Improper ferroelectricity at antiferromagnetic domain walls of perovskite oxides

First-principles calculations are performed on magnetic multidomain structures in the $\mathrm{SmFe}{\mathrm{O}}_3$ rare-earth orthoferrite compound. We focus on the magnetic symmetry breaking at (001)-oriented antiphase domain walls, treating magnetism in the simplest (collinear) approximation without any relativistic (spin-orbit coupling) effects. We found that the number of $\mathrm{Fe}{\mathrm{O}}_2$ layers inside the domains determines the electrical nature of the whole system: multidomains with odd number of layers are paraelectric, while multidomains with even number of layers possess an electric polarization aligned along $b$ axis and a resulting multiferroic $Pmc{2}_1$ ground state. Our ab initio data and model for ferroelectricity induced by spin order reveal that this polarization is of the improper type and originates from an exchange striction mechanism that drives a polar displacement of the oxygen ions located at the magnetic domain walls. Additional calculations ratify that this effect is general among magnetic perovskites with an orthorhombic $\mathrm{SmFe}{\mathrm{O}}_3\text{−}\mathrm{like}$ structure.

Figure 1

Schematic of the $\mathrm{F}{\mathrm{e}}^{3+}$ spin arrangement in the studied $X_0$ magnetic monodomains and some $Xn\text{−}m$ multidomains (see text) of SFO for (a) $X=\mathrm{G}$, (b) C, (c) A, and (d) F. The green planes locate the domain walls, while blue and red arrows represent spin up and spin down, respectively.

Figure 2

Computed magnitude of the electrical polarization for the various studied combinations of $n$ and $m$ for Case 1 (see text) in the (a) $\mathrm{G}n\text{−}m$, (b) $\mathrm{C}n\text{−}m$, (c) $\mathrm{A}n\text{−}m$, and (d) $\mathrm{F}n\text{−}m$ structures.

Figure 3

Displacements of O ions (represented by black arrows) located at domain walls (represented by green lines) in the (a) $\mathrm{G}3\text{−}3$ and (b) $\mathrm{G}4\text{−}4$ spin configurations for Case 1 (see text).

Figure 4

Schematic illustration of the four polarization coefficient vectors ${\stackrel{\rightharpoonup }{P}}_{\mathrm{es}}^{\mathrm{I}},{\stackrel{\rightharpoonup }{P}}_{\mathrm{es}}^{\mathrm{II}},{\stackrel{\rightharpoonup }{P}}_{\mathrm{es}}^{\mathrm{III}},{\stackrel{\rightharpoonup }{P}}_{\mathrm{es}}^{\mathrm{IV}}$ (represented by purple arrows). The brown spheres represent the Fe atoms, and the purple arrows center on the O atoms that located on SmO layer. Sm and O atoms are not shown for clarity.