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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
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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ARTICLE IN PRESSZ.V. Popovic et al. / Physica B 378–380 (2006) 1072–10741074
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