Coupling between improper ferroelectricity and ferrimagnetism in the hexagonal LuFeO₃ type ferrite systems

In magnetic oxide materials, the anti-symmetric anisotropic Dzyaloshinskii-Moriya (DM) exchange interactions between the localized spins are often weaker compared to their symmetric isotropic exchange counterpart. Therefore, they induce either weak magnetoelectric (ME) effect or the magnetization (M) in single-phase systems, thereby impairing their device applicability. Here, we aim to realize non-collinear ferrimagnetic orders having a considerably high M and their strong coupling with an improper ferroelectric (FE) order in hexagonal LuFeO₃ type systems which exhibit interesting topological orders [Nat. Commun. 5, 2998 (2014), Nature 537, 523–527 (2016), Nat Commun 11, 5582 (2020), Phys. Rev. Lett. 126, 157601 (2021)] driven by the DM interactions between the magnetic ions and their coupling with the FE order. The proposed two-sublattice magnetic system forms multiple energetically close, non-collinear ferrimagnetic orders, enabling the manipulation of the microscopic magnetic interactions and the triggering of spin-reorientation (SR) transitions by various efficient means. The electron doped hexagonal phase of LuFeO₃, where the two-sublattice structure was realized, exhibits electric polarization P ~ 15 μC/cm² and M ~ 1.1 μ_B/Fe with magnetic transition near room temperature (~ 290 K). The microscopic mechanisms to achieve electric field E induced SR transitions and switching of the direction of M have been discussed here.