Abstract
Our studies have significantly modified the conventionally held view of the phase diagram of ${\text{La}}_{2\ensuremath{-}2x}{\text{Sr}}_{1+2x}{\text{Mn}}_{2}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ for two compositions exhibiting charge (and orbital) order (CO), i.e., at hole-doping levels, $h=x\ensuremath{-}\ensuremath{\delta}$, of $\ensuremath{\sim}0.5$ and $\ensuremath{\sim}0.6$. These CO states are stable over very narrow doping ranges $(\ensuremath{\Delta}h\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}0.005)$ at the lowest temperatures, but those ranges increase at higher temperatures (to $\ensuremath{\Delta}h\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}0.02$) in a manner consistent with simple entropy considerations. Such narrow ranges dictate the crucial need for crystal homogeneity. Attesting to such homogeneity is a conductivity ratio of $g{10}^{10}$ upon crossing the first-order phase boundary from CO at $h=0.60$ to $\text{A}$-type antiferromagnetic (AAFM) at $h\ensuremath{\sim}0.59$ or $h\ensuremath{\sim}0.61$ plus two findings that were missed in the existing literature: that these CO phases are the ground state at the lowest temperatures, and for $h\ensuremath{\sim}0.5$, that coexistence of the CO and AAFM phase is absent at any temperature.
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