Charge Order Driven Multiferroic Behaviour in Sr${}_4$Fe${}_6$O${}_{12}$: An $\text{Ab-initio}$ Study

Abstract

In this letter, we report the structural, electronic and ferroelectric properties of the layered mixed-valent transition-metal compound, Sr${}_4$Fe${}_6$O${}_{12}$ (SFO). We demonstrate how SFO undergoes a phase transition from a high-temperature (T) centrosymmetric tetragonal phase ($P{4}_2/mnm$) to a low-T polar orthorhombic phase ($Pmn{2}_1$). The transition is primarily driven by charge ordering at tetrahedral Fe-layer creating Fe${}^{3+}$ and Fe${}^{2+}$ cations between two edge sharing tetrahedra. This charge ordering induces electronic polarization, which is remarkably larger (3.5 times) in magnitude than ionic polarization and oppositely directed, giving a net polarization of 0.05 C/m${}^2$ which is comparable to the state-of-the-art rare-earth nickelets and manganite perovskites. The direction of structural distortion, governed by the polar mode irrep $\hat{I}{“}_5^{-}$, depends sensitively on the type of magnetic ordering in the Fe-octahedral layer. Consequently, both the ionic and electronic polarization directions are influenced by magnetic ordering, suggesting the potential for multiferroic behavior with strong magneto-electric coupling in this material.