Theoretical investigation of excitonic magnetism in LaSrCoO$_{4}$

We use the LDA+U approach to search for possible ordered ground states of LaSrCoO$_4$. We find a staggered arrangement of magnetic multipoles to be stable over a broad range of Co $3d$ interaction parameters. This ordered state can be described as a spin-denity-wave-type condensate of $d_{xy} \otimes d_{x^2-y^2}$ excitons carrying spin $S=1$. Further, we construct an effective strong-coupling model, calculate the exciton dispersion and investigate closing of the exciton gap, which marks the exciton condensation instability. Comparing the layered LaSrCoO$_4$ with its pseudo cubic analog LaCoO$_3$, we find that for the same interaction parameters the excitonic gap is smaller (possibly vanishing) in the layered cobaltite.