Designing strong second order magnetoelectric coupling in ABO₃/A'BO₃ superlattices

The key requirement of multiferroic materials is strong coupling between polarization (P) and magnetization (M). In magnetoelectric (ME) multiferroic materials, M is a function of P and hence electric field (E), M = f(E). The function f(E) can be linear or quadratic (second order). Here we report prediction of strong second-order ME coupling in oxide superlattices using first-principles density-functional-theory calculations. We consider LaFeO₃/LnFeO₃ (Ln = La, Sm, Gd, Y, Tm) 1/1 superlattices and show that these systems give rise to ME coupling that is an order of magnitude higher than that of the prototype linear ME Cr₂O₃. The origin of P in LaFeO₃/LnFeO₃ is hybrid improper ferroelectricity while M is weak, arising from canted Fe spins. Phonon calculations for the Pmc2₁ symmetry reveal that three IR active structural modes drive such ME couplings, one leads to linear ME coupling and remains in the Pmc2₁ symmetry, and the other two modes lead to second order ME coupling (Pm and Pc). We found that the origin of second-order ME coupling is the biquadratic relation between M and the tilting of the BO₆ octahedra (a-a-c0). Finally, we discuss how the strength of the second-order ME coupling can be enhanced by strain and by tuning the La/Ln cation radius mismatch.