Two-component electronic phase separation in the doped Mott insulator ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$

One of the major puzzles in condensed matter physics has been the observation of a Mott-insulating state away from half-filling. Several theoretical proposals aimed to elucidate this phenomenon have been put forth, a notable one being phase separation and an associated percolation-induced Mott insulator-metal transition. In the present work we study the prototypical doped Mott-insulating rare-earth titanate ${\mathrm{YTiO}}_3$, in which the insulating state survives up to a large hole concentration of 35%. Single crystals of ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$ with $0\le x\le 0.5$, spanning the insulator-metal transition, are grown and investigated. Using x-ray absorption spectroscopy, a powerful technique capable of probing element-specific electronic states, we find that the primary effect of hole doping is to induce electronic phase separation into hole-rich and hole-poor regions. The data reveal the formation of electronic states within the Mott-Hubbard gap, near the Fermi level, which increase in spectral weight with increasing doping. From a comparison with $\mathrm{DFT}+U$ calculations, we infer that the hole-poor and hole-rich components have charge densities that correspond to the insulating $x=0$ and metallic $x\sim 0.5$ states, respectively, and that the new electronic states arise from the metallic component. Our results indicate that the doping-induced insulator-metal transition in ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$ is indeed percolative in nature, and thus of inherent first-order character.

Figure 1

Doping and temperature dependence of resistivity in ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$.

Figure 2

(a) $\mathrm{Ti}L$-edge XAS spectra for ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$, including both YTO ($x=0$) and CTO ($x=1$). (b) XAS spectra for $x=0.5$ compared with an equally weighted linear combination of the YTO and CTO spectra in (a). (c)–(f) XAS spectra at four doping levels, compared with a linear combination of the $x=0$ and $x=0.5$ spectra (ratio of weights as indicated). All spectra were obtained at 15 K and normalized to the highest peak intensity.

Figure 3

(a) Doping dependence of $\mathrm{O}K$-edge XAS at 15 K. The spectra are shifted vertically for clarity. In order to extract the pre-edge peaks, we fit the data around 535 eV to two Gaussians (fits shown for $x=0$ as a dashed line) and subsequently subtracted the fit result from the data to obtain the result in (b). Black markers are guides to the eye and track the higher-energy component of the pre-edge. (b) Pre-edge peaks at the $\mathrm{O}K$ edge. The lines are the results of fits to two or three Gaussians, as described in the text. The vertical black dashed lines track the distinct peak positions. (c) and (d) Energy-integrated intensities and peak positions, respectively, of the Gaussian peaks in (b). The thick lines are guides to the eye. (e) Doping dependence of the Ti PDOS obtained from $\mathrm{DFT}+U$ calculations. The PDOS at $x=0$ ($p=0$) and $x=0.5$ ($p=0.5$) are obtained directly from the calculations, whereas those at intermediate doping levels are obtained by taking a weighted average of $x=0$ and $x=0.5$ PDOS, with the weights chosen in accordance with Fig. 2. The results of the calculation are convolved with a Gaussian function of width 0.1 eV (full-width-at-half-maximum) to mimic the experimental resolution. The vertical black dashed lines track the three distinct peaks that correspond to the pre-edge peaks observed in (b). The dashed green lines are Gaussian fits to the broad high-energy component at $x=0.5$, used to highlight the transfer of PDOS from the high-energy region to low-energy region, forming peak C. (f) Doping dependence of the peak positions obtained from (e) (filled symbols); the position for A is chosen as the midpoint of the nonzero-PDOS region just above the Fermi level, as XAS only sees states above the Fermi level. The thick lines are guides to the eye. The integrated Ti PDOS for the region corresponding to A (above the Fermi level) is presented on the right axis in (c), with a dashed line as a guide to the eye. The peak positions in (d) and (f) are plotted relative to the peak A position at $x=0.05$. The open symbols in (f) are the peak positions obtained from Ti PDOS, directly calculated by $\mathrm{DFT}+U$, without considering phase separation. In displaying this, we assume $x=p$. The dashed lines are guides to the eye. A clear qualitative difference (continuous vs discontinuous) in the peak B position is observed between the data and calculation, in this case.

Figure 4

$\mathrm{O}K$-edge XAS spectra at $x=0.4$ at different temperatures spanning the IMT. The data were obtained on heating. The inset shows a magnified view of the pre-edge region. The spectra have been normalized to the intensity at 560 eV.