Spin and orbital ordering in bilayer Sr3Cr2 O7

Abstract

Using maximally localized Wannier functions obtained from density functional theory calculations, we derive an effective Hubbard Hamiltonian for a bilayer of Sr3Cr2O7, the n=2 member of the Ruddlesden-Popper Srn+1CrnO3n+1 system. The model consists of effective t2g orbitals of Cr in two square lattices, one above the other. The model is further reduced at low energies and two electrons per site to an effective Kugel-Khomskii Hamiltonian that describes interacting spins 1 and pseudospins 1/2 at each site describing spin and orbital degrees of freedom, respectively. We solve this Hamiltonian at zero temperature using pseudospin bond operators and spin waves. Our results confirm a previous experimental and theoretical study that proposes spin ordering is antiferromagnetic in the planes and ferromagnetic between planes, while pseudospins form vertical singlets, although the interplane separation is larger than the nearest-neighbor distance in the plane. We explain the physics behind this rather unexpected behavior.