Understanding the Interplay of Polar, Magnetic, and Electronic Order in Ferroic (LuFeO$_{3})_{m}$/LuFe$_{2}$O$_{4}$ Superlattices

Multiferroics are not only important from a technological point of view but also because of the rich and complex physics that results from the interplay between spin, charge and structural distortions. Hexagonal LuFeO$_{3}$ has recently been understood theoretical and experimentally, and shown to be an improper structural ferroelectric directly analogous to the hexagonal manganites. LuFe$_{2}$O$_{4}$ is structurally homologous to LuFeO$_{3}$ --both are characterized by a FeO$_{5}$ bipyramidal crystal field- but unlike the latter it exhibits a much larger magnetic moment and it is still a matter of debate whether it is ferroelectric. The double Fe-layer in LuFe$_{2}$O$_{4}$ is thought to be charge ordered and highly frustrated, resulting in possible polar, non-polar or anti-polar charge arrangements. Here we first investigate the relation between different charge and magnetic orders and structural distortions in bulk LuFe$_{2}$O$_{4}$ by DFT and Monte Carlo calculations. Then we concentrate on a system that combines both mechanisms -a structural improper ferroelectric and a charge frustrated polar structure- such as the (LuFeO$_{3})_{m}$/LuFe$_{2}$O$_{4\, \, }$superlattices.