Ferrielectricity controlled widely-tunable magnetoelectric coupling in van der Waals multiferroics

The discovery of various primary ferroic phases in atomically-thin van der Waals crystals have created a new two-dimensional wonderland for exploring and manipulating exotic quantum phases. It may also bring technical breakthroughs in device applications, as evident by prototypical functionalities of giant tunneling magnetoresistance, gate-tunable ferromagnetism and non-volatile ferroelectric memory etc. However, two-dimensional multiferroics with effective magnetoelectric coupling, which ultimately decides the future of multiferroic-based information technology, has not been realized yet. Here, we show that an unconventional magnetoelectric coupling mechanism interlocked with heterogeneous ferrielectric transitions emerges at the two-dimensional limit in van der Waals multiferroic CuCrP₂S₆ with inherent antiferromagnetism and antiferroelectricity. Distinct from the homogeneous antiferroelectric bulk, thin-layer CuCrP₂S₆ under external electric field makes layer-dependent heterogeneous ferrielectric transitions, minimizing the depolarization effect introduced by the rearrangements of Cu⁺ ions within the ferromagnetic van der Waals cages of CrS₆ and P₂S₆ octahedrons. The resulting ferrielectric phases are characterized by substantially reduced interlayer magnetic coupling energy of nearly 50% with a moderate electric field of 0.3 V nm^-1, producing widely-tunable magnetoelectric coupling which can be further engineered by asymmetrical electrode work functions.