Improper Ferroelectricity at antiferromagnetic domain walls of Perovskite oxides

SmFeO₃ (SFO) was reported to present ferroelectric order at high temperature 670 K, an effect which is still unclear and under debate. We are motivated to explore if a specific mechanism can generate an electrical polarization in SmFeO₃ or, more generally, in perovskites possessing magnetic ordering. In this work, first-principles calculations have been performed on a variety of (initially paraelectric) Xn-m magnetic multidomains in SmFeO₃, with X= G, C, A or F being the predominant magnetic ordering existing inside each domain. These calculations allow us to reveal that (i) domains with even n and m integers become polar and thus multiferroic, with a polarization pointing along the b-axis; (ii) the polarization of these even n and m domains decreases as the sum of n and m increases for a given predominant magnetic ordering X; and (iii) this improper polarization is related to the motions of oxygen ions at the domain walls. A unified model for the spin-order induced ferroelectricity demonstrates that the polarization arises from symmetric magnetic exchange striction interactions due to magnetic domain walls.