Possible adiabatic polaronic hopping inCa1−xEuxB6(x=0.005, 0.01, and 0.05)

Abstract

Using temperature- and field-dependent resistivity $\ensuremath{\rho}(T,H)$ measurements, we investigate the anomalous transport properties of a series of compounds of ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{B}}_{6}$ ($x=0.005$, 0.01, and 0.05). It is found that the electrical transport in ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{B}}_{6}$ ($x=0.005$, 0.01, and 0.05) at high temperatures $(T\ensuremath{\geqslant}100\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ is dominated by polaron hopping in an adiabatic regime. Magnetoresistance, defined by $\ensuremath{\Delta}\ensuremath{\rho}∕{\ensuremath{\rho}}_{0}=[\ensuremath{\rho}(H)\ensuremath{-}\ensuremath{\rho}(0)]∕\ensuremath{\rho}(0)$, is also found to be positive and follows Kohler's rule for compounds of $x=0.005$ and 0.01, indicating that the transport property is also dominated by a normal metallic conduction. Comparing the results in this study with the polaron hopping model in a nonadiabatic regime for ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{B}}_{6}$ $(x\ensuremath{\geqslant}0.1)$ [Jong-Soo Rhyee et al., Phys. Rev. B 67, 125102 (2003)], we suggest that the hopping mechanism changes gradually from adiabatic to nonadiabatic hopping with increasing Eu concentration.