Signatures of polaronic excitations in quasi-one-dimensional
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PHYSICAL REVIEW B 67, 035105 ~2003!Signatures of polaronic excitations in quasi-one-dimensional LaTiO3.41
C. A. Kuntscher*Material Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlandsand 1. Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
D. van der MarelMaterial Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
M. Dressel1. Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
F. Lichtenberg and J. MannhartExperimentalphysik VI, Institut fur Physik, EKM, Universitat Augsburg, Universitatsstr. 1, D-86135 Augsburg, Germany
~Received 16 July 2002; published 15 January 2003!
The optical properties of quasi-one-dimensional metallic LaTiO3.41 are studied for the polarization along thea andb axes. With decreasing temperature modes appear along both directions suggestive for a phase transi-tion. The broadness of these modes along the conducting axis might be due to the coupling of the phonons tolow-energy electronic excitations across an energy gap. We observe a pronounced midinfrared band with atemperature dependence consistent with~interacting! polaron models. The polaronic picture is corroborated bythe presence of strong electron-phonon coupling and the temperature dependence of the dc conductivity.
DOI: 10.1103/PhysRevB.67.035105 PACS number~s!: 78.20.2e, 71.38.2kteveheing.e-ar
inTitanium oxide compounds have been investigated exsively over the last decades, at the latest since the discoof high-Tc superconductivity in the cuprates, to study trole of electronic correlations and to explore the dopingduced transition from a Mott insulator to a metal, like, e.in La12ySryTiO3.
1,2 Of further interest are the titanates bcause of the proposed polaronic nature of their charge cers. For example, the existence of small polaronsLa12gTiO36d was shown by dc resistivity and thermoelectpower measurements.2,3 Signatures of polaronic carrierwere also found in the optical response of TiO2 , BaTiO3,and SrTiO3 in the form of a midinfrared~MIR! band.
Since a MIR band of ~spin-!polaronic origin at'1000 cm21 was also found in several cuprates912 itseems to be a characteristic feature of this class of cpounds for low doping as well. The proposal that~bi!po-larons might play a major role for the high-Tcsuperconductivity13 stimulated a vast amount of experimetal investigations on this issue.
On the other hand, the nature of the polaronic carriersthe titanates is still under discussion. In this paper we prethe optical properties of another titanium oxide compouLaTiO3.41, to search for polaronic signatures and test thcompatibility with the existing models. Indeed, we findstrong MIR band in the optical response showing a strotemperature dependence. A particular property of LaTiO3.41is its quasi-one-dimensional~quasi-1D! metallic characterwhich was recently found by resistivity measurements.14 It isinteresting to note that a MIR band was also observed fovariety of organic and anorganic quasi-1D metals, lTTF-TCNQ,15 the Bechgaard salts,16 b-Na0.33V2O5,
18 Whether this band is related to the 1D transpand, in particular, is of~vibrational or spin-!polaronic origin,are open questions which we want to address here.0163-1829/2003/67~3!/035105~5!/$20.00 67 0351n-ry
Single crystals of LaTiO3.41 were grown by a floatingzone melting process;14 the oxygen content was determineby thermogravimetry. The layered crystal structure@see Fig.1~a!# is built from slabs of distorted TiO6 octahedra paralleto the (a,b) plane; it is monoclinic with lattice constantsa57.86 , b55.53 , c531.48 , andb597.1. Like forthe closely related compound SrNbO3.41 a characteristicproperty of the structure are the 1D chains of octahedra al
FIG. 1. ~a! Projection along theb axis of the schematic LaTiO3.4crystal structure. The TiO6 octahedra~light grey! are connectedcontinuously via their apical sites forming 1D chains alonga ~greycircles: O atoms, white circles: La atoms; Ti atoms hidden withthe TiO6 octahedra!. ~b! dc resistivityr of LaTiO3.41 versus tem-peratureT along the three crystal axes. Inset: Fit~dashed line! ofsT between 200 and 300 K according to Eq.~2! for small polaronhopping.2003 The American Physical Society05-1
C. A. KUNTSCHERet al. PHYSICAL REVIEW B 67, 035105 ~2003!the a axis.14 LaTiO3.41 belongs to the homologous serieLanTinO3n12 which exhibits a very rich phase diagram:
stoichiometric LaTiO3.00 (n5`, Ti 3d1) is an antiferromag-
netic Mott insulator, while for off-stoichiometricLa12gTiO36d metallic character of polaronic type waobserved;2,3 LaTiOx for 3.00,x,3.50 is conducting,
14 andin particular LaTiO3.41 ~Ti 3d
0.18) shows a quasi-1D metallicbehavior;14 LaTiO3.50 (n54, Ti 3d
0) is a ferroelectric bandinsulator.19 The dc resistivity as a function of temperatureTdepicted in Fig. 1~b! demonstrates the strongly anisotropcharacter of LaTiO3.41. Along the b direction and perpendicular to the (a,b) plane the compound shows a semicoducting behavior, whereas along thea direction theT depen-dence is more complicated: Below 60 Kra rises steeply withdecreasingT, between 60 and 200 K itsT dependence ismetallike, and above 200 Kra slightly decreases with increasingT. This temperature dependence will be discussemore detail later.
Near-normal incidence reflectivity spectra were measufrom 40 to 6000 cm21 ~5 meV0.74 eV! utilizing a Fourier-transform spectrometer equipped with an ultrastable optcryostat. To obtain absolute reflectivities the spectra wdivided by the reflectivity spectra of a gold film recordedthe same set of temperatures, where the film was depositinsitu on the sample. Since no temperature dependencefound above 6000 cm21, the spectra were extended36 000 cm21 by the room-temperature~RT! reflectivity datarecorded with a variable angle spectroscopic ellipsomeEach reflectivity spectrum was extrapolated to low and hfrequencies according to a Drude-Lorentz fit; from the ssequent Kramers-Kronig transformation the phase of the
FIG. 2. Reflectivity R of LaTiO3.41 for Eia and Eib. Inset:Detailed temperature dependence of a phonon mode forEib ap-pearing below 200 K.03510-
flection coefficient and thus the complex dielectric functicould be obtained.
The polarization-dependent reflectivity spectraR(v) ofLaTiO3.41 for several temperatures are shown in Fig. 2. Thclearly demonstrate its quasi-1D metallic character: ForpolarizationEia, i.e., along the chains, we find a metallbehavior with a high reflectivity at low frequencies andsharp plasma edge (vp'3600 cm
21), while the overall lowreflectivity for Eib indicates an insulating character. The otical conductivitys1(v) is presented in Fig. 3. ForEib noelectronic absorption is observed in the far infrared~FIR!;the spectrum below 1000 cm21 consists of a large number ophonon lines, and the onset of interband transitions is foabove 1000 cm21. Along the chainss1 consists of a Drudepeak superimposed by vibrational lines and a pronounMIR band.20 With decreasing temperature we observe tmajor changes in theEia conductivity:~i! in the FIR region,between 50 and 300 cm21, modes~indicated by ticks in theinset of Fig. 3! possibly of vibrational origin appear below100 K which are broader than the others, and~ii ! the MIRband, located around 2500 cm21 at RT, continuously shifts tolower frequencies and its intensity increases; besides, anditional feature appears around 940 cm21. The changes areillustrated by the normalized difference,
Ds1~v,T!5@s1~v,T!2s1~v,300 K!#/s1~v,300 K!,~1!
shown in Fig. 4. In the FIR, below 150 cm21, for T>100 KDs1(v) has slope zero and it increases with dcreasingT due to the increase ofsdc ; but below 100 K the
FIG. 3. Optical conductivitys1 of LaTiO3.41 for Eia andEib.Inset: Phonon contributions1,phononsto s1 for Eia from 35 to 350cm21, obtained by subtracting the Drude term and the MIR ba~from the Drude-Lorentz fit! from the measured spectrum; tickindicate the broad modes which appear below 100 K.5-2
SIGNATURES OF POLARONIC EXCITATIONS IN . . . PHYSICAL REVIEW B67, 035105 ~2003!slope clearly changes and in particular for 45100 cm21
Ds1 increases strongly, indicating additional excitationsthis frequency range.
To quantify these changes we fitted theEia conductivityspectra with the Drude-Lorentz model. The MIR band wmodelled by two Lorentzian functions. As an exampleshow the fit for the RT spectrum in Fig. 5. This way we weable to extract the various contributions~Drude peak, pho-non modes, MIR band! for each temperature. From thspectral weights we calculated the effective number of caers ~per Ti atom! for each contribution according toNeff5@2meV/(pe
2)#/20*0vms1(v)dv, where me is the free-
electron mass, andV the unit-cell volume~containing 20formula units!. The upper integration limitvm was set to15 000 cm21, where the onset of the interband transitionslocated. As is shown in the inset of Fig. 4, the effecticarrier number of the MIR absorption increases as the tperature decreases, but below 75 K a saturation sets in. Fthe integrated intensities of the phonon modes and by uthe ionic charges of the atoms we calculated the effecchargee* according to the sum rule.21 The temperature de
FIG. 4. Normalized differenceDs1 @Eq. ~1!# of LaTiO3.41 forEia, illustrating the appearance of broad modes and the MIR bshift with decreasing temperature. Inset: Effective chargee* of thephonon modes and effective carrier numberNeff per Ti atom of theMIR band as a function of temperature.
FIG. 5. Fit of the RT conductivitys1 of LaTiO3.41 with theDrude-Lorentz model.03510s
pendence ofe* ~inset of Fig. 4! illustrates the substantiaspectral weight growth of the modes with decreasing teperature.
We now want to discuss the observed changes in thetical conductivity in more detail.~i! The appearance of vibrational modes in general suggests a breaking of the crysymmetry. Some of the new modes forEia are already veryweakly present in the 125-K spectrum, but the substangrowth of their spectral weight sets in below 100 K. Thoccurrence of a phase transition in LaTiO3.41 is corroboratedby the development of ten phonon lines forEib with de-creasing temperature~an example is shown in the inset oFig. 2!. A remarkable finding is the broadness of the nelines along the conductinga axis ~see inset of Fig. 3! whichmight be due to the coupling of the phonons to electroexcitations. These low-energy excitations might be exctions across an energy gap atEF which develops below 100K due to the phase transition. A coupling of the phononsthese excitations could also explain their significant specweight growth below this temperature. Since the bromodes appear at frequencies above 50 cm21, one could es-timate the size of the gap to'6 meV. The appearance ostrong modes along the metallic axis caused by a couplinphonon bands to the electronic density was in fact predicby Rice22 when considering organic linear-chain conductowhich undergo a charge-density wave transition. FLaTiO3.41 the presence of strong electron-phonon couplingindicated by the enhanced effective chargee* 51.6 at RT~see inset of Fig. 4! compared to the valuee* 51 if there isno coupling. In general, the interaction between a discrlevel and a continuum of states gives rise to asymmepeaks in the excitation spectra.23 Unfortunately, the largeelectronic background~Drude contribution! and the strongoverlap of the modes render a line-shape analysis and thproof of the asymmetry of the new modes in LaTiO3.41 dif-ficult.
Within this scenario two open questions remain, howevFirst, the dc resisitivity of LaTiO3.41 shows no anomaly andthus no clear signature of a phase transition over the whmeasured temperature range; a possible explanation couthe small number of carriers involved. Second, there isdirect evidence in the optical conductivity spectrum for ecitations across an energy gap. Based on the present exmental results the occurrence of a phase transition thereremains speculative. Additional experimental investigatiofor instance x-ray diffraction or neutron-scattering measuments at low temperature, would be needed to clarify tissue.
~ii ! The strong temperature dependence of the MIR banamely its shift to lower frequencies and intensity increafor decreasingT with a saturation at a specific temperaturrenders an interpretation of the band in terms of interbatransitions unlikely. The observed evolution with tempeture is similar to that of the MIR absorption in the cuprasuperconductors which was attributed to polaroexcitations.10,11 The formation of polarons in LaTiO3.41 iscorroborated by the presence of strong electron-phononpling indicated by the enhanced effective chargee* . Atemperature-dependent MIR band was also found for
C. A. KUNTSCHERet al. PHYSICAL REVIEW B 67, 035105 ~2003!nickelates La22xSrxNiO41d , where it was explained byphoton-assisted hopping of small polarons:24,25 photons inthe MIR range excite self-trapped carriers from a localizstate to localized states at neighboring sites, and the abstion is peaked at an energy twice the polaron binding eneEP .
26 The position of the MIR band thus provides an esmate of EP , which yields EP'\v/2'155 meV forLaTiO3.41at RT. A conduction mechanism due to the hoppiof small polarons, as suggested by the existence otemperature-dependent MIR band, is corroborated by thTdependence ofra ~see Fig. 1!: Starting from the lowest temperature, the steep drop ofra denotes the thermal activatioof charge carriers. At'60 K the carriers are free and witfurther temperature increasera rises since the carriers arincreasingly scattered by phonons; metallic transport isserved. The decrease ofra above 200 K indicates that thcontribution due to hopping of polaronic carriers prevaFor the dc conductivitys(T) due to small polaron hoppingone expects the thermally activated form27
Ts~T!}exp@2EH /~kBT!#, ~2!
whereEH is the hopping energy; the disorder energy is omted since it is negligibly small compared toEH in crystallinebulk materials. In the range 200300 Ksa(T) can be fittedaccording to Eq.~2! ~see inset of Fig. 1! which yieldsEH'35 meV. This thermal activation energy is a factor'2.2 smaller than the activation energyEA5EP/2'78 meV,27 obtained from our optical data; such a discreancy between the thermal and optical activation energieexpected since in the thermally activated process the lahas time to relax andEP is thus reduced.
On the other hand, the temperature dependence ofMIR band in LaTiO3.41the softening with decreasingtemperatureis not compatible with a noncorrelated smpolaron model for strong electron-phonon coupling.4,24,28 Inthe case of the high-Tc cuprate superconductors the MIband softening was interpreted in terms of large polamodels including polaron-polaron interactions.11,2931A dif-ferent approach was recently used by Fratiniet al.32 whoconsidered small polaron absorption for intermedielectron-phonon coupling: Their calculated optical condtivity exhibits a noticeable transfer of spectral weight frohigh to low frequencies with decreasing temperature, likeobserve in LaTiO3.41. Besides, the calculated spectra sh
*Electronic address: email@example.comA. Fujimori, I. Hase, M. Nakamura, H. Namatame, Y. Fujishim
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anomalous peaks at frequencies comparable to the phofrequencies with a strongly temperature-dependent intenThese peaks, denoted as polaron interband transitions,purely electronic in nature and due to transitions betwedifferent subbands in the polaron excitation spectrum. Thmight serve as an alternative explanation for the broad pefound in LaTiO3.41 along the conducting direction.
Whether one of these polaron models actually appliesLaTiO3.41, may be judged from a detailed comparison of tobserved features~MIR absorption features, broad modes! tothe theoretical absorption spectra, thereby consideringnot only vibrational but also spin degrees of freedom cobe involved in the polaron formation, as it was proposedother materials with strong electronic correlations like tcuprates12 or the manganites.33 The clarification of these is-sues is of general importance, since a band in the MIRquency range is a characteristic feature in the optical sptrum of quasi-1D conductors.34 According to the presenresults for LaTiO3.41 the MIR band contains important information on the transport mechanism in quasi-1D systemsthe careful study of its temperature and doping dependenctherefore worthwhile.
In summary, we studied the polarization dependent optresponse of quasi-1D metallic LaTiO3.41as a function of tem-perature. With decreasing temperature modes appear aboth studied crystal axes suggestive for a phase transiThe new modes found along the conducting directiona be-low 100 K are broader than the other modes, which mightcaused by the coupling of the phonons to low-energy etronic excitations across an energy gap. TheEia conductiv-ity spectrum contains a pronounced MIR band whose teperature dependence is similar to that of the MIR absorpin the cuprate superconductors and consistent with~interact-ing! polaron models. The polaron formation in LaTiO3.41 iscorroborated by the presence of strong electron-phononpling and the temperature dependence of the dc conductiThe findings for LaTiO3.41 suggest the general importancepolaronic quasiparticles for the transport mechanismquasi-1D conductors.
We thank P. Haas for providing additional data. This wowas supported by the BMBF~Project No. 13N6918/1! andthe Deutsche Forschungsgemeinschaft.
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