Reentrant orbital order and the true ground state of LaSr$_{2}$Mn$_{2}$O$_{7}$.

Strongly correlated electron systems, and colossal magnetoresistive materials in particular, exhibit a strong competition among orbital, charge and spin order. The phase diagram of the bilayer manganites, La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$, display interesting features near half doping, $x\approx0.5$, and it has been commonly accepted that CE order at $x=0.5$ is reentrant. Here, we present x-ray and neutron diffraction data of our purified La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ crystals contrasting the conventional wisdom. Our crystals exhibit CE-type orbital and charge order as the low-temperature ground state for $x=0.5$. For small deviations from $x=0.5$, the high temperature CE phase is replaced at low temperatures by an A-type antiferromagnetic phase {\sl without coexistence}. Larger deviations from $x=0.5$ result in a lack of CE-order at any temperature. Thus small compositional variations could explain why others commonly see this reentrance with coexistence.