Metal-insulator transition in ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$

We investigated single crystals of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ with a tetragonal tungsten bronze (TTB) structure, which exhibits a metal-insulator transition with $x$. We found that there is a one-dimensional anisotropy with a higher dc conductivity along the $c$ axis in the metallic phase, but it disappears in the insulating phase. The optical conductivity spectra of the metallic samples show similar anisotropy to the dc conductivity, but the anisotropy persists even in the insulating phase. These experimental results, together with the result of magnetic susceptibility, indicate that the disorder caused by the Sr ions loosely bound to the surrounding oxygen ions plays an important role in the metal-insulator transition.

Figure 1

Crystal structures of (a) perovskite structure (${\mathrm{ABO}}_3$) and (b) tetragonal tungsten bronze (TTB) structure (${\mathrm{A}}_3{\mathrm{B}}_5{\mathrm{O}}_{15}$). Each square corresponds to a ${\mathrm{BO}}_6$ octahedron viewed from the vertical direction and each circle corresponds to an A ion. The B ions exist at the centers of the squares, and the oxygen ions exist at the corners of the squares. Note that the A ion is shifted from the B ion by half the height of the ${\mathrm{BO}}_6$ octahedron perpendicular to the plane. In (b), blue squares are newly inserted whereas the blue circles in (a) disappear. The three dotted lines from the A2 ion indicate the six oxygen ions (three above and three below are overlapped in the figure) nearest to it.

Figure 2

Temperature dependence of resistivity for ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ along the (a) $c$ and (b) $a$ axes. The dashed lines in (b) refer to the resistivity along the $c$ axis shown in (a).

Figure 3

Temperature dependence of resistivity for two different samples, No. 1 (thick lines) and No. 2 (thin lines), of ${\mathrm{Ba}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ along the $a$ axis (${\rho }_a$) and $c$ axis (${\rho }_c$). The data of ${\rho }_c$ is multiplied by four for clarity.

Figure 4

(a) Resistivity of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ at 280 K (red circles) and 20 K (blue squares) along the $c$ axis (${\rho }_c$, closed symbols) and $a$ axis (${\rho }_a$, open symbols) as a function of $x$. (b) Anisotropy of resistivity, ${\sigma }_c/{\sigma }_a$, at 280 K (red circles) and 20 K (blue squares) as a function of $x$.

Figure 5

Reflectivity spectra of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ at room temperature with the polarization along (a) the $c$ axis ($R_c$) and (b) $a$ axis ($R_a$). The dashed line in (b) is $R_c$ with $x=0$ shown in (a). The arrows show the position of the plasma edge $\hslash {\omega }_p$ for $x=0$ and 2.

Figure 6

Optical conductivity spectra of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ at room temperature along (a) the $c$ axis (${\sigma }_c$) and (b) $a$ axis (${\sigma }_a$). The dashed line in (b) is ${\sigma }_c$ with $x=0$ shown in (a). The open circle in (a) corresponds to the dc conductivity along the $c$ axis for $x=2$.

Figure 7

Spectral weight of optical conductivity below 1.4 eV as a function of $x$ for ${\sigma }_c$ ($W_c$, closed circles) and ${\sigma }_a$ ($W_a$, open circles) of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$.

Figure 8

Hall coefficient along the $ac$ plane ($R_{ac}$, closed circles) and $ab$ plane ($R_{ab}$, open circles) as a function of temperature for ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ with (a) $x=0$, (b) $x=0.5$, and (c) $x=1.0$.

Figure 9

(a) Seebeck coefficient (thick lines, left axis) and resistivity (thin lines, right axis) for ${\mathrm{Ba}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ from 300 to 900 K along the $c$ and $a$ axes. (b) Power factor $PF=S^2/\rho$ for ${\mathrm{Ba}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ along the $c$ and $a$ axes.

Figure 10

Band structure of ${\mathrm{Ba}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$. The inset shows the symmetry labels for the primitive tetragonal lattice.

Figure 11

Fermi velocities $v_x(i,\mathit{k})$ and $v_z(i,\mathit{k})$ and relative inverse effective mass tensor $M_{yy}^{-1}\left(i,\mathit{k}\right)$ at $E=E_{\mathrm{F}}$ (upper panels) and $E=E_{\mathrm{F}}-0.15$ eV (lower panels).

Figure 12

(a) Calculated Hall coefficients $R_{ab}$ and $R_{ac}$, the anisotropy in the conductivity ${\sigma }_c/{\sigma }_a$, (b) Seebeck coefficients $S_a, S_c$, and the anisotropy in the Seebeck coefficient $S_a/S_b$, as functions of the number of electrons per Nb site. In both panels, dotted horizontal lines correspond to the experimental values for ${\mathrm{Ba}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$, and vertical solid lines correspond to the number of electrons per Nb for the stoichiometric (0.2) and slightly hole-doped (0.08, where $E_{\mathrm{F}}$ is lower by 0.15 eV) compositions.

Figure 13

Magnetic susceptibility of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ along (a) the $c$ axis and (b) the $a$ axis.

Figure 14

The resistivity along the $c$ axis (${\rho }_c$) and the $a$ axis (${\rho }_a$) of ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ with $x=2$ in a log scale as functions of (a) $T^{-1/2}$, (b) $T^{-1/3}$, and (c) $T^{-1/4}$. The dashed-straight line in each figure is guide to the eye.