  Akali superoxides AO2 (A=Na, K, Rb, Cs), due to an open p shell of the oxygen
ion O2^- with degenerate pi orbitals, have spin and orbital degrees of freedom.
The complex magnetic, orbital, and structural phase transitions observed
experimentally in this family of materials are only partially understood. Based
on density functional theory, we derive a strong-coupling effective model for
the isostructural compounds AO2 (A=K, Rb, Cs) from a two-orbital Hubbard model.
We find that CsO2 has highly frustrated exchange interactions in the a-b plane,
while the frustration is weaker for RbO2 and KO2. We solve the resulting
Kugel-Khomskii model in the mean-field approximation. We show that CsO2
exhibits an antiferro-orbital (AFO) order with the ordering vector q=(1,0,0)
and a stripe antiferromagnetic order with q=(1/2,0,0), which is consistent with
recent neutron scattering experiments. We discuss the role of the pi-orbital
degrees of freedom for the experimentally observed magnetic transitions and
interpret the as-yet-unidentified T_s2=70K transition in CsO2 as an orbital
ordering transition.
