Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

Abstract

Motivated by recent experimental progress in transition metal oxides with the K2NiF4 structure, we investigate the magnetic and orbital ordering in α-Sr2CrO4. Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of t2g orbitals in α-Sr2CrO4, with the 3d 2 electronic configuration for the Cr 4+ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground state phase diagram for the two dimensional compound α-Sr2CrO4. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of α-Sr2CrO4, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound α-Sr2CrO4, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with dxy driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the dxz and dyz orbitals driving the orbital order.