Broadband dielectric response of CaCu3Ti4O12: From dc to the electronic transition regime
Ch. Kant, T. Rudolf, F. Mayr, S. Krohns, P. Lunkenheimer, S. G. Ebbinghaus, A. Loidl
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Broadband dielectric response of CaCu Ti O : From dc to the electronic transitionregime Ch. Kant, T. Rudolf, F. Mayr, S. Krohns, P. Lunkenheimer, S. G. Ebbinghaus, and A. Loidl Experimental Physics V, Center for Electronic Correlations and Magnetism,University of Augsburg, 86135 Augsburg, Germany Solid State Chemistry, University of Augsburg, 86135 Augsburg, Germany (Dated: November 7, 2018)We report on phonon properties and electronic transitions in CaCu Ti O , a material whichreveals a colossal dielectric constant at room temperature without any ferroelectric transition. Theresults of far- and mid-infrared measurements are compared to those obtained by broadband di-electric and millimeter-wave spectroscopy on the same single crystal. The unusual temperaturedependence of phonon eigenfrequencies, dampings and ionic plasma frequencies of low lying phononmodes are analyzed and discussed in detail. Electronic excitations below 4 eV are identified astransitions between full and empty hybridized oxygen-copper bands and between oxygen-copperand unoccupied Ti 3 d bands. The unusually small band gap determined from the dc-conductivity( ∼
200 meV) compares well with the optical results.
PACS numbers: 63.20.-e, 78.30.-j, 77.22.Ch
I. INTRODUCTION
After first reports of very large dielectric constants oforder up to 10 in CaCu Ti O (CCTO) in ceramicsamples, single crystals, and thin films, experimen-tal evidence has been provided that these colossal valueshave their origin in Maxwell-Wagner like relaxation phe-nomena, characteristic for inhomogeneous media. Planardefects in single crystals or grain boundaries in ceramics as well as contact phenomena and surface effects wereconsidered as possible sources for the unconventional di-electric response in CCTO. However, also intense searchfor intrinsic mechanisms still keeps going on, an examplebeing a recent report on nanoscale Ca/Cu disorder. In addition to this unsettled dispute about the origin ofcolossal dielectric constants in CCTO, another interest-ing phenomenon was detected: The dielectric constant asmeasured by far-infrared (FIR) spectroscopy is as largeas 80 at room temperature and increases with decreasingtemperature contrary to what is expected for a nor-mal anharmonic solid. This effect was investigated insome detail by Homes et al . and explained in terms ofcharge-transfer processes.The present investigation deals with the following top-ics: i) The complete phononic response, which has beenmeasured by FIR spectroscopy as function of tempera-ture, is analyzed in full detail: eigenfrequencies, damp-ings, and ionic plasma frequencies are determined forall modes to study the unusual temperature dependence.Our results are compared to published results and tomodel calculations of the lattice dielectric response ofCCTO from first principles. ii) Within the lowfrequency reflectivity spectrum, which is dominated byphonon modes, we detect an unusually large number ofcrossing points in the reflectivity ( ∂R/∂T = 0), whichseems to be too significant to be ignored or to be ex-plained by accidental effects. iii) Electronic excitations for energy transfers up to 4 eV are studied via the dy-namic conductivity and are compared to ab-initio bandstructure calculations. iv) The dynamic conductivityand dielectric constant from infrared and millimeter-wavespectroscopy are directly compared to broadband dielec-tric results to visualize the full dielectric response ofCCTO to electromagnetic fields over 15 decades in fre-quency and finally, v), we derive the band gap from thedc conductivity obtained from the dielectric results andfind good agreement with the theoretically predicted op-tical band gap, which is in accord with the IR results. II. EXPERIMENTAL DETAILS
Single crystals were grown by the floating-zone tech-nique using a growth furnace equipped with two 1000 Whalogen lamps, with the radiation focused by gold-coatedellipsoidal mirrors. Polycrystalline bars, prepared as re-ported in Ref. 6, cold-pressed and sintered in air for 12 hat 1000 ◦ C, served as seed and feed rods. The rods wererotated with a speed of 30 rpm, while the feed was keptstill. The growth rate was adjusted to 5 mm/h. Crystalgrowth was performed in oxygen (flow rate 0.2 l/min)at a pressure of 4 bar, to avoid thermal reduction ofcopper. High purity single crystals with a lattice con-stant of 0.7391 nm and free of impurity phases were ob-tained. CaCu Ti O belongs to a unique class of per-ovskite derived structures in which the TiO octahedraare strongly tilted to form an ideal square planar coor-dination for the Cu cations. The tilting of the octa-hedra and the concomitant non-cubic site symmetry ofTi strongly reduces the possibilities for off-center dis-placements and rules out long-range polar order of theTi ions. Thus this class of compounds usually does notdisplay ferroelectricity. For the dielectric measurements silver paint contactswere applied to opposite faces of the disc like single crys- log [ (Hz)] ’ ( - c m - )
300 K 40 K
CCTO ’ -6 -3 s n FIG. 1: Dielectric constant and dynamic conductivity ofCCTO over 15 decades in frequency for various temperatures.Symbols and the lines at ν > Hz show experimental data.Dashed lines are fits of the data beyond the relaxation tak-ing into account dc and ac conductivities, the latter describedby sub- and super-linear power laws ν s and ν n , respectively(dash-dotted lines, see text). tals. The complex dielectric permittivity as function oftemperature was measured over nine frequency decadesfrom 1 Hz up to 1.3 GHz (for experimental details seeRef. 14). Additional measurements using a quasiopticspectrometer in Mach-Zehnder configuration were per-formed in a frequency range from 60 to 120 GHz. In thefar- and mid-infrared range, reflectivity measurementswere carried out using the Bruker Fourier-transform spec-trometers IFS 113v and IFS 66v/S, which both areequipped with He bath cryostats. In most cases the re-flectivity spectra were directly analyzed using a general-ized oscillator model with four parameters per phononmode.
To calculate the dielectric loss from the ex-perimentally obtained reflectivity, we used a smooth ω − h extrapolation to high frequencies. The low-frequency ex-trapolation was based on the measured dielectric data. III. RESULTS AND ANALYSIS
A survey of the dielectric constant ε ′ ( ω ) and the dy-namic conductivity σ ′ ( ω ) over 15 decades in frequencyis shown in Fig. 1 for temperatures between 40 K and300 K. Fig. 1 impressively documents how, at least at
250 500 750 1000 wave number (cm -1 ) r e f l e c t i v i t y CCTO
295 K
400 50002040 d i e l e c t r i c l o ss LSDA
FIG. 2: (Color online) Reflectivity spectrum of CCTO at295 K. The solid line is the result of a fit using ten oscil-lators as described in the text. Inset: Dielectric loss obtainedby Kramers-Kronig analysis. The arrows indicate the posi-tions of expected loss peaks according to Ref. 11. Note thatthe predicted resonance at 471 cm − is completely absent. room temperature, the “relaxational” dielectric responsefor frequencies below 10 GHz is decoupled from the ionic( ν = 10 Hz - 2 × Hz) and from the electronic( ν > × Hz) processes. The upper frame indicatesthat the relatively high intrinsic dielectric constant of theorder of 100 detected at the higher frequencies and lowertemperatures of the dielectric experiments can beascribed to the ionic polarizability. ε ∞ , defined as ε ′ be-yond the phonon modes and determined by the electronicpolarizability only, is well below 10. The intrinsic conduc-tivity of CCTO in the lower frame of Fig. 1, specifically at40 K, follows a universal behavior where the dc conduc-tivity with ν at low frequencies is followed by Jonscher’suniversal dielectric response with ν . (Ref. 18) and by asuper linear power-law with ν . at even higher frequen-cies. Fits using this approach are indicated as dashedlines for ε ′ and σ ′ in Fig. 1. This sequence of dc, as wellas sub-linear and super-linear ac conductivity regimes hasbeen observed in a number of disordered semiconductorsand transition-metal oxides. A. Phonon excitations
Fig. 2 shows the measured reflectivity of CCTO at295 K including the results of a fit using ten oscilla-tors described by four parameters each. The theoret-ical modeling which has been used in this work is out-lined in detail in Ref. 20. For each phonon mode the fitparameters are the transverse optical (TO) and longitu-dinal optical (LO) eigenfrequencies ω T O and ω LO and thedamping functions γ T O and γ LO . In addition, the elec-tronic polarizability is taken into account by ε ∞ , whichis treated as free parameter. This model yields an al-most perfect description of all eigenmodes as observed
100 12005001000 mode 1 d i e l e c t r i c l o ss wave number (cm -1 )
380 400 050100150
5K 50K 100K 150K 200K 250K 295K mode 7
FIG. 3: Dielectric loss of mode 1 (left panel) and mode 7 (rightpanel) as function of wave number for various temperatures. in the reflectivity spectrum. Similar results have beenobtained for a series of measurements at different tem-peratures down to 5 K. From fits up to 2000 cm − ε ∞ ,which is due to electronic polarizability only, has beendetermined. ε ∞ obtained from these fits was found toscatter between 6 and 7, with no systematic tempera-ture variation. Hence, for all further analysis we usedan average value of 6.5 for all temperatures. A list ofthe LO and TO mode frequencies and dampings as wellas the effective ionic plasma frequencies Ω and the di-electric strengths ∆ ε are given in Tab. I. For the def-inition of plasma frequency and dielectric strength seeRef. 20. The experimental results documented in Tab. Icompare reasonably well with first-principle calculationsof the TO eigenfrequencies of CCTO within local spin-density approximation (LSDA) by He et al ., which areshown in the second row of Tab. I. All experimentallyobserved eigenfrequencies lie in a frequency range of ap-proximately ±
10 cm − when compared to the theoreti-cal predictions. However a mode of moderate strength,predicted to occur at 471 cm − (Ref. 11) is fully miss-ing in the reflectivity data. Indeed while the symmetryof the crystal allows for 11 IR-active modes, only tenare observed experimentally. A closer look into Fig. 2shows that fit and experimental result almost coincideand it is hard to believe that an extra mode of consider-able strength can be hidden in this reflectivity spectrum,if not two eigenfrequencies are accidentally degeneratedwithin ± − . To check this possibility in more de-tail, the inset of Fig. 2 shows the dielectric loss vs. wavenumber in the frequency range from 400 to 530 cm − .The arrows in the inset indicate the eigenfrequencies astheoretically predicted. While theory meets the modesclose to 420 and 500 cm − there is not the slightest indi-cation of an additional mode close to 471 cm − . Due tothe rather low intensity of the mode close to 500 cm − ,it seems unreliable that the missing mode is hidden un-derneath it. This obvious disagreement between theoryand experiment remains to be settled. mode ω (cm − ) γ (cm − ) Ω (cm − ) ∆ ε TO LO TO LO1 125 119.2 129.8 11.8 1.3 478.2 16.12 135 134.5 152.7 5.2 2.5 591.1 19.43 158 158.1 181.1 4.2 2.4 630.7 15.94 199 195.1 216.1 5.2 4.7 599.3 9.45 261 250.4 303.9 11.9 3.4 914.6 13.36 310 307.7 352.9 4.5 4.3 799.9 6.87 385 382.9 407.7 8.8 5.5 608.7 2.58 416 421.3 487.3 9.1 12.2 920.6 4.89 47110 494 506.9 542.4 13.2 10.2 677.9 1.811 547 551.6 760.3 10.2 32.2 1333.8 5.8TABLE I: Eigenfrequencies ω and dampings γ of both trans-verse (TO) and longitudinal optical (LO) phonon modes ofCCTO at 5 K. Additionally the plasma frequencies Ω anddielectric strengths ∆ ε are provided for each mode. The sec-ond row contains the frequencies of IR-active phonon modescalculated by He et al .. In the following we will address the different phononmodes with numbers as indicated in Tab. I. A closerinspection of this table reveals rather unusual details.Specifically, for modes 1 and 5, γ T O is much larger com-pared to γ LO , contrary to what is expected in a canon-ical anharmonic solid. This may be at least partly re-lated to the unconventional temperature dependence ofeigenfrequencies and damping (see below). In what fol-lows we will give a detailed description of the tempera-ture dependence of some of the polar phonon modes inCCTO. The modes can be grouped into two fractions:the first 5 modes reveal an unusual temperature depen-dence which cannot be explained by normal anharmoniceffects. Phonons number six up to number eleven canbe classified as phonon excitations of a classical anhar-monic solid. As prototypical examples, Fig. 3 shows thedielectric loss of phonon 1 and phonon 7 as function ofwave number for a series of temperatures. With decreas-ing temperature, phonon 1 which lies close to 120 cm − at room temperature, broadens, shifts to lower frequen-cies and strongly increases in dielectric strength. On thecontrary phonon 7, which appears close to 380 cm − at295 K, becomes narrow and shifts to higher frequencieson lowering the temperature, a behavior reflecting anhar-monicity due to phonon-phonon scattering processes. Aswill be shown later, in this case the dielectric strengthalmost remains constant which is expected in a purelyionic solid with no charge transfer processes and no fer-roelectric instability.The results of a detailed 4-parameter analysis are doc-umented in Fig. 4: LO and TO eigenfrequencies (upperframes) and dampings (middle frames), as well as theionic plasma frequencies (lower frames) are shown forphonon 1 (left frames) and phonon 7 (right frames). For ( c m - ) temperature (K) LO TO ( c m - ) mode 1 LO ( c m - ) TO mode 7 LOTO
CCTO
LOTO
FIG. 4: (Color online) Eigenfrequencies, dampings andplasma frequencies for mode 1 (left frames) and mode 7 (rightframes) as function of temperature. The lines are drawn toguide the eyes. mode 1 the TO mode softens considerably and its damp-ing is unusually large and increases on decreasing tem-perature. As has been documented already by Homes etal ., the plasma frequency increases by as much as 60%when the temperature is lowered from room temperaturedown to 5 K. On the other hand, mode 7 shows con-ventional behavior. LO and TO eigenfrequencies slightlyincrease and the inverse life times decrease when tem-perature is lowered. The plasma frequency almost re-mains constant at a value of (609 ±
2) cm − , whichcertainly is within the experimental uncertainties. Asthe ionic plasma frequency, which corresponds to the ef-fective charges, is proportional to the difference of thesquared LO and TO eigenfrequencies, it is obvious thatthe increase of the plasma frequency Ω of mode 1 pre-dominantly corresponds to the softening of the transverseoptic mode (see upper left frame in Fig. 4). At presentit is unclear whether this observation indicates an un-derlying ferroelectric instability or points towards chargetransfer processes as driving forces.As documented in Tab. I for 5 K, we calculated thedielectric strength for all modes and determined thesevalues as function of temperature. The lower frame inFig. 5 shows the static dielectric constant ε s , which cor-responds to ε ∞ plus the sum over the dielectric strengthsof all modes. According to this FIR result, ε s increasesfrom 83 at room temperature to approximately 100 at low ’ s temperature (K)CCTO FIG. 5: (Color online) Upper panel: Dielectric constant forvarious frequencies as function of temperature obtained by di-electric spectroscopy. Lower panel: static dielectric constantderived from FIR experiments. temperatures. This has to be compared to measurementsof the dielectric constant at GHz frequencies, which cor-responds to the intrinsic static dielectric constant. Theseresults are documented in the upper frame of Fig. 5. TheGHz dielectric constant indeed roughly follows the FIRresults, especially it shows similar temperature depen-dence. The strong increase of ε ′ as detected at lower fre-quencies corresponds to Maxwell-Wagner like effects. In discussing the phonon properties we would like topoint towards another interesting phenomenon, whosenature and origin are unclear at present. Each pair of TOand LO modes creates a rectangular shaped band in thereflectivity: In an ideal harmonic solid one would expectthat the reflectivity R is close to unity between the TOand the LO modes. The decrease of R ( ω ) with increas-ing temperature follows from an increasing anharmonic-ity. In the temperature dependent reflectivity spectra ofCCTO, each band exhibits two striking crossing points.In optical spectroscopy of chemical species, a so-calledisosbestic point usually defines a point on the wavelengthscale, where two species have exactly the same absorp-tion. Isosbestic points have sometimes also been iden-tified in the dynamical conductivity of transition metaloxides and were explained in terms of spectral weighttransfer driven by strong electronic correlations. Quitegenerally it can be stated that whenever a system can bedescribed by a superposition of two components with dy-namic quantities which only depend linearly on density,isosbestic points are expected to occur. In particularthis also applies to the temperature dependence as long
130 140 1500.60.70.80.9 r e f l e c t i v i t y wave number (cm -1 ) CCTO mode 2
380 400 0.20.40.60.8 mode 7
FIG. 6: Raw reflectivity data for mode 2 (left panel) and mode7 (right panel) for various temperatures. Note the isosbesticpoints, i.e. points of temperature independent reflectivity. as the total density is constant. In our case each reflectiv-ity band exhibits two wavelengths where the reflectivityexactly is temperature independent, i.e. ∂R/∂T = 0.As an example Fig. 6 shows the reflectivity at around140 and 390 cm − . Close to each TO and LO mode wefind these crossing points where indeed the reflectivityis temperature independent within experimental uncer-tainty. Again we would like to stress that similar obser-vations can be made for each reflectivity band of CCTO.At present, however, it is unclear how the reflectivity ofCCTO can be described by the interaction of light withtwo components. One could think of microscopic (elec-tronic) phase separation. Indeed reports on nanoscaledisorder of Cu and Ca sites from x-ray absorption finestructure measurements and reports of the coexistenceof strained and unstrained domains by scanning electronmicroscopy provide some arguments in favor of this ex-planation. One also could speculate that in CCTO theCuO planes and the TiO octahedra behave like two in-dependent components being responsible for the occur-rence of isosbestic points in all absorption bands. B. Electronic exitations
Finally we studied the low-lying electronic transitionsup to 30000 cm − , corresponding to an energy of 3.8 eV.The results are documented in Fig. 7, which shows thereal part of the dynamic conductivity vs . wave number ona double-logarithmic scale. The spectral response below700 cm − is dominated by the phonon response. Beyondthe phonon regime the conductivity gradually increasesup to 10000 cm − and then shows a stronger increasewith a peak close to 24000 cm − corresponding to 3.0 eV.We would like to stress that the conductivity below 1 eV( ≈ − ) is relatively small (note the double loga-rithmic scale of Fig. 7) and slightly depends on the ex-trapolation scheme beyond 4 eV, used for the Kramers-Kronig analysis. However, all reasonable extrapolationsyield similar results with only slight differences in the tail c ondu c t i v i t y ( - c m - ) wave number (cm -1 ) CCTO
295 K
Cu 3d - O 2p Ti 3d
FIG. 7: (Color online) Dynamic conductivity of CCTO at295 K. The spectral response can be divided into three majorcontributions: a phonon part (shaded area), transitions intoempty Cu 3 d - O 2 p orbitals (left hatched area) and transitionsinto unoccupied Ti 3 d states (right hatched area). towards the lowest frequencies. When comparing our re-sults to first principle density-functional theory withinthe local spin-density approximation (LSDA) from He etal ., we identify the continuous increase of the conduc-tivity from about 2000 cm − to 10000 cm − with tran-sitions between the empty and filled strongly hybridizedCu 3 d and O 2 p orbitals. The filled bands are locatedjust below the Fermi level while the empty states extendup to 0.7 eV with a maximum close to 0.5 eV and anonset at about 0.25 eV, which corresponds to approxi-mately 2000 cm − . According to theory, the dominantpeak close to 24000 cm − ( ∼ . d -derived empty states from the Ti ions. In the LSDAcalculations this Ti 3 d band of mainly t g character ex-tends from 1.5 to 3.5 eV with a peak maximum close to2.8 eV. Thus, overall the dynamical conductivity at highfrequencies could be determined by the superposition oftwo electronic transition bands located at around 0.75 eVand 3.0 eV as schematically indicated by the hatched ar-eas in Fig. 7. It should be noted that the conductivitytail due to transitions between the hybridized copper-oxygen bands extends to rather low frequencies. In thechosen double-logarithmic plot, the band gap should beread off at a limiting vertical decrease of σ ′ ( ν ) at low fre-quencies. This is not observed in the data, most likelydue to the mentioned uncertainties at very low conductiv-ity values or possible phonon tails as expected for indirecttransitions. Clearly, while our results are not a proof ofthe bandstructure of CCTO, they at least are compat-ible with the LSDA calculations, especially concerningthe predicted small band gap. It can be expected, that this optical band gap alsodetermines the dc conductivity. In Fig. 8 we show theconductivity of CCTO deduced from the dielectric ex-periments over 9 decades of frequency for a series oftemperatures. At high frequencies and low temperatures -9 -6 -3 log [ (Hz)] ’ ( - c m - ) CCTO
40 K60 K80 K 100 K140 K180 K220 K300 K5 10 10 -4 -2 / [T(K)] d c E g = FIG. 8: (Color online) Dynamic conductivity over 9 decades offrequency for CCTO for various temperatures. Solid lines rep-resent the results of an equivalent-circuit analysis (see text).The inset shows the resulting dc conductivity at T ≥
100 Kin an Arrhenius-type representation. σ ′ ( ν ) of CCTO is dominated by ac conductivity, result-ing in a power-law increase towards the highest frequen-cies. At the highest temperatures the conductivity in theMHz to GHz range is purely of dc type and independentof frequency. Towards lower frequencies, the well-knownMaxwell-Wagner relaxation leads to a step like decreaseof σ ′ . The dc plateaus for each temperature can easilybe identified. At 40 K the dc plateau is located between50 Hz and 10 kHz and shifts to higher frequencies withincreasing temperature. It is located beyond 10 MHz for300 K. These dc conductivity plateaus also show up inthe lower frame in Fig. 1.The complex frequency-temperature dependence of theconductivity can only be exactly analyzed utilizing anequivalent-circuit analysis including elements for the bulksample and surface layers. The solid lines in Fig. 8 re-sult from fits assuming two RC circuits for two types ofbarriers (e.g., external and internal) and one RC circuitincluding ac conductivity for the bulk sample. For de-tails see Refs. 5, 6, and 7. The resulting dc conductivityat T ≥
100 K is indicated in the inset of Fig. 8 in an Ar-rhenius type of presentation. The energy barrier derivedfrom the Arrhenius fit is of the order of 200 meV, in goodagreement with the theoretical band gap and consistentwith the optical results (cf. Fig. 7). Here we assumedan intrinsic semiconductor with constant mobility and acharge-carrier density proportional to exp[ − E g / (2 k B T )].At lower temperatures, deviations from Arrhenius behav-ior show up, which may be ascribed to hopping conduc-tivity of localized charge carriers as will be discussed ina forthcoming paper. IV. CONCLUDING REMARKS
In summary, our detailed optical characterization ofCCTO and the comparison with broadband dielectricspectroscopy performed on the same single crystal re-vealed a number of unusual properties of this material, inaddition to the well-known colossal dielectric constants.We analyzed in detail the temperature dependence ofthe phonon modes and determined LO and TO eigenfre-quencies and dampings as well as the ionic plasma fre-quencies. The low lying modes (numbers 1 to 5, see Ta-ble I) do not behave like phonons of normal anharmonicsolids. The TO modes soften and the plasma frequenciesstrongly increase. At present it is unclear if this is dueto an underlying ferroelectric instability, which howeverdoes not lead to a transition even for lowest temperaturesor if this indicates significant charge-transfer processes ashas been assumed by Homes et al .. The phonon modeswhich are higher in frequency (numbers 6 to 11) exhibitcanonical behavior; i.e. eigenfrequencies and dampingsreveal a temperature dependence characteristic for an an-harmonic solid, which is dominated by phonon-phononinteractions. The damping of the TO mode at 120 cm − shows a cusp close to the antiferromagnetic phase transi-tion. In CCTO the Cu d electrons constitute almostlocalized S = 1 / T N = 24 K. In strongly correlated electron sys-tems often strong spin-phonon coupling is observed. InCCTO, however, only mode 1 shows an anomaly at T N and overall it seems that the phonons are not stronglycoupled to the spin system.The static dielectric constant arising from the phononmodes as derived from the measurements of this work in-creases from roughly 80 at room temperature to approx-imately 100 at 5 K. It nicely scales with the dielectricconstants measured at 1 GHz by dielectric spectroscopy.The purely electronic polarizability leads to ε ∞ = 6 . − , compared to the the-oretical value of 2700 cm − that assumes ideal ionicityfor all atoms. In calculating the ionic plasma frequencyof CCTO, the main contributions result from Ti andO − while Ca and Cu ions contribute less than 1%.The fact that the experimentally observed plasma fre-quency is so close to that calculated for an ideal ionicsolid, demonstrates that at least the TiO octahedra arepurely ionically bonded while the Cu-O subsystem canreveal partly covalent bonds. This seems to be in accordwith the LSDA calculations. The strong ionicity and the weak hybridization be-tween the oxygen 2 p levels and the titanium 3 d states indicate that the underlying nature of the anomalies inCCTO are different to the origin of ferroelectricity in per-ovskite oxides: These model ferroelectrics require stronghybridization, charge distortion, and covalency. How-ever also alternative routes to ferroelectricity were pro-posed, taking into account the strong polarizability ofthe O − ion and recently an attempt has been madeto explain the optical response of CCTO utilizing theseideas. The dynamic conductivity beyond the phonon modesis consistent with two electronic excitations as theoreti-cally predicted from LSDA band structure calculations. They can be ascribed to transitions from the filled hy-bridized O 2 p and Cu 3 d bands to the empty O 2 p /Cu 3 d states and to the empty Ti 3 d orbitals, arsing close to0.75 eV and 3.0 eV, respectively. Acknowledgments
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