Title: Theoretical investigation of excitonic magnetism in LaSrCoO$_{4}$,
Abstract: 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.