Structural characterization

The formation of the Ti 4 O 7 and γ-Ti 3 O 5 phases was verified using x-ray diffraction (XRD). The out-of-plane XRD patterns showed intense reflections from the Ti 4 O 7 films grown on (LaAlO 3 ) 0.3 –(SrAl 0.5 Ta 0.5 O 3 ) 0.7﻿ (LSAT) (100) substrates and the γ-Ti 3 O 5 film grown on α-Al 2 O 3 (0001) substrates [Fig. 2(a) and (b), respectively]. These substrates are insulating, non-magnetic, and exhibit high reduction resistance, providing advantages in the growth and search of a superconducting sample. Irrespective of the growth condition, Ti 4 O 7 202 reflection was detected at 2θ = 42.38°, corresponding to d 202 = 2.13 Å. No other film reflections except for the 404 reflection at 2θ = 92.60° was detected in wide-range XRD patterns. The γ-Ti 3 O 5 022 reflection was detected at 2θ = 37.83°, corresponding to d 022 = 2.38 Å. The out-of-plane single orientation was verified using wide-range XRD patterns (not shown). Surface morphology of the films are shown in the inset of Fig. 2. The small grains were observed and the root mean square roughness was about 1 nm for both films. Their surface morphology was different from that of TiO and Ti 2 O 3 (see Fig. S1 in Supplementary information)8.

Figure 2 Structural characterization of titanate films. (a) Out-of-plane XRD patterns for Ti 4 O 7 films grown on LSAT (100) substrates under Ar gas at 1 × 10−3 Torr (top) and under oxygen gas at 1 × 10−7 Torr (bottom). (b) Out-of-plane XRD pattern for the γ-Ti 3 O 5 film grown on α-Al 2 O 3 (0001) substrates under oxygen gas at 1 × 10−7 Torr. The insets show AFM images (5 µm × 5 µm) taken for the same films. Colour codes are 13 nm and 8 nm in height for (a) and (b), respectively. Full size image

Because of various polymorphisms with different ratios of oxygen to titanium, their crystal structures must be carefully distinguished. Then, we used the tilt angle χ-dependence of 2θ-θ XRD profiles to survey the asymmetric film reflections (see Figs S2 and S6 in Supplementary Information). Reflections coming from the substrate and film were found at characteristic χ angles. Since the intensities of the film reflections were too weak to determine the d values of interplanar spacing precisely, synchrotron radiation XRD measurements were also performed (see Figs S3–S5,S7 and S8 in Supplementary Information). From the d values and χ angles, we identified the Miller indices as those listed in Tables S2 and S3. In comparison to the previous structural analyses of titanates1,2,3,4,5,6,7, we concluded that the films grown on LSAT (100) and α-Al 2 O 3 (0001) substrates were Ti 4 O 7 and γ-Ti 3 O 5 , respectively. Furthermore, using the d values and Miller indices (Tables S1 and S3), we evaluated lattice parameters of our titanate films: Ti 4 O 7 film grown under P O2 = 1 × 10−7 Torr (a = 5.52 Å, b = 7.12 Å, c = 20.43 Å, α = 67.5°, β = 57.3°, γ = 108.8°), Ti 4 O 7 film grown under P Ar = 1 × 10−7 Torr (a = 5.52 Å, b = 7.11 Å, c = 20.46 Å, α = 67.5°, β = 57.2°, γ = 108.8°), and γ-Ti 3 O 5 film (a = 4.99 Å, b = 9.80 Å, c = 7.06 Å, α = 110.3°). The a-axis lattice constant of both Ti 4 O 7 films is smaller than that of bulk. In contrast, b- and c-axes lattice constants of the former Ti 4 O 7 films were in agreement with those of bulk. The b- (c-) axis lattice constant of the latter Ti 4 O 7 film was smaller (larger) than that of bulk. We note that the c-axis length directly corresponds to the Ti–Ti bond length in the TiO 6 tetramer [see Fig. 1(a)] and c-axis lattice constant of the former Ti 4 O 7 film is larger than that of the latter Ti 4 O 7 film. For the γ-Ti 3 O 5 film, all of the lattice constants were smaller than those of bulk. The lattice parameters of the titanate films and bulk are listed in Tables S2 and S4 for comparison.

Formation of the different titanate phases under the identical growth condition suggests that epitaxial effects play an important role for stabilizing the Ti 4 O 7 and γ-Ti 3 O 5 films on each substrate (see Fig. S9 in Supplementary Information). In fact, we have grown neither γ-Ti 3 O 5 films on LSAT (100) substrates nor Ti 4 O 7 films on α-Al 2 O 3 (0001) substrates. The in-plane epitaxial relationship between the substrates and films were also investigated and described in Supplementary Information.

Temperature dependence of resistivity

The electrical properties of the films were investigated using the temperature dependence of resistivity (Fig. 3). The resistivity curves strongly depended on the growth atmosphere for Ti 4 O 7 films [Fig. 3(a)]. For the film grown under P O2 = 1 × 10−7 Torr, MIT accompanied by clear hysteresis was found at around 150 K, which is in agreement with the behaviour of a bipolaron insulator of bulk Ti 4 O 7 9,10,11. In contrast, the insulating behaviours were strongly suppressed for the film grown under P Ar = 1 × 10−3 Torr; the upturn in resistivity was weak. The different behaviour across MIT was in agreement with the difference in c-axis lattice constants of the Ti 4 O 7 films: the larger c-axis length weakened the Ti3+–Ti3+ bond in the TiO 6 tetramers for the Ti 4 O 7 films grown under P Ar = 1 × 10−3 Torr. The weak resistivity upturn was also reported on V-doped bulk Ti 4 O 7 12. When V content exceeds 0.35 at%, the disordered bipolarons dominate the electronic properties in the insulating phase. If we account for the lower degree of oxidation at P Ar = 1 × 10−3 Torr, oxygen deficiency would play a similar role to substitution of the Ti site with V and be responsible for the suppression of the insulating states. Furthermore, superconductivity was observed at low temperatures. The Ti 4 O 7 film grown under an intermediate condition (P Ar = 1 × 10−6 Torr) exhibited both hysteresis and superconducting characteristics in the resistivity curve (also see Fig. S10 in Supplementary Information). We will refer to the Ti 4 O 7 films grown under P O2 = 1 × 10−7 Torr (P Ar = 1 × 10−3 Torr) as insulating (superconducting) ones in the following discussion.

Figure 3 Temperature dependence of resistivity of titanate films. (a) Temperature dependence of resistivity for Ti 4 O 7 films grown under three different conditions. The inset shows the temperature dependence of the Hall measurement. (b) Temperature dependence of resistivity for the γ-Ti 3 O 5 film. The inset shows the temperature dependence of the Hall measurement. Full size image

The variation in the Hall coefficient (R H ) during warming exhibited a tendency similar to that of resistivity. At 300 K (10 K), the inverse R H was 3.6 × 103 (1.5) and 1.2 × 104 (1.2 × 104) C/cm3 for the films grown under P O2 = 1 × 10−7 Torr and P Ar = 1 × 10−3 Torr, respectively. For the insulating Ti 4 O 7 film, the temperature dependence of the inverse R H [inset of Fig. 3(a)] suddenly decreased at around 150 K, suggesting that the MIT was induced by the depletion of hole carriers. The inverse R H at 10 K was four orders of magnitude smaller than that at 300 K. The MIT in the bulk is associated with the formation of bipolarons9,10,11, which remains robust in the insulating Ti 4 O 7 film at low temperatures. In contrast, the inverse R H for the superconducting Ti 4 O 7 film was almost independent of temperatures, and even the value at 10 K was comparable to that at 300 K, suggesting the suppression of a bipolaronic insulating state.

The temperature dependence of the resistivity for the γ-Ti 3 O 5 film exhibited a complex curve along three electronic phase transitions: MIT around 350 K, insulator–insulator transition around 100 K, and superconducting transition [Fig. 3(b)]. The intermediate transition would be related to the MIT of Ti 4 O 7 due to their similar transition temperatures. Nevertheless, the resistivity upturn was much weaker, suggesting the suppression of the insulating states, as with the case of the superconducting Ti 4 O 7 film. The inverse R H almost [inset of Fig. 3(b)] remained the same (~103 cm3/C) over the entire temperature range. The sign and magnitude of the R H also reflected this correspondence.

Superconducting properties

The temperature dependence of resistivity around the temperature of liquid helium indicates further similarity between the superconducting Ti 4 O 7 and γ-Ti 3 O 5 films [Fig. 4(a) and (b), respectively]. The T C of Ti 4 O 7 and γ-Ti 3 O 5 were 3.0 K and 7.1 K for T C,onset , 2.7 K and 6.6 K for T C,mid , and 5.8 K and 2.5 K for T C,zero , respectively. Note that the T C of both films exceeded that of other simple-oxide superconductors in bulk [TiO (T C = 2.3 K), NbO (T C ~1.4 K), and SnO (T C = 1.4 K under 9.3 GPa)]13,14,15,16. We also note that enhancement of T C = ~7 K in TiO films has been reported in recent17. The superconducting states were gradually degraded under applied magnetic fields. Here, the magnetic fields were applied perpendicular to the film surface. T C shifted toward a lower temperature under a higher magnetic field, and the superconducting phase finally disappeared for the Ti 4 O 7 film at above 2 K. As for the γ-Ti 3 O 5 films, superconductivity remained robust even under 9 T. In addition, from the temperature dependence of magnetization measurements, where magnetic field was applied parallel to the film surface, clear diamagnetic signals were observed [insets of Fig. 4(a) and (b)], respectively. The observation of diamagnetic signals in field-cooling curves indicates the Meissner effect of bulk superconductivity inTi 4 O 7 and γ-Ti 3 O 5 films, and roles out major influences arising from impurity, filament, and/or surface states.