Magnetotransport and noise in lightly doped La$_{2-x}$Sr$_x$CuO$_4$ and La$_{2}$Cu$_{1-x}$Li$_{x}$O$_4$

We report a detailed comparative study of magnetotransport and noise in high quality single crystals of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and La$_{2}$Cu$_{1-x}$Li$_{x}$O$_4$ ($x=0.03$) at temperatures 0.100$\leq T$(K)$\leq 150$ and fields $0\leq B$(T)$\leq 18$ parallel and perpendicular to the c-axis. Our results demonstrate that, in both materials at low $T$, the positive magnetoresistance (MR) exhibits signatures of glassiness, such as hysteretic behavior and memory. At such low $T\ll T_{sg} $ ($T_{sg}$ -- spin glass transition temperature) , the resistance noise data reveal other glassy features, such as slowing down of the charge dynamics and the onset of cooperativity as $T$ is reduced. The crossover to negative MR takes place at higher $T$ and $B$ in all samples and for both $B$ orientations. However, for $B\parallel c$, a steplike decrease in MR has been observed only in La$_{2}$Cu$_{1-x}$Li$_{x}$O$_4$ at high $T$, as the system enters the N\'{e}el state, similar to the result obtained on antiferromagnetic LSCO with $x=0.01$~[1]. *Supported by NSF No. DMR-0403491, NHMFL via NSF No. DMR-0084173, and The Royal Society.\\ \noindent [1] Y. Ando \textit{et al.}, Phys. Rev. Lett. \textbf{90}, 247003 (2003).