Orbital-ordered ferromagnetic insulating state in tensile-strained SrCoO$_{3}$ thin films

At ambient pressure, bulk SrCoO$_{3}$ is a ferromagnetic (FM) metal in cubic perovskite structure. By contrast, magnetic properties of epitaxial SrCoO$_{3}$ thin films, especially at high tensile strain ($\varepsilon \gtrsim 3$\%), remain unclear: Previous calculations had predicted antiferromagnetic (AFM) states more energetically favorable in this regime, but recent experiments indicated a FM insulating state. In this work, using first-principles calculations, we perform an extensive search for the structural, spin, magnetic, and orbital states of SrCoO$_{3}$ thin films. Our calculations indicate that at $0 < \varepsilon \lesssim 2.5$\%, SrCoO$_{3}$ favors a FM half-metallic state with intermediate-spin ($t_{2g}^{5}e_{g}^{1}$-like) Co exhibiting $d^{6}\underline L$ character. At $\varepsilon \gtrsim 2.5$\%, a FM insulating state with high-spin ($t_{2g}^{4}e_{g}^{2}$-like) Co dominates. This FM insulating state is achieved via complicated orbital ordering, cooperative Jahn--Teller distortion, and octahedral tilting about all three crystal axes.