Electron-lattice coupling, orbital stability and the phase diagram of Ca${}_{2-x}$Sr${}_x$RuO${}_4$

Hartree-Fock calculations are presented of a theoretical model describing the Sr/CaRuO${}_4$ family of compounds. Both commensurate and incommensurate magnetic states are considered, along with orbital ordering and the effect of lattice distortions. For reasonable parameter values, interactions disfavor orbital disproportionation. A coherent description of the observed phase diagram is obtained.