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

In the first-principles search for new ferromagnetic-ferroelectric multiferroics, one key indicator is the softening of the lowest frequency polar phonon with ferromagnetic ordering from a paraelectric antiferromagnetic bulk state. In a first-principles survey of the phonon dispersions of a wide range of magnetic perovskites, we identified SrMnO$_3$ as a promising candidate system. We find that a ferromagnetic-ferroelectric phase is stabilized by both compressive and tensile epitaxial strain. For compressive strain, there is a sequence of intermediate magnetic transitions, first to $C$-AFM and then to $A$-AFM ordering, with an increasing fraction of ferromagnetically aligned nearest neighbor Mn. At each of these, the change in magnetic order is accompanied by a jump in the magnitude of the electric polarization, so, near the $A$-AFM-FE$\rightarrow$FE-FM phase boundary at 3.4\% and $G$-AFM-FE$\rightarrow$FE-FM phase boundary at -2.9\%, an applied electric field can induce a nonzero magnetization, and the jump in $c$-lattice constant at -2.9\% strain can generate a large piezomagnetic response. The origin of the large phonon softening in SrMnO$_3$ will be examined, which should provide guidance in identifying additional candidate systems for epitaxial-strain-induced multiferroicity.