Magnetic, optical, and electron transport properties of $n\text{-type} {\mathrm{CeO}}_2$: Small polarons versus Anderson localization

We report magnetic susceptibility, electrical conductivity and optical absorption of ${\mathrm{Ce}}_{1-x}{M}_x{\mathrm{O}}_2$ where $M$ = Nb,Ta and $0\le x\le 0.03$. The dc conductivity follows a simple thermally activated Arrhenius-type behavior in the $T=70$–700 K range with a change in slope at $T^{*}\approx 155$ K. The high-temperature activation energy shows gradual increase from $\approx 170$ to 220 meV as the dopant concentration increases. The activation energy of the low-temperature conductivity shows a broad minimum of $\approx 77$ meV at $x\approx 0.01$. Electron transport and localization mechanisms are analyzed in the framework of the Holstein small polaron, Anderson localization, and Jahn-Teller distortion models. The fit to the small polaron mobility is dramatically improved when, instead of the longitudinal phonons, the transverse optical phonons are considered in the phonon-assisted electron transport. This serves as an indirect evidence of a strong $4f^1$ orbital interaction with the oxygen ligands, similar to the case of ${\mathrm{PrO}}_2$. Based on comparison of the experimental data to the models, it is proposed that the defect-induced random electric fields make the dominant contribution to the electron localization in donor-doped ceria.

Figure 1

Inverse magnetic susceptibility of ${\mathrm{Ce}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_2$. The lines are the fit to Eq. (2).

Figure 2

Magnetic parameters obtained from the fit of magnetic susceptibility to Eq. (2).

Figure 3

Electrical conductivity of ${\mathrm{Ce}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_2$ as a function of reciprocal temperature.

Figure 4

Electrical conductivity of ${\mathrm{Ce}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_2$ as a function of reciprocal temperature.

Figure 5

$\text{Low-}T, E_{\mathrm{LT}}$, and $\text{high-}T, E_{\mathrm{HT}}$, activation energies of electrical conductivity of ${\mathrm{Ce}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_2$ and ${\mathrm{Ce}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_2$.

Figure 6

Optical absorption of ${\mathrm{Ce}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_2$.

Figure 7

Room-temperature electron mobility in ${\mathrm{Ce}}_{1-x}{M}_x{\mathrm{O}}_2$ as a function of ${\mathrm{Ce}}^{3+}$ concentration. Solid and dashed lines are calculated adiabatic SP mobilities for LO and TO coupling, respectively.

Figure 8

Temperature dependence of the electron mobility in ${\mathrm{Ce}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_2$ with $x=0.0005$ and 0.02. The solid and dashed lines are the fit to the nonadiabatic SP mobility with SP coupling to the TO and LO phonons, respectively. The fitting parameter $J_p$ is shown in the data legend.

Figure 9

Energy-level diagram for localized SP. The $E_0$ is the energy of the atomic state, $2J_p$ is the SP bandwidth, $E_b$ is the polaron binding energy, and $W$ is the average energy separation between the neighbor SP sites due to the random field potential.