Pressure-induced spin-state ordering in Sr${}_2$CoO${}_3$F

We study theoretically low-temperature phases of a recently synthesized compound Sr${}_2$CoO${}_3$F under pressure. The analysis combining LDA+DMFT and a strong-coupling effective model points to the existence of not only normal paramagnetic and antiferromagnetic regimes, but also a spin-state ordered phase in a certain range of applied pressure and low temperature. This order is characterized by a checkerboard arrangement of different spin states of cobalt atoms in the lattice.