We investigated the transport properties of BaFe$_2$As$_2$ single crystals before and after annealing with BaAs powder. The annealing remarkably improves transport properties, in particular the magnitude of residual resistivity which decreases by a factor of more than 10. From the resistivity measurement on detwinned crystals we found that the anisotropy of the in-plane resistivity is remarkably diminished after annealing, indicative of dominant contributions to the charge transport from the carriers with isotropic and high mobility below magnetostructural transition temperature $T_{rm s}$ and the absence of nematic state above $T_{rm s}$. We found that the Hall resistivity shows strong non-linearity against magnetic field and the magnetoresistance becomes very large at low temperatures. These results give evidence for the manifestation of multiple carriers with distinct characters in the ordered phase below $T_{rm s}$. By analyzing the magnetic field dependences, we found that at least three carriers equally contribute to the charge transport in the ordered phase, which is in good agreement with the results of recent quantum oscillation measurements.
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