Metallic ground states of undoped Ti2O3 films induced by elongated c-axis lattice constant

Ti2O3 exhibits unique metal–insulator transition (MIT) at ~ 450 K over a wide temperature range of ~ 150 K. The close relationship between MIT and crystal deformation has been proposed. However, as physical properties are governed by the thermodynamic equilibrium in bulk systems, conducting experimental studies under different lattice deformations remains challenging. Epitaxial thin films can offer high flexibility to accommodate adaptive crystal lattices and provide efficient platforms for investigating the MIT. In this study, we report the synthesis of corundum-type Ti2O3 films on various growth temperatures. We found that the metallic ground states appeared in the films grown at low temperatures. The electronic ground states were further investigated by the electronic-structure calculations. Results suggest that the electrical properties of Ti2O3 films were governed by the c/a ratio of the crystal structure, and the absence of the MIT was attributed to the lattice deformation characterized by an elongated c lattice constant.


Scientific Reports
| (2020) 10:22109 | https://doi.org/10.1038/s41598-020-79182-5 www.nature.com/scientificreports/ lower than that of the bulk 23,24 . Besides, a significant increase in the c lattice constant was detected in the films (at RT c ~ 13.8 Å in the films and c = 13.61 Å in the bulk). Considering the close relationship between the c/a ratio and MIT observed in the bulk system, it can be presumed that the suppression of the insulating states in the films is equally related to the lattice deformations. Unfortunately, lattice deformations are not expected in the films grown coherently on α-Al 2 O 3 (0001) substrates due to the large lattice mismatch between α-Al 2 O 3 and Ti 2 O 3 (~ 8.3%). Furthermore, in contrast to the perovskite-type oxides, corundum-type oxides have the only option of α-Al 2 O 3 as an isostructural substrate, which makes it difficult to investigate the physical properties as a function of the c/a ratio by conventional epitaxial-strain manipulations.
To investigate the relationship between c/a ratios and MIT in Ti 2 O 3 , we demonstrate another approach to control the lattice deformation in Ti 2 O 3 films, which involves different growth temperatures to manipulate domain sizes and thereby different c/a ratios. The substrate temperature plays a crucial role in the nucleation of films, and domain sizes vary depending on the growth conditions 26 . In corundum-type oxides such as Ti 2 O 3 and V 2 O 3 , it is known that a and c lattice constants evolve with the size of nanoparticles 15,27 . Therefore, Ti 2 O 3 films grown under different temperatures are expected to render different a and c lattice constants and electrical properties. In this study, we have grown corundum-type Ti 2 O 3 films at high (1000 ºC) and low (500 ºC) temperatures. The successful synthesis of corundum-type Ti 2 O 3 films on α-Al 2 O 3 substrates at different temperatures was confirmed by Raman spectroscopy and X-ray diffraction (XRD) experiments. The c/a ratios at RT were determined as 2.696 and 2.781 for the films grown at high and low temperatures, respectively. Notably, metallic ground states appeared for the film grown under low temperatures, manifesting a large c/a ratio with domain sizes of the order of 10 nm, whereas MIT was observed in the film grown at high temperatures. We discuss the origin of this MIT behavior in the Ti 2 O 3 films by adopting density functional theory (DFT)-based electronic-structure calculations. Figure 1 shows the Raman spectra of the high-temperature-Ti 2 O 3 (HT-Ti 2 O 3 ) and low-temperature-Ti 2 O 3 (LT-Ti 2 O 3 ) films. The Raman spectrum of the HT-Ti 2 O 3 film recorded using a He-Ne laser shows seven peaks, which is consistent with previous reports [11][12][13]24,25 . In corundum-type crystal structures, two A 1g and five E g modes are Raman active following the symmetry considerations 28 . To reveal the vibrational modes in the HT-Ti 2 O 3 film, we further performed Raman spectroscopy using another light source of a Nd:Y 3 Al 5 O 12 (YAG) laser, as shown in Fig. 1a. Evidently, the lowest-frequency mode was not observed in the spectrum due to the resonant Raman effect reflecting the electronic structures of corundum-type Ti 2 O 3 13 . Therefore, the 1st and 2nd low-frequency modes were assigned to the A 1g and E g modes, respectively, which are consistent with the earlier report by Shin et al. 12,13 (see Supplementary Note 1). Our results indicate that both peak structures and resonant Raman effects are good fingerprints to elucidate corundum-type Ti 2 O 3 11-13,24,25,29-34 . Similar Raman spectra were obtained for the LT-Ti 2 O 3 film, as shown in Fig. 1b, confirming the same crystal structure as that of the HT-Ti 2 O 3 film. The Raman spectrum recorded using the He-Ne laser also shows seven peaks, although the peak shapes were slightly different from those of the HT-Ti 2 O 3 film. The E g modes softened, and in contrast, the frequency of the low-frequency A 1g mode increased, as shown by the filled triangle in Fig. 1b. Therefore, the A 1g and E g modes at ~ 230 cm −1 were overlapped with each other. These behaviors were also observed in the bulk systems at high temperatures rendering large c/a ratios 12 . We will discuss the difference in the Raman spectra between the HT-and LT-Ti 2 O 3 films later in connection with the transport properties. Nevertheless, the Raman spectrum of the LT-Ti 2 O 3 film measured using the YAG laser was in good agreement with that Corundum-type crystal structure of the LT-Ti 2 O 3 film was further confirmed from the two-dimensional (2D) XRD contour map, as shown in Fig. 2. At the tilt angle χ = 0º, which corresponds to out-of-plane direction, α-Al 2 O 3 0006 and 00,012 reflections were detected at 2θ = ~ 42º and 91º, respectively. The reflections from the film were detected at 2θ = ~ 38º and 84º at the tilt angle χ = 0º, which can be assigned to 0006 and 00012 reflections of Ti 2 O 3 , respectively. All the film reflections were detected at lower 2θ angles than the substrate reflections at the same tilt angle χ. Such pairs of film and substrate reflections observed from the 2D XRD contour maps confirm the identical crystal symmetry of the film and substrate. The 2D XRD contour maps taken along other in-plane directions are shown in Supplementary Fig. 1. These results confirm that the LT-Ti 2 O 3 film also exhibits corundum-type crystal structure. Both in-plane and out-of-plane orientations were identical in the LT-Ti 2 O 3 film and α-Al 2 O 3 substrates.

Results and discussion
The detailed lattice constants of the Ti 2 O 3 films were determined from the XRD measurements. Figure  , which is much larger than that of the bulk Ti 2 O 3 (c/a = 2.639). Note that the c/a ratio of the LT-Ti 2 O 3 film is also much larger than that of typical corundum-type oxides such as α-Al 2 O 3 (c/a = 2.732 where a = 4.759 Å and c = 12.99 Å), but relatively smaller than that of another corundum-type oxide V 2 O 3 (c/a = 2.828 where a = 4.9717 Å and c = 14.005 Å) 35 .
The different growth temperatures also significantly affected the surface morphologies of the films. As shown in Fig. 4a, the atomic force microscope (AFM) image of the HT-Ti 2 O 3 film reflected a trace of spiral growths 36 , which was also reported previously 23 . The in-plane size of the spirals was ~ 0.5 µm. In contrast, the LT-Ti 2 O 3 film did not exhibit such spiral growths in the AFM image as shown in Fig. 4b. Instead, smaller grains of less than 50 nm were detected at the surface, which can be attributed to the reduced migration energies during the low-temperature growth process 26 . Out-of-plane grain sizes were roughly estimated from the out-of-plane XRD patterns (See Supplementary Note 2). The broad peaks in the LT-Ti 2 O 3 film, as shown in Fig. 3a, also suggested small grain sizes. Grain sizes of the LT-Ti 2 O 3 film were estimated as 23 nm from the Scherrer equation, which is comparable to the estimation from the AFM image (See Supplementary Note 2 for the detailed analyses). In corundum-type Ti 2 O 3 and V 2 O 3 nanoparticles, it was reported that lattice constants evolved greatly with the particle sizes 15,27 . In the case of Ti 2 O 3 , the c (a) lattice constant becomes longer (shorter) as the grain size www.nature.com/scientificreports/ decreases, resulting in an increased c/a ratio for the nanoparticles 15 . Considering the larger size (~ 1 mm scale) of the Ti 2 O 3 single crystal, the negative correlation between the domain size and c/a ratio is plausible in the films. It is well established that the c/a ratio is strongly related to the MIT in the bulk Ti 2 O 3 4 . To elucidate the relationship between the MIT and c/a ratios in the Ti 2 O 3 films, we performed temperature-dependent resistivity measurements for the HT-and LT-Ti 2 O 3 films, as shown in Fig. 5a. For the HT-Ti 2 O 3 film, the resistivity at 2 K was ~ 10 mΩ cm. The resistivity gradually decreased with increasing temperatures and the broad MIT appeared at 200-300 K accompanying a substantial change in the resistivity. Even beyond the MIT, dρ/dT remained negative up to 400 K (ρ and T denote resistivity and temperature, respectively). Such resistivity behaviors suggest the suppression of insulating states in Ti 2 O 3 films in comparison with bulk, which is also consistent with the previous reports 23, 24 . In bulk, the resistivity at ~ 10 K is more than 10 2 Ω cm 2,3 , which is four orders of magnitude larger than that of the HT-Ti 2 O 3 film. In addition, the MIT temperature in bulk is ~ 450 K, which is ~ 200 K higher than that of the film 23,24 .
Suppression of the insulating states is further examined in the LT-Ti 2 O 3 film that show a completely different resistivity curve, as shown in Fig. 5a. The MIT was not observed and metallic conductivity (dρ/dT > 0) appeared until ~ 50 K. However, at temperatures < 50 K, a slight upturn of the resistivity curve was noticed, suggesting a trap of conductive carriers in defects at low temperatures, which can be related to the poor crystallinity of the LT-Ti 2 O 3 film (See Supplementary Fig. 2). In bulk (Ti 1−x V x ) 2 O 3 , resistivity of low-temperature insulating phases decrease drastically with V doping, but another phase transition was detected at high-temperature regions (~ 450 K) 2 . To eliminate the possible phase transition in the LT-Ti 2 O 3 film, we further performed high-temperature resistivity measurements, as shown in the inset of Fig. 5a. The metallic conductivity continued up to 600 K with a linear ρ-T relationship. We note that metallic conductivity first appears at ~ 500 K for the HT-Ti 2 O 3 film 23 , but it is never observed for a bulk system up to 575 K 2,3 .
The electric properties were further investigated from Hall-effect measurements. The clear linear dependence of the Hall resistance on the magnetic field was observed for both films (see Supplementary Fig. 3). We plot the resultant inverse Hall coefficient (1/R H ) in Fig. 5b as a function of temperature. The positive 1/R H indicates the hole-carrier conduction of both films, which is consistent with the previous reports 1, 37 . The 1/R H became smaller  The metallic states of the LT-Ti 2 O 3 film are further supported by Raman spectroscopy (Fig. 1). Shin et al. reported that the low-frequency A 1g mode is an excellent indicator of the electrical behaviors of Ti 2 O 3 12,13 . The A 1g vibrational modes correspond to breathing against one another for the Ti atom pairs along the c-axis. Simultaneously, oxygen atoms forming triangles between each Ti pair are moving in and out alternately with respect to each other. In the low-frequency A 1g mode, oxygen atoms move out when the Ti atoms move in, so that the screening effect of the oxygens becomes lowest, and the modulation of the trigonal component to the crystalline field rises to its largest value. In a phenomenological model, the intensity of Raman mode is related to the polarizability of the electron cloud. As shown in Fig. 1a, the Raman spectrum of the HT-Ti 2 O 3 film collected using the He-Ne laser showed the strongest intensity for the low-frequency A 1g mode, which is consistent with the phenomenological model. In contrast, the intensity of the A 1g mode was strongly suppressed in the LT-Ti 2 O 3 film due to conduction-carrier screening of the electric field caused by the electron cloud motions. Since the screening effect from the oxygens is weakest in the low-frequency A 1g mode, its intensity gets most affected. Therefore, the strong suppression of the low-frequency A 1g mode provides further evidence for the metallic conductivity in the LT-Ti 2 O 3 film.
One might suspect that different carrier densities (4.8 × 10 20 cm −3 for the HT-Ti 2 O 3 film and 2.5 × 10 21 cm −3 for the LT-Ti 2 O 3 film at 300 K) are caused by extrinsic effects such as oxygen non-stoichiometry. However, it is unlikely in the present case. In Ti 2 O 3 , the atomic density of Ti in the crystal lattice is calculated to be 3.8 × 10 22 cm -3 . The carrier densities correspond to be 1.3 and 6.6% holes /Ti for the HT-and LT-Ti 2 O 3 films, respectively. Meanwhile, Andersson et al. revealed that the corundum-type Ti 2 O 3 phase was only stable with the oxygen non-stoichiometry of less than 1%, corresponding to the chemical formula of Ti 2 O 2.98 -Ti 2 O 3.02 38 . These results suggest that the carrier density of the LT-Ti 2 O 3 film is not explained by the oxygen non-stoichiometry.
The plausible scenario to explain different hole-carrier densities between the HT-and LT-Ti 2 O 3 films is the intrinsic holes whose densities are varied by the c/a ratio. Chang et al. revealed the change of the Ti 3d electron occupation in the a 1g and e g π orbitals by the c/a ratio 3 . We note that the c/a ratio directly corresponds to the degree of the trigonal distortion in TiO 6 octahedra and the distance of Ti-Ti pair along the c-axis. When the c/a ratio was small enough, the Ti 3d electrons completely filled the most stable a 1g orbital, resulting in the formation of 100% a 1g a 1g singlet state in the Ti-Ti pair. With increasing the c/a ratio, the occupation in the a 1g orbital systematically decreased. According to Ref. 3, the a 1g a 1g singlet state was reduced to be 49% at 575 K (c/a = 2.70). The reduction in the a 1g a 1g singlet state is responsible for increasing the hole carriers in the a 1g bands. Moreover, the rest of the Ti 3d electrons is partially filled with the e g π orbital that expands in the a-b plane. The partially-filled e g π orbital forms conducting paths to the neighboring Ti-Ti pairs, resulting in the large hole-carrier densities and metallic conductivity in the LT-Ti 2 O 3 film.
Next, to reveal the origin of different electronic states in the films and bulk materials, we performed DFT + U calculations using the Quantum ESPESSO simulation software 39,40 . Since insulating ground states were not  Fig. 5a.
We will discuss the plausible origin behind the occurrence of the MIT in the HT-Ti 2 O 3 film and the absence of the MIT in the LT-Ti 2 O 3 film at low temperatures. The a and c lattice constants should be modulated as a function of temperature due to the thermal expansion. To experimentally estimate thermal expansion coefficients (α) of the Ti 2 O 3 films, we performed the temperature-dependent XRD measurements (see Supplementary Figs. [6][7][8]. The α along the c-axis (α c ) and a-axis (α a ) were estimated to be α c = 1.86 ± 0.17 × 10 -5 K −1 and α a = 2.10 ± 2.97 × 10 -6 K −1 for the HT-Ti 2 O 3 film and to be α c = 1.70 ± 0.11 × 10 -5 K −1 and α a = − 0.37 ± 3.32 × 10 -6 K −1 for the LT-Ti 2 O 3 film. The relative errors of the α a look large, which originates temperature-independent a lattice constants. We also referred to the α of bulk Ti 2 O 3 that was estimated to be α c = 3.263 × 10 -5 K −1 and α a = − 1.088 × 10 -6 K −1 using previous results (see Supplementary Fig. 9) 4 . We found that the α c of the films was approximately half of the α c of the bulk specimen. We utilized the α determined from the present experiments and the bulk reference and then obtained the c/a ratios of the films below RT by the linear extrapolation of the values in the high-temperature metallic region to low temperatures (See Supplementary Fig. 10). In the HT-Ti 2 O 3 film, the c/a ratio reached the critical value of 2.68 at ~ 150 K using the α of the bulk reference and at ~ 50 K using the experimentally determined α. Although these critical MIT temperatures are much lower than that revealed from the temperature dependence of resistivity (~ 250 K in Fig. 5a), the results qualitatively demonstrate that the MIT in the HT-Ti 2 O 3 film is due to the temperature dependence of the crystal deformation. In contrast, the LT-Ti 2 O 3 film did not reach the critical c/a ratio of 2.68 even at the lowest temperature limit. The estimated c/a ratio at 2 K was larger than 2.754, where the metallic states appeared in the DFT calculations and in experiments for the bulk materials. These results suggest that the electrical properties of both HT-and LT-Ti 2 O 3 films can be explained by the c/a ratio as in the bulk systems. Absence of the MIT in the LT-Ti 2 O 3 film can be attributed to the elongated c lattice constant (at RT c = 14.00 Å in the film and c = 13.61 Å in the bulk) caused by the nano-sized domains.
We presume that treatment of the empirical parameter U is responsible for the quantitative discrepancies in the critical temperatures between the experiment and the calculation. In the DFT + U calculations, the critical c/a ratio had a positive correlation with U. Moreover, the energy gap quite sensitively depended on U, as shown in Fig. 6. In this study, we merely selected U = 2.2 eV to reproduce the energy gap (~ 100 meV) for bulk Ti 2 O 3 . Therefore, it is quite difficult to determine the critical c/a ratio from the DFT + U calculations quantitatively at the moment, although the close relationship between c/a ratios and MIT in Ti 2 O 3 is clearly demonstrated on the qualitative level. To resolve the quantitative discrepancies between the experiments and calculations, further experimental studies to determine the energy gap of bulk Ti 2 O 3 precisely and more accurate theoretical studies would be required. www.nature.com/scientificreports/ Herein, we have grown Ti 2 O 3 films on α-Al 2 O 3 (0001) substrates at high and low temperatures to control domain sizes and c/a ratios of the structure. Successful synthesis of films exhibiting corundum-type crystal structure in both conditions was confirmed by Raman spectroscopy and XRD measurements. The c/a ratios at RT were significantly different in the HT-Ti 2 O 3 (2.696) and LT-Ti 2 O 3 (2.781) films. The HT-Ti 2 O 3 film showed the broad MIT at ~ 200-300 K, which was ~ 200 K lower than that of the bulk. However, the LT-Ti 2 O 3 film exhibited metallic conductivity and did not show any MIT up to 600 K. The DFT + U calculations predicted the critical c/a ratio of 2.68 to induce the MIT. The detailed analyses revealed that the observed electrical properties of the Ti 2 O 3 films can be explained by the critical c/a ratio and anisotropic thermal expansion coefficients. These results suggest that the electrical properties of Ti 2 O 3 films are also governed by the c/a ratio of the structure and the absence of the MIT in the LT-Ti 2 O 3 film is due to the lattice deformations characterized by an increased c lattice constant leading to an enhanced c/a = 2.781 at RT.

Methods
Thin-film growth. Ti 2 O 3 films were grown on α-Al 2 O 3 (0001) substrates using the pulsed-laser deposition (PLD) method. Polycrystalline ceramics of TiO (3 N purity, purchased from Toshima Manufacturing Co., Ltd.) were used as the PLD target. A KrF excimer laser (0.8 J/cm 2 , 5 Hz) was used for target ablations. The substrate temperature and oxygen partial pressure were set 1000 ºC and 1.5 × 10 -6 Torr, respectively, for the production of the HT-Ti 2 O 3 film, whereas those for the preparation of the LT-Ti 2 O 3 film with single-phases were 500 ºC and 5.0 × 10 -7 Torr, respectively. Notably, when the temperature was set between 500 and 1000 °C, another superconducting-titanate phase was stabilized and consequently, single-phase corundum-type Ti 2 O 3 films were not obtained (See Supplementary Figs. 11-14). At the end of the growth process, the oxygen flow to the PLD chamber was stopped immediately and films were quenched to RT to avoid the occurrence of additional oxidations 23,41 . Film thickness (~ 100 nm) was measured using a stylus-type profiler.
Thin-film characterizations. Crystal structures of the films were revealed by Raman spectroscopy and XRD measurements conducted at RT. Raman spectra were acquired using a LabRAM HR-800 (Horiba) equipped with YAG (λ = 532 nm) and He-Ne (λ = 633 nm) lasers. The laser incident and Raman scattering directions were parallel to the c-axis. The polarization vector of the lasers was set parallel to the Ti 2 O 3  direction. XRD patterns and contour maps were measured using the Cu-Kα 1 radiation available in a SmartLab 9 kW diffractometer (Rigaku). Surface morphology was examined via AFM. Temperature dependence of resistivity was measured by implementing a standard four-probe method using PPMS (Quantum Design) at low temperatures (2 ≤ T ≤ 400 K) and PPHL-800 (Pascal) at high temperatures (300 ≤ T ≤ 600 K). Au electrodes were deposited by the sputtering method. Ohmic contacts between the films and electrodes were confirmed from the two probe I-V measurements at RT. Hall-effect measurements were carried out in a Hall-bar geometry using PPMS.
Electronic structure calculations. DFT calculations were performed using the Quantum ESPRESSO simulation software 39,40 . Ultrasoft pseudopotentials were used, wherein atomic Ti 3s, 3p, 3d, and 4s, O 2s, and 2p levels were included as valence-band states. The Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) function was utilized for the exchange-correlation potentials 42 . The kinetic energy (charge density) cut-off was set as 60 Ry (600 Ry). Ti and O positions were optimized by a structural relaxation routine implementing Monkhorst-Pack scheme with a 6 × 6 × 6 k-mesh in self-consistent calculations 43 . Accuracy in total energy after the convergence of the self-consistent calculations was less than 10 -10 Ry. After the structural optimization, the density of states (DOS) was calculated in non-self-consistent fields using a denser 12 × 12 × 12 k-mesh. The tetrahedron method was applied to integrate the DOS in the Brillouin zone 44 . Further computing details are described in Supplementary Methods.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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