Electrical transport properties and small polarons in Eu_1-xCa_xB_6

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 Ca for the magnetic element Eu exhibits drastic changes in the ρ(T) although the Ca and Eu is of isoelectronic configuration. While Eu_0.8Ca_0.2B₆ shows similar phase transition with pure EuB_6, the ρ(T) of Eu_1-xCa_xB₆ (x= 0.4, and 0.6) shows a gap-like feature at low temperatures (T< 10 K). The upturn of ρ(T) is suppressed with increasing magnetic field, resulting in negative magnetoresistance (MR) behavior. For Eu_0.1Ca_0.9B_6, the MR changes from positive at 10 K < T < 50 K to negative at T 2 K. It is found that the observed exotic ρ(T) is due to the change of the effective carrier density, n_eff(T,H), and Hall mobility, μ_H(T), determined from the Hall measurements. Analysis of the Hall mobility based on a small polaronic model shows that the carrier transport is dominated by hopping between the polaron sites in non-adiabatic regime with four-sites hopping for Eu-rich side and with three-sites hopping for 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 with temperature and field.