Multilevel resistance states in van der Waals multiferroic tunnel junctions with asymmetric electrodes

Multiferroic tunnel junctions (MFTJs) with a ferroelectric barrier sandwiched between two ferromagnetic electrodes are promising candidates for nonvolatile memory applications. The existence of ferromagnetism and ferroelectricity in van der Waals (vdW) materials provides a significant potential for constructing multifunctional MFTJs using vdW heterojunctions. Here we develop MFTJs with asymmetric electrodes, ${\mathrm{Fe}}_{3}{\mathrm{GaTe}}_{2}$/\ensuremath{\alpha}-${\mathrm{In}}_{2}{\mathrm{Se}}_{3}/{\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$, to achieve up to eight resistance states and high device performance using first-principles calculations combined with the nonequilibrium Green's function approach. The MFTJs with a monolayer \ensuremath{\alpha}-${\mathrm{In}}_{2}{\mathrm{Se}}_{3}$ barrier exhibit four resistive states with a large tunneling magnetoresistance (TMR) of $1.13\ifmmode\times\else\texttimes\fi{}{10}^{4}%$ and a tunneling electroresistance (TER) of 285%. Furthermore, eight resistive states are achieved in MFTJs with a bilayer \ensuremath{\alpha}-${\mathrm{In}}_{2}{\mathrm{Se}}_{3}$ barrier with the TMR (1.89 \ifmmode\times\else\texttimes\fi{} ${10}^{5}%$) and the TER (1161%). The TMR (TER) can be further improved to 1.23 \ifmmode\times\else\texttimes\fi{} ${10}^{6}%$ (3241%) by inserting an insulating layer $h$-BN. The physical origin of these exceptional transport properties is discussed, revealing that the giant TMR arises from the high spin polarization of the magnetic electrodes (${\mathrm{Fe}}_{3}{\mathrm{GaTe}}_{2}$ and ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$), while the high TER stems from the distinct band alignment between the magnetic electrodes and the ferroelectric barrier layer under different polarization states. Our results highlight the potential of electrode asymmetric vdW MFTJs as viable platforms for designing multistate nonvolatile memory devices.