First-principles study of nonlinear magnetoelectric effects in improper LuFeO3 multiferroics

Hexagonal LuFeO3 is known as an improper multiferroic material because of its ferroelectric structural distortion, measured by the Γ2− polar mode, and is driven by a trimerization structural distortion represented by the K3 non-polar mode [Fennie and Rabe, Phys. Rev. B 72, 100103(R) (2005)]. The K3 mode is also the primary structural origin of net weak ferromagnetism, associated with the ferromagnetic coupling between the in-plane geometrically frustrated spins. Here, we study the magnetoelectric coupling in LuFeO3 using first-principles calculations and applied external electric fields. We find that the weak ferromagnetism responds to the electric field polarization through the K3–Γ2− coupling, which is an intrinsic characteristic of improper multiferroics. Interestingly, the magnetoelectric coupling exhibits strong asymmetry under positive and negative electric fields. This nonlinearity is due to the competition between the K3 and the Γ2− modes according to Landau's theory and is related to asymmetrical interatomic interactions at the atomic level.