Stacking Order, Perfect Spin Polarization, and Giant Magnetoresistance in Zigzag Graphene/ h - BN Heterobilayer Nanoribbons

In a van der Waals heterostructure of two-dimensional materials, electronic properties are tunable by means of stacking orders. Here, we study the spin-dependent quantum transport in the bilayer of ferromagnetic zigzag-edged graphene/hexagonal-$\mathrm{BN}$ nanoribbons (ZGr-BNNRs) using density-functional theory combined with the Keldysh nonequilibrium Green's-function method. We reveal a strong odd-even effect of transport across the ZGr-BNNRs and a giant magnetoresistance value observed only in even-width ZGr-BNNRs. More interestingly, this value can be optimized by engineering stacking orders, yielding the perfect spin polarization efficiency of 100% and the magnetoresistance value of over ${10}^{4}$ in even-width ZGr-BNNRs. Our results provide a route to design and fabricate high-performance spin filters and magnetic storage devices.