Machine-learning-identified two-dimensional van der Waals multiferroics for four-state nonvolatile memory

Two-dimensional (2D) van der Waals (vdW) multiferroics offer an attractive platform for four-state nonvolatile memory by combining switchable ferroelectric (FE) polarization and magnetization within a single material system. However, their development is hindered by the scarcity of synthesizable candidates and the lack of nondestructive readout schemes. Here, we develop a synthesizability-aware machine-learning workflow that combines positive-unlabeled bagging ensembles with transfer learning and integrate it with first-principles calculations to explore the 2D vdW ABC2X6 family, yielding a set of high-confidence multiferroic candidates together with interpretable chemical design rules. Among them, AuCrP2S6 monolayer emerges as a representative system with a ferromagnetic ground state, a sizable out-of-plane polarization of 7.46 pC/m, and a moderate FE switching barrier of ∼130 meV/f.u. Moreover, the nonlinear optical response mediated by the bulk photovoltaic effect in AuCrP2S6 provides a dual-channel probe of the ferroic orders, in which the polarization direction governs the photocurrent sign while the magnetic order selects the spin channel via robust exchange splitting. This intrinsic coupling enables the nondestructive readout of four logic states within a single atomic layer, thereby providing an optoelectronic readout scheme for next-generation multistate memory.