The local magnetic field response of $\mathrm{La_{2-x}Sr_{x}CuO_{4}}$ on the overdoped side of the phase diagram as revealed by $\mathrm{\mu SR}$

There is now a large body of evidence from local probes which point to intrinsic heterogeneity in the cuprates. One example is the recent reports of an inhomogenous magnetic field response in the underdoped materials, as revealed by muon spin rotation experiments. In an effort to explore this field response, we have measured the $\mathrm{/mu SR}$ spectra of $\mathrm{La_{2-x}Sr_{x}CuO_{4}}$ in a number of applied magnetic fields and with $x$ ranging from the underdoped to heavily overdoped materials. I will summarize these efforts, and present the resultant data in the context of existing literature. Possible interpretations and directions for future research will be discussed.