Spin blockade, orbital occupation, and charge ordering in La$_{1.5}$Sr$_{0.5}$CoO$_{4}$

Using Co-$L_{2,3}$ and O-$K$ x-ray absorption spectroscopy, we reveal that the charge ordering in La$_{1.5}$Sr$_{0.5}$CoO$_{4}$ involves high spin ($S$=3/2) Co$^{2+}$ and low spin ($S$=0) Co$^{3+}$ ions. This provides evidence for the spin blockade phenomenon as a source for the extremely insulating nature of the La$_{2-x}$Sr$_{x}$CoO$_{4}$ series. The associated $e_g^2$ and $e_g^0$ orbital occupation accounts for the large contrast in the Co-O bond lengths and, in turn, the high charge ordering temperature. Yet, the low magnetic ordering temperature is naturally explained by the presence of the non-magnetic ($S$=0) Co$^{3+}$ ions. From the identification of the bands we infer that La$_{1.5}$Sr$_{0.5}$CoO$_{4}$ is a narrow band material.