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 polarization and magnetization within a single material system. However, their development is hindered by the scarcity of synthesizable candidates and the lack of non-destructive readout schemes. Here, we combine machine-learning screening with first-principles calculations to explore the 2D vdW ABC$_2$X$_6$ family and identify a set of high-confidence multiferroic candidates. Among them, AuCrP$_2$S$_6$ 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 ferroelectric switching barrier of $\sim$130 meV/f.u. Moreover, the nonlinear optical response mediated by the bulk photovoltaic effect (BPVE) in AuCrP$_2$S$_6$ 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 non-destructive readout of four logic states within a single atomic layer, thereby providing a practical blueprint for next-generation multistate optoelectronic memory.