Charge dynamics in thermally and doping induced insulator-metal transitions of (Ti1-xVx)2O3
aa r X i v : . [ c ond - m a t . s t r- e l ] M a y Charge dynamics in thermally and doping induced insulator-metal transitions of(Ti − x V x ) O M. Uchida , J. Fujioka , Y. Onose , , and Y. Tokura , , Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan Multiferroics Project, ERATO, Japan Science and Technology Agency (JST), Tokyo 113-8656, Japan Cross-Correlated Materials Research Group (CMRG), ASI, RIKEN, Wako 351-0198, Japan (Dated:)Charge dynamics of (Ti − x V x ) O with x = 0 − .
06 has been investigated by measurements ofcharge transport and optical conductivity spectra in a wide temperature range of 2 − d t g manifold are observed in the bothinsulating and metallic states, while their large variation (by ∼ . PACS numbers:
Insulator-metal transition (IMT) has been an impor-tant issue of condensed matter physics [1]. In the conven-tional semiconductor, the IMT is achieved by the shift ofthe chemical potential due to the chemical or electrostaticdoping, where the electronic band structure is almostrigid in the course of IMT. Even in the metallic state, thecarrier density is small and proportional to the amountof doping. In typical Mott transitions of correlated d -electron systems such as V O [2] and La − x Sr x TiO [3],on the contrary, the Mott gap collapses with the temper-ature change or the chemical doping as a result of thereconstruction of the electronic structure on a large en-ergy scale comparable to the Coulomb repulsion ( ∼ sev-eral eV) upon the IMT. The carrier number estimatedby the Hall coefficient is large ( ∼ / site) compared withthe dopant concentration in the metallic state. In thehigh- T c cuprate system [4], the parent compound is aMott insulator (to be precise, a charge transfer insula-tor), but the carrier number is comparable to the dopantconcentration in the low-doping and low-temperature re-gion. One of the plausible scenarios for the origin of thedoped-insulator-like feature in the normal state is thepseudogap formation due to the preformed singlet pairsor the resonating valence bond (RVB) state [5].Ti O with an α -corundum structure (Fig. 1(a)) showsa unique IMT [6]. Nominally, there is one 3 d electronper Ti site in Ti O . The nearest neighbor Ti ions alongthe c -axis show dimerization in the crystal lattice andthe two electrons on the Ti-Ti dimer form a singlet pairbelow the insulator-metal transition temperature T IM ( ∼
450 K). As temperature increases, the dimerizationbecomes weaker and the metallic state emerges. Thelow-temperature insulating state cannot be reproducedby the LDA calculations without the explicit considera-tion of the on-site Coulomb correlation [7]. There are twopossible scenarios to explain the IMT. One is the bandcrossing scenario [8, 9, 10]; the IMT is viewed as the tran- (a)(b) -4 -3 -2 -1 R e s i s t i v i t y ( W c m ) Temperature (K) I I ^ c (c) || c x = 00.006 (Ti x V x ) O FIG. 1: (color online). (a) The corundum structure of Ti O .The dashed lines represent the bonds in Ti-Ti dimer. (b)Schematic diagram for the proposed electronic structure inTi O [8]. For clarity, the notation e πg indicates both e π ∗ g and e πg bands, as the e πg - e π ∗ g splitting is small. (c) Temperaturedependence of the resistivity in (Ti − x V x ) O with x = 0,0.006, 0.02, and 0.06 for the current I k c and I ⊥ c . sition from the dimerized insulator to the semimetal. Ifthe singlet state is destabilized, the conducting e πg statemay cross the Fermi energy. The other is the Mott tran-sition [11]. In this scenario, the formation of the singletstate is compatible with the large on-site Coulomb re-pulsion, and the electronic structure is expected to betotally reconstructed on a large energy scale in the courseof the Mott transition as observed in the optical conduc-tivity spectra for a similar dimer system VO [12]. Itis known that the metallic state remains down to thelowest temperature when Ti ions are partially replacedby V ions [13]. In order to elucidate the origin of theIMTs in Ti O , we have investigated the thermally anddoping induced IMTs in (Ti − x V x ) O by optical andtransport measurements. We observe the pseudogap fea-ture in optical spectra even in the metallic state. Drudeweight as well as the carrier number obtained by the Hallmeasurement at low temperature is proportional to theV concentration. These features are consistent with thepicture of the doped band insulator, while the strongelectron correlation on Ti site is essential for the robustsinglet formation.Single crystals of (Ti − x V x ) O with x = 0, 0.006,0.02, and 0.06 were prepared by the floating-zone methodin Ar (93%) and H (7%) atmosphere. The longitudinaland Hall resistivities were measured with PPMS (Quan-tum Design). Polarized reflectivity in the temperaturerange of 10 −
600 K were measured between 0.01 eV and5 eV. The measurements above room temperature wereperformed in the Ar/H or vacuum atmosphere. Reflec-tivity spectra above 5 eV (up to 40 eV) were measured atroom temperature with use of the synchrotron radiationat UV-SOR, Institute of Molecular Science, Okazaki. Forthe Kramers-Kronig analysis to deduce the optical con-ductivity, the spectrum above 40 eV was extrapolatedby ω − function, while below 0.01 eV the Hagen-Rubensrelation and the constant reflectivity were assumed formetallic and insulating samples, respectively. Variationof these extrapolation procedures was confirmed to causenegligible difference in the conductivity spectrum.We show the temperature and doping dependences ofthe resistivity in Fig. 1(c). The resistivity for Ti O shows a steep increase around T IM [6]. The resistivity forthe current parallel to the c -axis ( I k c ) is about threetimes as high as that for I ⊥ c [14]. For x = 0 . x = 0 .
02, the resistivity shows a metallicbehavior, and for x = 0 .
06 the increase of the resistiv-ity around T IM is hardly observed. The anisotropy isobserved even in the metallic state up to x = 0 .
06. Themeasurements of the Hall resistivity [15] and the Seebeckcoefficient [14] indicate that V ion is nominally divalentin (Ti − x V x ) O and thus the holes are introduced intothe valence band (see also Fig. 3(d)).In Figs. 2(a)-(d), we show the optical conductivityspectra at various temperatures in (Ti − x V x ) O with x = 0 and 0.06 for E k c and E ⊥ c . For Ti O , the E k c spectrum shows a clear gap structure of about 0.2eVat the ground state (10 K). (Sharp spikes below 0.1 eVare due to the optical phonon modes [16].) The proposedelectronic structure of Ti O [8] is shown in Fig. 1(b).The t g levels in cubic symmetry split into the a g and e πg levels due to the trigonal ligand field. Furthermore,the a g band splits into the bonding a g and the anti-bonding a ∗ g bands mainly because of the hybridizationwithin the Ti-Ti dimer. Two peaks around 1 eV and3 eV are assigned to the a g - e πg and a g - a ∗ g interbandtransitions, respectively [17]. The a g - a ∗ g dipole transi- (Ti x V x ) O ( x =0) a g - a g * a g - e g p a g - e g p (a) E || c Photon Energy (eV) O p t i c a l C ondu c t i v i t y ( W - c m - ) E ^ c (b) (Ti x V x ) O ( x =0.06) a g - e g p a g - e g p a g - a g * (c) E || c Photon Energy (eV) O p t i c a l C ondu c t i v i t y ( W - c m - ) E ^ c (d) Photon Energy (eV) O p t i c a l C ondu c t i v i t y ( W - c m - ) (f) d = 0.010.040.080.10 R.T. La x Sr x TiO y /2 (e) a g - e g p O p t i c a l C ondu c t i v i t y ( W - c m - ) Photon Energy (eV) d = 00.0060.060.02 ^ (Ti x V x ) O E c Okimoto et al.
FIG. 2: (color online). Optical conductivity spectra at varioustemperatures in (Ti − x V x ) O with x = 0 for (a) E k c and(b) E ⊥ c , and with x = 0 .
06 for (c) E k c and (d) E ⊥ c .Hole-doping dependence of the optical conductivity spectra in(e) (Ti − x V x ) O and (f) La − x Sr x TiO y/ [3]. δ = x (or δ = x + y ) is nominal hole concentration, i.e., δ = 1 − n where n is the number of d electrons per Ti site. A dashed straightline in (f) indicates the hypothetical energy gap feature for δ = 0 . tion in the dimer is prohibited for E ⊥ c . Because of theanisotropic extension of the a g orbital along the c -axis,the a g - e πg transition appears stronger for E k c thanfor E ⊥ c . With increasing temperature, these peaksmarkedly shift to lower energy by about 0.4 eV. Nev-ertheless, the clear band gap feature remains to be ob-served in the whole temperature up to 600 K. For E ⊥ c ,a similar gap structure as well as the conspicuous low-energy shift of the interband transition is also observed.This result is incompatible with the theoretical picturefor the IMT of Ti O based on the Mott-Hubbard scheme[11]. For x = 0 .
06, a Drude peak is observed in the low-energy region, while the peak originating from the a g - e πg transition is robust as in the high-temperature region ofTi O . In Fig. 2(e), we show the doping dependence ofthe ground-state optical conductivity spectra for E ⊥ c in (Ti − x V x ) O at 10K. With V-doping, the peak en-ergy of the a g - e πg transition decreases, while the Druderesponse evolves below 0.2 eV. Nevertheless, the Drudeweight remains small compared with the spectral weightof the interband transitions within the t g manifold. P ea k E ne r g y ( e V ) a g - e g p x = 00.02 Temperature (K) (b) E a g - a g * x = 00.0060.06 (Ti x V x ) O (a) || c N e ff x = 0 0.06 E E (Ti x V x ) O ^ c (e) c || Temperature (K) s ( ) ( W - c m - ) x = 0 E E ^ c (f) c || d T i - T i ( Å ) x (Ti x V x ) O E p ( e V ) d Ti-Ti E p (Ti x V x ) O N e ff (d) x n h / T i - s i t e FIG. 3: (color online). Temperature variation of the peakenergies for the interband transitions (a) a g - a ∗ g and (b) a g - e πg for E k c in (Ti − x V x ) O . (c) Temperature and dopingvariation of the Ti-Ti dimer bond length d Ti − Ti (open circles)reproduced from the structural data in literature [18, 19] incomparison with the a g - e πg ( E k c ) peak energy E p (closedcircles). (d) x dependence of the hole type carrier density n h per Ti site and the effective number of the electrons N eff at0.2 eV for E ⊥ c as a measure of the Drude weight (see text).Temperature dependence of (f) the N eff at 0.2 eV and (g) theconductivity σ (0) in (Ti − x V x ) O ( x = 0 and 0.06). In Figs. 3(a) and (b), the peak energies for the a g - a ∗ g and a g - e πg interband transitions for E k c in(Ti − x V x ) O are plotted as a function of temperature,respectively. The shift of the peaks is clearly related withthe change of the a g , e πg , and a ∗ g band positions. Bothpeak energies for E k c in Ti O are nearly tempera-ture independent at low temperatures but show rapiddecreases around T IM . The amount of the shift is compa-rable to, or even larger than, the band gap E g ( ∼ O below room temperature. As x increases, thepeak energy at low temperatures also reduces. However,the peak position around 600 K is almost independent of x , indicating that the conducting state above T IM is com-mon in nature irrespective of the V-doping level. In Figs.3(c), we plot the peak energy E p of the a g - e πg transitionfor E k c at 300 and 600 K in comparison with x depen-dence of the Ti-Ti dimer bond length d Ti − Ti estimatedfrom the c/a ratio [18, 19]. Notably, the temperatureand doping variation of the interband transition energyis parallel to that of the d Ti − Ti . The V-doping inducesthe hole type carriers at a rate of x/ Ti-site, as shownin Fig. 3(d). Therefore, the hole accumulation in the a g valence band appears to relax the Ti-Ti dimer bond, x = 00.0060.020.06 x = 0 (a) E c (b) x = 0 O p t i c a l C ondu c t i v i t y ( W - c m - ) (Ti x V x ) O Photon Energy (eV) (c) x = 00.0060.020.06 O p t i c a l C ondu c t i v i t y ( W - c m - ) c (d) E ^ (e) x = 00.006 0.020.06 (Ti x V x ) O Photon Energy (eV) (f) x = 00.0060.020.06 FIG. 4: (color online). Magnified view of the optical conduc-tivity spectra below 0.5 eV in (Ti − x V x ) O at (a) 600 K,(b) 400 K, and (c) 10 K for the polarization E k c and (d)-(f)those for E ⊥ c . Closed circles represent the measured dcconductivity in each x . Dashed lines interpolating betweenthe dc and optical conductivities are merely the guide to theeyes. leading to the reduction of the energy gap between the a g and e πg bands. These results unambiguously showthat the local singlet formation on the Ti-Ti dimer is re-sponsible for the robust band gap but amenable to thethermal band-gap excitation or the hole-doping.To see the carrier dynamics in more detail, we showin Fig. 4 the low-energy part of the optical conductivityspectra in (Ti − x V x ) O at various temperatures belowand above T IM . At 600 K, the low-energy optical con-ductivity shows rather ω -flat and less x -dependent fea-tures both for E k c and E ⊥ c , indicating the incoher-ent carrier dynamics in the conducting state above T IM .The spectral weight in the low-energy region decreaseswith decreasing temperature for any x . Above x = 0 . N eff at 0.2 eV in (Ti − x V x ) O , respectively, as a measureof Drude weight. The N eff is defined by the followingrelation, N eff = 2 m Vπe Z ω c σ ( ω ) dω. (1)Here m , V , and ω c (= 0 . a g - e πg gap energy, respectively.(The contribution of the optical phonon was subtractedin Figs 3(d) and (e).) As seen in Fig. 3(d), the N eff at250K is nearly proportional to the doping level x , as wellas the hole density n h . Thus, the metallic conductivityin the V-doped crystal is caused by the doped holes ac-cumulated in the a g valence band, whose concentrationis proportional to x as in the doped semiconductor; theconventional Drude formula suggests that m ∗ (effectivemass) ∼ m at low temperatures. The N eff for Ti O shows a sudden increase around T IM (Fig. 3(e)) and itstemperature dependence roughly agrees with that of thedc conductivity σ (0) for both E k c and E ⊥ c (Fig. 3(f)).For x = 0 .
06, the σ (0) increases with decreasing temper-ature below T IM , while the N eff decreases monotonically.This can be explained by the temperature dependenceof the scattering rate (or mobility) of the carriers in themetallic state. The N eff values at 600 K suggest the ef-fective carrier density as low as 0 . − . / Ti in thehigh-temperature conducting state.The comparison of these results with those in Motttransition system is meaningful. We show in Fig. 2(f)the doping variation of the optical conductivity spectrain the typical Mott transition system La − x Sr x TiO y/ (LSTO) reported by Okimoto et al. [3]. In LSTO, thelarge amount of the spectral weight is transferred fromthe high-energy Mott gap excitation to the low-energyDrude part in the course of the doping ( x + y/ Ti-site) in-duced IMT. This behavior is quite contrastive with thatin (Ti − x V x ) O shown in Fig. 2(e). The coexistence ofthe pseudo gap feature and the Drude peak with smallspectral weight in (Ti − x V x ) O is consistent with thepicture of the doped band insulator. Nevertheless, thedoping induced low-energy shift of the whole interbandtransition bands (see Figs. 3(a) and (b)) is appreciable.Thus, the band gap arising from a g -electron singlet for-mation in the bond dimer is critically affected by the holedoping level or the thermal gap excitation above T IM .The thermally induced IMT in Ti O can be interpretedwith band-crossing picture via the weakened singlet bondby the thermal gap excitation. The recent LDA+DMFTcalculation suggests that the effective band width is re-duced by the electron correlation, which stabilizes thedimerized state as well [20].In summary, we have investigated the optical andtransport properties for (Ti − x V x ) O in the wide tem-perature range of 2 −
600 K. We identify that in theoptical conductivity spectra the peaks due to the inter-band transitions remain to be observed in the thermally and V-doping induced metallic state. The variation ofthe gap energy in the course of the IMT well scales withthat of the Ti-Ti bond length reflecting the singlet-bondstrength. The Drude component is small compared withthe weight of the interband transition bands and propor-tional to x , as well as the carrier number obtained bythe Hall coefficient, whereas the magnitude of the bandgap is sensitively affected by the thermal gap excitationand the hole doping. These observations are contrastedwith the case of the canonical Mott transition in cor-related electron systems, which accompanies the largespectral weight transfer from the gap excitation to theDrude weight.This work was partly supported by Grants-In-Aid forScientific Research (Grant No. 15104006, 16076205,20340086) from the MEXT of Japan. [1] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. et al. , Phys. Rev. Lett.
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