Spin and orbital states in La_1.5Sr_0.5CoO₄ studied by electronic structure calculations

Electronic structure of the layered perovskite La_1.5Sr_0.5CoO₄ with a checkerboard Co²⁺/Co³⁺ charge order is studied, using the local-spin-density approximation plus Hubbard U calculations including also the spin-orbit coupling and multiplet effect. Our results show that the Co²⁺ ion is in a high spin state (HS, t_2g⁵e_g²) and Co³⁺ low spin state (LS, t_2g⁶). Due to a small Co²⁺ t_2g crystal field splitting, the spin-orbit interaction produces an orbital moment of 0.26μ_B and accounts for the observed easy in-plane magnetism. Moreover, we find that the Co³⁺ intermediate spin state (IS, t_2g⁵e_g¹) has a multiplet splitting of several tenths of eV and the lowest-lying one is still higher than the LS ground state by 120 meV, and that the Co³⁺ HS state (t_2g⁴e_g²) is more unstable by 310 meV. Either the IS or HS Co³⁺ ions would give rise to a wrong magnetic order and anisotropy.