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. With increasing tensile epitaxial strain, there is a series of structural and magnetic phase transitions, with a ferromagnetic ferroelectric structure appearing as the equilibrium phase above a critical strain of 4.5 $\pm$ 1%.