Electric Control of Magnetism in Multiferroic Rare-Earth-Substituted BiFeO_{3} with Ferrielectricity

The multiferroic rare-earth-substituted BiFeO_{3} has emerged as a promising candidate to achieve ultralow-energy-dissipation logic or memory devices, but the fundamental details of the switching mechanism involving the electrical, structural, and magnetic degrees of freedom is not fully understood, in particular, in its single-phase form. Here, a first-principles-based computational scheme is used to study Nd-doped BiFeO_{3} as a model system. The structure that yields a reduced P-E hysteresis loop is found to be ferrielectric with modulated octahedral tiltings, and it is shown that both the in-plane and out-of-plane ferromagnetization can be controlled by an applied electric field. The switching behaviors can be well interpreted by a Landau-type model, in which the magnetoelectric coupling is indirect and mediated by octahedral tiltings. The effects of varied composition and temperature are further discussed, revealing important correlations between the polarization switching and the robustness of the control of magnetization.