Electrical and magnetic properties of hexagonal $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$

The electrical resistivity, Hall coefficient, and magnetic susceptibility of $n$-type hexagonal $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ $\left(\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }\right)$ have been measured in the $5–400\mathrm{K}$ temperature range. Above $200\mathrm{K}$ this compound undergoes a transition from an insulating to a semiconducting state. Below $140\mathrm{K}$ Hall effect data indicate the existence of an energy gap of approximately $43\mathrm{meV}$ separating the localized electron ground state from the conduction band. Magnetic measurements reveal a strong magnetic anomaly in $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ with a maximum in the susceptibility at around $160–200\mathrm{K}$. This anomaly is quite similar to that of the hexagonal $\mathrm{Ba}{\mathrm{Mg}}_{1∕3}{\mathrm{Ru}}_{2∕3}{\mathrm{O}}_3$ which may indicate that the electron ground state in $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ is comprised of spin singlet ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{3+}$ dimers. We further propose that the thermal dissociation of these dimers is responsible for the change in the electron transport mechanism in $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$.

Figure 1

Room-temperature x-ray diffraction pattern of sample C1 (+). Calculated diffraction pattern from Rietveld refinement of $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ (solid line). The vertical bars indicate the positions of expected Bragg peaks. The difference between observed and calculated data is shown at the bottom of the plot.

Figure 2

Electrical resistivity of the $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ single crystal (solid line), C1 ceramic (dotted line), and C2 ceramic (dashed line) as a function of temperature. The inset shows an Arrhenius plot of the resistivity as a function of $1∕T$ for the same samples.

Figure 3

The best linear fit of the low-temperature part of the electrical resistivity of the $\mathrm{hex}\text{−}\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3-\delta }$ samples as a function of $T^{-m}$. (a) C1 ceramic $m=0.67$; (b) single crystal $m=0.50$; (c) C2 ceramic $m=0.20$.

Figure 4

Temperature dependence of the Hall coefficient of the C1 ceramic (squares), single crystal (circles), and C2 ceramic (triangles). The solid line indicates an activation energy of $43\mathrm{meV}$.

Figure 5

Temperature dependence of the Hall mobility of electrons in C1 ceramic (squares), single crystal (circles), and C2 ceramic (triangles).

Figure 6

Molar magnetic susceptibility of C0 ceramic (solid squares), C1 ceramic (open squares), single crystal (circles), and C2 ceramic (triangles). Solid lines are fits to the low-temperature data as described in the text.