Supplemental Materials
Effects of phase fraction on superconductivity
of low-valence eutectic titanate films
Hikaru Kurokawa1, Kohei Yoshimatsu1,*, Osami Sakata2,3, and Akira Ohtomo1, 3
1Department of Chemical Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
2Synchrotron X-ray Station at SPring-8, National Institute for Materials Science (NIMS), Sayo, Hyogo 679-5148, Japan
3Materials Research Center for Element Strategy (MCES), Tokyo Institute of Technology, Yokohama 226-8503, Japan
(Received )
*Author to whom correspondence should be addressed; Electronic mail:
Synchrotron radiation X-ray diffraction data for titanate films.
In order to evaluate the volume fractions among TiO, Ti2O3, and g-Ti3O5 in eutectic titanate films, we performed X-ray diffraction (XRD) measurements using synchrotron radiation with photon energy of 15.0 keV (l = 0.826 Å) at BL15XU in SPring-8. Figure S1 shows the rocking curve profiles of several reflections for the eutectic film (Sample D). The clear peaks were detected at each reflection. Using the synchrotron XRD data and the parameters listed in Table S1, we estimated the volume fractions for the as-grown eutectic films (Samples B−D), which is shown in Fig. 5(a).
The volume fractions for annealed films were calculated as follows. Figures S2(a) and S2(b) show scaling of volume ratio of TiO to Ti2O3 and TiO to g-Ti3O5 with respect to the integrated intensities ratios for the as-grown samples, respectively. Here, the data points except for that at the origins were referred to the as-grown eutectic films (Samples B−D). The integrated intensities were obtained from XRD data taken with Cu Ka1 radiation. A liner relationship between volume ratios and integrated intensity ones was found in Figs. S2. Using least square fit to the data as a standard (red lines), the volume fractions of the annealed eutectic films were estimated as shown in Fig. 5(b).
111 / Ti2O3
0006 / TiO
200 / g-Ti3O5
13 / Ti2O3
012 / g-Ti3O5
110
d (Å) / 2.39 / 2.30 / 2.09 / 2.14 / 3.73 / 3.64
χ (°) / 0 / 0 / 54 / 54 / 57 / 57
ϕ (°) / 0 / 0 / 30 / 30 / 0 / 0
v (Å3) / 7.30×10 / 3.14×103 / 7.30×10 / 3.42×103 / 3.14×103 / 3.42×103
j / 8 / 2 / 1 / 1 / 1 / 1
F (Å3) / 4.06×10 / 7.22×10 / 7.61×10 / 2.07×10 / 8.73×10 / 3.50×10
LP (θ) / 8.41 / 7.69 / 6.15 / 6.46 / 5.07 / 4.74
I0 / 2.08×10 / 8.10×10–1 / 6.67 / 2.38 / 3.90×10–1 / 4.98×10–2
Table S1. List of the parameters used to calculate the volume fractions of the eutectic films where ν: volume of unit cell, j: multiplicity factor, F: structure factor, LP(θ): Lorentz polarization factor as a function of θ, Ia0: ideal value of integrated intensity of phase a. Noe that we describe j = 1 for the asymmetric reflections.
Figure S1. Rocking curve profiles of (a) TiO 111, (b) Ti2O3 0006, (c) TiO 200, (d) g-Ti3O5 13, (e) Ti2O3 012, and (f) g-Ti3O5 110 reflections for Sample D obtained by synchrotron radiation XRD measurements.
Figure S2. The standard lines to estimate volume ratios of (a) TiO to Ti2O3 and (b) TiO to g-Ti3O5 from XRD data taken with Cu Ka1 radiation.
Superconductivity of eutectic titanate films under magnetic field
Figure S3 shows temperature dependence of the resistivity at low temperatures for eutectic titanate films (Samples B and C) under magnetic field applied perpendicular to the plane. The onset of superconductivity systematically shifted toward lower temperature with increasing magnetic field. The superconducting phase completely disappeared at H = 9 T for Sample B above 2 K. In contrast, superconductivity still remained at H = 9 T for Sample C.
Figure S3. Temperature dependence of the resistivity for the eutectic titanate films [Samples (a) B and (b) C] under perpendicular magnetic fields.
Superconducting phase diagram of TiOx
Figure S4 shows TC,onset vs. average oxygen content (x), which is intended to make a normal superconducting phase diagram. Note that x values are deduced from volume fractions by assuming stoichiometric compositions for each phase. No systematic behaiviors of TC,onset are seen from x = 1.0 to 1.5. At x 1.6, data points are somewhat scattered presumably due to variation of oxygen content in the g-Ti3O5 phase.
Figure S4. Superconducting transition temperature as a function of average oxygen content x. Note that several data points with red circles at x = 1.67 (pure g-Ti3O5 phase) are referred from our previous study.
3