Epitaxial-strain-induced multiferroicity in SrMnO$_{3}$ from first principles

First-principles density-functional calculations reveal a large spin-phonon coupling in cubic SrMnO$_{3}$, with ferromagnetic ordering producing a polar instability. Through combination of this coupling with the strain-polarization coupling characteristic of perovskites, the bulk antiferromagnetic paraelectric ground state of SrMnO$_3$ is shown to be driven to a previously unreported multiferroic ferroelectric-ferromagnetic state by increasing epitaxial strain, both tensile and compressive. This state has a computed polarization and estimated Curie temperature above 54 $\mu$C/cm$^2$ and 92 K. Large mixed magnetic-electric-elastic responses are predicted in the vicinity of the phase boundaries.