be regarded as

front matter r 2006 Elsevier B.V. All rights reserved.

ysb.2006.01.469

ng author. Tel.: +381 11 3161385; fax: +381 11 3162190.

ss: [email protected] (Z.V. Popovic).

uniform linear chains with S ¼ 1/2, 1, and 3/2 for M ¼ Ti,V, and Cr, respectively. The magnetic susceptibilitymeasurements of NaTiSi2O6 show Curie–Weiss behaviorat high temperatures, followed by sharp decrease below thecritical temperature Tc ¼ 210K, which is argued to be theindication of opening a spin-gap [1]. Below Tc a dimeriza-tion of Ti–Ti distances along the chain was observed usingthe X-ray scattering [2]. The phase transition in NaTiSi2O6

is described as an orbital order–disorder type of the phasetransition with concomitant magnetic and lattice changes.Moreover, Konstantinovic et al. [3] have shown that the t2gorbitals of Ti3+ ions dominate the exchange and fluctua-tions and argued that the phase transition in NaTiSi2O6

can be regarded as an orbital analogue of the spin-Peierlsphase transition.Fig. 1 shows room- and low-temperature Raman spectra

of NaMSi2O6. At a first glance we noted that the phononlines dramatically broaden in the Ti-pyroxene—an oxidewith the smallest spin value. Because of the phononbroadening, the NaTiSi2O6 Raman spectrum at 300Kcontains effectively less phonon modes than expected by

Page 2: Orbital and lattice dynamics in pyroxenes

ARTICLE IN PRESS

500 600 700 800 900 1000 1100

10 K

NaVSi2O6

Raman shift (cm-1)

10 K

NaTiSi2O6

Inte

nsity

(ar

b.un

its)

300 K

300 K NaVSi2O6

NaTiSi2O6

300 KNaCrSi2O6

Fig. 1. Room and 10K temperature Raman spectra of NaMSi2O6

(M ¼ Ti, V, Cr). The laser excitation wavelength was 514.5 nm.

600 800 1000 12000.00

0.01

0.02

0.03

0.04 300 K 200 K 150 K 80 K

Wavenumber (cm-1)

Ref

lect

ivity

, R

0.000.050.100.150.200.250.300.35

NaVaSi2O6

NaTiSi2O6

Fig. 2. Infrared reflectivity spectra of NaTi(V)Si2O6 at different tempera-

tures.

0 50 100 150 200 250 300388389390391392393394395

ω0= 395.6 cm-1

C= - 3.2 cm-1

ω0= 625 cm-1

C= - 1.15 cm-1

Fre

quen

cy (

cm-1

)

Temperature (K)

Ag (O1 -Ti-O1 bending)

NaTiSi2O6

623

624

625

626

627B11 (Ti-O2, Si-O1 stretching)

6

g

Fig. 3. Frequency versus temperature of 388 and 623 cm�1 Raman modes.

Dashed lines represent the anharmonic phonon–phonon scattering

spectra.

Z.V. Popovic et al. / Physica B 378–380 (2006) 1072–1074 1073

factor group analysis [4], and observed in M ¼ V, Cr-pyroxenes.

The infrared (IR) reflectivity spectra of NaMSi2O6

(M ¼ Ti, V), measured at different temperatures between80 and 300K, are given in Fig. 2. By lowering thetemperature, dramatic changes (appearance of new modesor mode splitting) appear in our Raman and IR spectra ofNaTiSi2O6, only (see Figs. 1 and 2). At the phase transitiontemperature Tc ¼ 210K, the anti-symmetric (B) modesbecome symmetric (A), and energy-close modes start tocouple, the case of IR oscillators with energies close to1020 cm�1, Fig. 2.

In Fig. 3 we show the temperature dependence of thefrequency of 388 and 623 cm�1 modes of NaTiSi2O6,obtained by the Lorentzian profile fitting procedure. Thesemodes are isolated, that means they do not couple with

surrounding Raman modes in the low-temperature phase.The frequencies of these modes increase monotonicallyfrom room temperature to the phase transition tempera-ture, where an abrupt change of frequency is observed. Thedrastic frequency variation is a consequence of the changeof crystal and magnetic structure at the phase transitiondue to the orbital ordering [3]. In order to distinguish thephonon–phonon contribution due to the anharmoniceffects from spin-related contribution we have fitted thehigh-temperature part of frequency versus temperaturedependence using a model for the anharmonic phonon–phonon scattering: ophðTÞ ¼ o0 þ C 1þ 2=ðex � 1Þ

� �,

where o0 and C have the values indicated in Fig. 3 andx ¼ _o0/2kT. The calculated spectra are represented bydashed lines in Fig. 3. It is obvious that the dominantcontribution in the frequency versus temperature depen-dence of the 388 and 623 cm�1 modes below the phasetransition arises from lattice and orbital rearrangement butnot from phonon–phonon scattering due to the anharmo-nic effects.We concluded that in NaTiSi2O6 the orbital fluctuations

lead to a dynamic Jahn–Teller phase with anomalousphonon broadening. Below phase transition the dimerizedorbital ordered state takes place leading to huge change ofphonon frequency and broadening.

This work was supported by Serbian Ministry of Scienceand environmental protection under project 141047.

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