Epitaxial-Strain-Induced Multiferroicity in ${\mathrm{SrMnO}}_3$ from First Principles

First-principles calculations reveal a large spin-phonon coupling in cubic ${\mathrm{SrMnO}}_3$, 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 is driven to a previously unreported multiferroic ferroelectric-ferromagnetic state by increasing epitaxial strain. This state has a computed $P_s>54\mu \mathrm{C}/{\mathrm{cm}}^2$ and magnetic $T_c>92\mathrm{K}$. Large mixed magnetic-electric-elastic responses are predicted in the vicinity of the phase boundaries.

Figure 1

$\mathrm{GGA}+U$ total energies of various structures, per formula unit, obtained by freezing in the given mode(s). Calculations were performed at integer values of strain and interpolated. The energies of structures with FM ordering are shown in red, for $G$-AFM in blue, $C$-AFM in green and $A$-AFM in violet. Vertical black dotted lines at 1.0%, 2.0%, 2.8%, and 3.4% strain indicate phase boundaries separating $Imma(G\mathrm{\text{−}}\mathrm{AFM})$, $Ima2(G\mathrm{\text{−}}\mathrm{AFM})$, $Ima2(C\mathrm{\text{−}}\mathrm{AFM})$, $Ima2(A\mathrm{\text{−}}\mathrm{AFM})$, and $Ima2(\mathrm{FM})$ states. The inset is a schematic showing the stability of the FM-FE state at large strain.

Figure 2

(a) Computed ferroelectric polarization of ${\mathrm{SrMnO}}_3$ $G$-AFM (square), $C$-AFM (down triangle), $A$-AFM (up triangle) and FM (circle) in the lowest energy structure at each strain value. The fractions of parallel nearest neighbor spins in each state are given. The bold black line follows the polarization of the lowest energy structure with changing strain. The linear phase diagram at the top, not on the same scale, shows the phases and phase boundaries as computed within $\mathrm{LSDA}+U$ for comparison. Open and solid symbols represent structures where $R$ rotation is along [110] and [001], respectively. (b) Magnetic ordering temperatures were estimated from computed values of $\Delta E$ as described in the text. (c) $c$ lattice parameter for the lowest energy structure at each strain value.