Response of the Lattice across the Filling-Controlled Mott Metal-Insulator Transition of a Rare Earth Titanate

The lattice response of a prototype Mott insulator, ${\mathrm{SmTiO}}_3$, to hole doping is investigated with atomic-scale spatial resolution. ${\mathrm{SmTiO}}_3$ films are doped with Sr on the Sm site with concentrations that span the insulating and metallic sides of the filling-controlled Mott metal-insulator transition (MIT). The ${\mathrm{GdFeO}}_3$-type distortions are investigated using an atomic resolution scanning transmission electron microscopy technique that can resolve small lattice distortions with picometer precision. We show that these distortions are gradually and uniformly reduced as the Sr concentration is increased without any phase separation. Significant distortions persist into the metallic state. The results present a new picture of the physics of this prototype filling-controlled MIT, which is discussed.

Figure 1

(a) Temperature dependence of the sheet resistance for 50-nm-thick ${\mathrm{Sm}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ films with $x=0.05$, 0.10, 0.15, and 0.20. (b) Apparent carrier density, ${(e{R}_H)}^{-1}$, measured from the Hall effect for ${\mathrm{Sm}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ films with different compositions, with the rightmost data point from the series investigated in the present study. The solid line indicates the expected values for the composition for a simple metal. The film thicknesses were 30 and 50 nm, respectively.

Figure 2

(a)–(b) Schematics showing two possible orientation variants of ${\mathrm{SmTiO}}_3$ films on LSAT (green): (a) ${(110)}_O\parallel {(010)}_C$ and (b) ${(001)}_O\parallel {(001)}_C$, respectively. (c)–(d) HAADF images of ${\mathrm{SmTiO}}_3$ films grown on LAST recorded along (c) ${[110]}_O$ and (d) ${[001]}_O$, respectively. Two angles, ${\theta }_{\mathrm{xx}}$ and ${\theta }_{\mathrm{xy}}$, which are used to quantify the orthorhombiclike unit cell distortions, are shown in (c).

Figure 3

HAADF images of ${\mathrm{Sm}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ films with Sr concentrations of (a) 5% and (b) 10%, respectively. (c) Distributions of measured deviation angles, ($180°\text{−}{\theta }_{xx}$), of ${\mathrm{SmTiO}}_3$ and ${\mathrm{Sm}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ films show the reduction in orthorhombiclike unit cell distortions with increasing $x$. The vertical axis (counts) are the number of measured deviation angles in all analyzed images.

Figure 4

HAADF images (left), $I_{\mathrm{Sm},\mathrm{Sr}}$ maps (middle), and deviation angle ($90°\text{−}{\theta }_{\mathrm{xy}}$) maps (right) of ${\mathrm{Sm}}_{1-x}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ films with $x=0.05$ (top row) and 0.1 (bottom row). The contrast of intensity maps is adjusted to maximize the intensity distribution. Low atomic column intensities marked by the white arrows in the $I_{\mathrm{Sm},\mathrm{Sr}}$ maps and are associated with the atomic columns containing Sr. Note that the pixel sizes of the intensity map and the deviation angle maps are different.