Design of magnetic polar double-double perovskite oxides through cation ordering

Starting from the centrosymmetric ${\mathrm{MnRMnSbO}}_6$ compound, we explore the realm of magnetic polar double-double perovskite oxides characterized by significant ferroelectric polarization. Employing symmetry operations, first-principles methodologies, and Monte Carlo simulations, our investigation delves into the structural, magnetic, ferroelectric, and electronic attributes of the polar ${\mathrm{LaFeMnNiO}}_6$ and ${\mathrm{LaTiMnNiO}}_6$ compounds. Structural analysis uncovers that the paraelectric-ferroelectric phase transition is intricately linked to the Fe/Ti displacement of square-planar $\mathrm{Fe}/{\mathrm{TiO}}_4$. Notably, the magnetic ${\mathrm{LaFeMnNiO}}_6$ and ${\mathrm{LaTiMnNiO}}_6$ compounds demonstrate robust ferroelectric polarizations, measuring 20.0 and $21.8\text{µ}C/{\mathrm{cm}}^2$, respectively, accompanied by minimalist forbidden energy gaps of 1.40 and 1.18 eV using the generalized gradient approximation $+U$ method. Furthermore, we pinpoint elevated magnetic transition temperatures for these compounds. Additionally, our study scrutinizes the energies associated with diverse spin configurations and identifies potential minimum decomposition pathways into stable oxides. This comprehensive analysis ensures the meticulous formation of the ${\mathrm{LaFeMnNiO}}_6$ and ${\mathrm{LaTiMnNiO}}_6$ compounds.