First principles study of the spin state transitions in GdBaCo$_2$O$_{5.5}$

Electronic structure calculations were carried out on the compound GdBaCo$_2$O$_{5.5}$. The electronic structure variation with a change in the spin state of the Co$^{3+}$ ion in an octahedral environment has been studied. All the insulating phases are described and possible scenarios for the metallic ones are presented. Orbital ordering is shown to take place and the electronic structure leading to it is determined. The Ising-like anisotropy shown experimentally can be predicted. Also, big unquenched orbital angular momenta are calculated and their origin is described.