Electrical transport properties and small polarons in Eu_1-xCa_xB₆

Temperature- and field-dependent resistivity ρ(T,H) and Hall effect measurements have been carried out for the Eu_1-xCa_xB₆ (x=0.2, 0.4, 0.6, and 0.9) compounds. The replacement of Eu with Ca invoked drastic changes in the ρ(T) although Ca and Eu are isoelectronic. While Eu_0.8Ca_0.2B₆ showed a phase transition similar to that of pure EuB₆, the ρ(T) of Eu_1-xCa_xB₆ with x = 0.4 and 0.6 showed a rapid increase at low temperatures (T ≤ 10 K). The upturn of the ρ(T) was suppressed as the magnetic field increased, resulting in negative magnetoresistance (MR). For Eu_0.1Ca_0.9B₆, the MR changed from positive at 10 K ≤ T ≤ 50 K to negative at T≊2 K. It was found that the observed exotic ρ(T) is due to the change of the effective carrier density n_eff and Hall mobility μ_H determined from the Hall measurements. Analysis of the Hall mobility based on a small polaronic model showed that the carrier transport is dominated by hopping between the polaron sites in a nonadiabatic regime with four-site hopping for the Eu-rich side and three-site hopping for the Eu-poor side of the compounds. This polaronic scenario of the transport is consistent with the observed ρ(T,H), MR(T), n_eff(T,H), and μ_H(T) variation.