Charge order driven multiferroic behavior in Sr₄ Fe₆ O₁₂: An <em>ab-initio</em> study

Here, in this paper, we report the structural, electronic, and ferroelectric properties of the layered mixed-valent transition-metal compound Sr₄⁢ Fe₆ ⁢O₁₂ (SFO). We demonstrate how SFO undergoes a phase transition from a high-temperature (𝑇) centrosymmetric tetragonal phase (𝑃⁢4₂/𝑚⁢𝑛⁢𝑚) to a low-𝑇 polar orthorhombic phase (𝑃⁢𝑚⁢𝑛⁢2₁). The transition is primarily driven by charge ordering at tetrahedral Fe-layer creating Fe³⁺ and Fe²⁺ 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/m² 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 $Γ^−_5$, 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 magnetoelectric coupling in this material.. Authors: Sarkar, Arindam [Indian Institute of Technology (IIT), Mumbai (India)] (ORCID:0009000519772910); Das, Hena [Tokyo Institute of Technology (Japan)]; Singh, Prashant [Ames Laboratory, and Iowa State Univ., Ames, IA (United States)] (ORCID:0000000234609290); Alam, Aftab [Indian Institute of Technology (IIT), Mumbai (India)] (ORCID:0000000184581006). DOE Contract: AC02-07CH11358. Subjects: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Ab initio calculations; Band structure methods; Charge order; Ferroelectric phase transition; Multiferroics