Quantized movement of magnetic skyrmions in moiré multiferroic heterostructures

Moir\'e superlattices made with van der Waals layers are an excellent platform for exploring a wide range of exotic and important physical phenomena. In this study, we used first-principles calculations and atomistic spin dynamics simulations to design a two-dimensional van der Waals $\mathrm{Mn}{\mathrm{S}}_{2}/\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ multiferroic moir\'e heterosuperlattice with tunable skyrmions through magnetoelectric coupling. The inherent lattice mismatch between the two monolayers of $\mathrm{Mn}{\mathrm{S}}_{2}$ and $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ creates incommensurate moir\'e patterns, along with modulated magnetic anisotropy and emerging magnetic skyrmions in $\mathrm{Mn}{\mathrm{S}}_{2}$. The magnetic skyrmion in $\mathrm{Mn}{\mathrm{S}}_{2}$ is strongly influenced by magnetoelectric coupling and can be tuned by the ferroelectric polarization of $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$. Furthermore, these magnetic skyrmions can be controlled by a pulsed current to move or freeze within the moir\'e period under different ferroelectric polarization states of the $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ layer. Our work showcases a two-dimensional van der Waals moir\'e heterosuperlattice with magnetoelectrically tuned magnetic skyrmions, which establishes a foundation for designing future spintronic devices.