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The origin of the $3 \times 1$ reconstruction observed in epitaxialLaCoO$_{3}$ films on SrTiO$_3(001)$ is assessed by using first-principlescalculations including a Coulomb repulsion term. We compile a phase diagram asa function of the oxygen pressure, which shows that ($3 \times 1$)-orderedoxygen vacancies (LaCoO$_{2.67}$) are favored under commonly used growthconditions, while stoichiometric films emerge under oxygen-rich conditions.Growth of further reduced LaCoO$_{2.5}$ brownmillerite films is impeded byphase separation. We report two competing ground-state candidates forstoichiometric films: a semimetallic phase with $3 \times 1$low-spin/intermediate-spin/intermediate-spin magnetic order and asemiconducting phase with intermediate-spin magnetic order. This demonstratesthat tensile strain induces ferromagnetism even in the absence of oxygenvacancies. Both phases exhibit an intriguing ($3 \times 1$)-reconstructedoctahedral rotation pattern and accordingly modulated La-La distances. Inparticular, charge and bond disproportionation and concomitant orbital order ofthe $t_{2g}$ hole emerge at the Co sites that are also observed for unstrainedbulk LaCoO$_3$ in the intermediate-spin state and explain structural dataobtained by x-ray diffraction at elevated temperature. Site disproportionationdrives a metal-to-semiconductor transition that reconciles theintermediate-spin state with the experimentally observed low conductivityduring spin-state crossover without Jahn-Teller distortions.

Competition of defect ordering and site disproportionation in strained LaCoO$_{3}$ on SrTiO$_3$(001)