  Although several multiferroic materials/heterostructures have been
extensively studied, finding strong magnetoelectric couplings for the electric
field control of the magnetization remains challenging. Here, a novel
interfacial magnetoelectric coupling based on three components (ferroelectric
dipole, magnetic moment, and antiferromagnetic order) is analytically
formulated. As an extension of carrier-mediated magnetoelectricity, the new
coupling is shown to induce an electric-magnetic hysteresis loop. Realizations
employing BiFeO$_3$ bilayers grown along the [$111$] axis are proposed. Without
involving magnetic phase transitions, the magnetization orientation can be
switched by the carrier modulation driven by the field effect, as confirmed
using first-principles calculations.
