Oxygen stoichiometry, crystal structure, and magnetism in La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$

We have prepared a series of polycrystalline samples La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$} with $0 < \delta \le 0.21$ and characterized their oxygen content, crystal structure, and magnetic properties. While the fully oxygenated samples are good ferromagnets, samples with larger $\delta$ values display increasingly broad magnetic transitions. The saturation magnetization at 5 K falls rapidly as $\delta$ increases. First principles electronic structure calculations provide insights into the magnetic behavior of the fully oxygenated compound, and the manner in which ferromagnetic ordering is affected by increasing oxygen non-stoichiometry.