Polaronic conduction in n-type ${\mathrm{BaTiO}}_3$ doped with ${\mathrm{La}}_2$${\mathrm{O}}_3$ or ${\mathrm{Gd}}_2$${\mathrm{O}}_3$

The dielectric properties and conductivities (σ) of ${\mathrm{BaTiO}}_3$ doped with 0.03 mol % of ${\mathrm{La}}_2$ ${\mathrm{O}}_3$ or ${\mathrm{Gd}}_2$ ${\mathrm{O}}_3$ were investigated in the temperature range of 10–300 K. A speculation over the experimental results, such as the temperature independence of conductivities below 30 K, linear Arrhenius relations between σ${\mathit{T}}^{3/2}$ and 1/T with an activation energy of 0.070±0.002 eV above 50 K, and relaxation absorptions in the loss tangents with an activation energy of 0.068±0.002 eV, leads to the conclusion that the dominant conduction in n-type ${\mathrm{BaTiO}}_3$ is due to hopping motions of nonadiabatic small polarons. This conclusion is confirmed theoretically. Based upon polaron energies obtained experimentally, several parameters relevant to a nonadiabatic small polaron in this material are estimated.