Magnetic-ferroelectric synergic control of multilevel conducting states in van der Waals multiferroic tunnel junctions towards in-memory computing.

van der Waals (vdW) multiferroic tunnel junctions (MFTJs) based on two-dimensional materials have gained significant interest due to their potential applications in next-generation data storage and in-memory computing devices. In this study, we construct vdW MFTJs by employing monolayer MnSe as the spin-filter tunnel barrier, TiTe as the electrodes and InS as the tunnel barrier to investigate the spin transport properties based on first-principles quantum transport calculations. It is highlighted that apparent tunneling magnetoresistance (TMR) and tunneling electroresistance (TER) effects with a maximum TMR ratio of 6237% and TER ratio of 1771% can be realized by using bilayer InS as the tunnel barrier under finite bias. Furthermore, the physical origin of the distinguished TMR and TER effects is unraveled from the -resolved transmission spectra and spin-dependent projected local density of states analysis. Interestingly, four distinguishable conductance states reveal the implementation of four-state nonvolatile data storage using one MFTJ unit. More importantly, in-memory logic computing and multilevel data storage can be achieved at the same time by magnetic switching and electrical control, respectively. These results shed light on vdW MFTJs in the applications of in-memory computing as well as multilevel data storage devices.