Novel positive magnetoresistance in lightly doped La$_{2}$CuO$_4$

We have measured magnetoresistance (MR) in single crystals of La$_{1.97}$Sr$_{0.03}$CuO$_4$ and La$_{2}$Cu$_{0.97}$Li$_{0.03}$O$_4$ at temperatures 0.050$\leq T$(K)$\leq 70$ and fields $0\leq B$(T)$\leq 18$ parallel and perpendicular to the c-axis. Our study reveals an unusual, low-field positive MR in both in-plane and c-axis transport in both materials and for both \emph{B} orientations. However, while the positive c-axis MR may persist up to \emph{T} as high as 40 K, the large positive in-plane MR occurs only at very low $T\ll T_{sg}$ ($T_{sg}$ -- spin glass transition temperature). In that regime, where the noise spectroscopy disclosed slow and correlated charge dynamics [1], both the in-plane and c-axis positive MR exhibit signatures of glassiness, such as memory and hysteresis. We discuss the possible mechanism responsible for this novel low-field positive MR that appears to be intimately related to the emergence of the charge glass dynamics. [1] I. Rai\v{c}evi\'c \textit{et al.}, Phys. Rev. Lett. \textbf{101}, 177004 (2008).