Anomalous Magnetoresistance in Pb-doped Bi$_2$Sr$_2$Co$_2$O$_y$ Single Crystals

Magnetoresistance (MR) of the Bi$_{2-x}$Pb$_x$Sr$_2$Co$_2$O$_y$ ($x$=0, 0.3, 0.4) single crystals is investigated systematically. A nonmonotonic variation of the isothermal in-plane and out-of-plane MR with the field is observed. The out-of-plane MR is positive in high temperatures and increases with decreasing $T$, and exhibits a pronounced hump, and changes the sign from positive to negative at a centain temperature. These results strongly suggest that the observed MR consists of two contributions: one \emph{negative} and one \emph{positive} component. The isothermal MR in high magnetic fields follows a $H^2$ law. While the negative contribution comes from spin scattering of carriers by localized-magnetic-moments based on the Khosla-Fischer model.