BaFe$_2$Se$_3$: a high $T_{\rm C}$ magnetic multiferroic with large ferrielectric polarization

The iron-selenides are important because of their superconducting properties. Here, an unexpected phenomenon is predicted to occur in an iron-selenide compound with a quasi-one-dimensional ladder geometry: BaFe$_2$Se$_3$ should be a magnetic ferrielectric system, driven by its magnetic block order via exchange striction. A robust performance (high $T_{\rm C}$ and large polarization) is expected. Different from most multiferroics, BaFe$_2$Se$_3$ is ferrielectric, with a polarization that mostly cancels between ladders. However, its strong magnetostriction still produces a net polarization that is large ($\sim$$0.1$ $\mu$C/cm$^2$) as compared with most magnetic multiferroics. Its fully ferroelectric state, with energy only slightly higher than the ferrielectric, has a giant improper polarization $\sim$$2-3$ $\mu$C/cm$^2$.