  By combining first-principles electronic-structure calculations with the
model Hamiltonian approach, we systematically study the magnetic properties of
sodium superoxide (NaO2), originating from interacting superoxide molecules. We
show that NaO2 exhibits a rich variety of magnetic properties, which are
controlled by relative alignment of the superoxide molecules as well as the
state of partially filled antibonding molecular \pi_g-orbitals. The orbital
degeneracy and disorder in the high-temperature pyrite phase gives rise to weak
isotropic antiferromagnetic (AFM) interactions between the molecules. The
transition to the low-temperature marcasite phase lifts the degeneracy, leading
to the orbital order and formation of the quasi-one-dimensional AFM spin
chains. Both tendencies are consistent with the behavior of experimental
magnetic susceptibility data. Furthermore, we evaluate the magnetic transition
temperature and type of the long-range magnetic order in the marcasite phase.
We argue that this magnetic order depends on the behavior of weak isotropic as
well as anisotropic and Dzyaloshinskii-Moriya exchange interactions between the
molecules. Finally, we predict the existence of a multiferroic phase, where the
inversion symmetry is broken by the long-range magnetic order, giving rise to
substantial ferroelectric polarization.
