Spin-polarized transport properties in magnetic moiré superlattices

Since the discovery of the fascinating properties in magic-angle graphene, the exploration of moir\'e systems in other two-dimensional materials has garnered significant attention and given rise to a field known as ``moir\'e physics.'' Within this realm, the magnetic van der Waals heterostructure and the magnetic proximity effect in moir\'e superlattices have also become subjects of great interest. However, the spin-polarized transport property in these moir\'e structures is still a problem to be explored. Here, we investigate the spin-polarized transport properties in a moir\'e superlattice formed by a two-dimensional ferromagnet ${\mathrm{CrI}}_{3}$ stacked on a monolayer BAs, where the spin degeneracy is lifted because of the magnetic proximity effect associated with the moir\'e superlattices. We find that the conductance exhibits spin-resolved miniband transport properties at a small twist angle because of the periodic moir\'e superlattices. When the incident energy is in the spin-resolved minigaps, the available states are spin polarized, thus providing a spin-polarized current from the superlattice. Moreover, only a finite number of moir\'e period is required to obtain a net spin polarization of 100%. In addition, the interlayer distance of the heterojunction is also moir\'e modifiable, so a perpendicular electric field can be applied to modulate the direction of the spin polarization. Our finding points to an opportunity to realize spin functionalities in magnetic moir\'e superlattices.