Electronic phase separation in La$_{2-x}$Sr$_x$CuO$_{4+y}$

We have performed a combination of $\mu $SR and bulk magnetization experiments on oxygen-intercalated single crystals of \textit{La}$_{2-x}$\textit{Sr}$_{x}$\textit{CuO}$_{4+y}$, with various Sr contents x. All of the samples were both superconducting with $T_{C}$\textit{$\sim $40 K} and magnetic with a spin density ordering temperature $T_{M}$\textit{$\sim $40 K}. Interpretation of our results suggests that the superconducting and magnetic states arise from separate regions of the sample and comprise separate phases. The coexistence of these phases implies a phase separation that is purely electronic. In fact, we have seen no evidence for a structural phase separation in x-ray diffraction studies. The magnetic region is not superconducting and appears to be closely related to the anomalous, 1/8 hole doped, weakly superconducting versions of \textit{La}$_{2-x}M_{x}$\textit{CuO}$_{4}$. While the superconducting regions are harder to characterize, there is evidence that these regions are completely non-magnetic. This work reveals the subtleties of a more complex relationship between magnetism and superconductivity in the copper oxides than has previously been assumed. This work was partially supported by the US-DOE through contract DE-FG02-00ER45801 and the Cottrell Scholar Program of the Research Corporation.