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The experimental observation of the Dirac fermion states in$\beta_{12}$-borophene sheets and the discovery of their novel topologicalproperties properties have made them a promising candidate for spintronicapplications. Here, by combining non-equilibrium Green's function (NEGF) andtight-binding (TB) approximation, we study the charge and spin transportproperties through a $\beta_{12}$-borophene nanoribbon (BNR) with the differentedge shapes. We show when a BNR exposed to a nonlocal exchange magnetic field,the spin filtering occurs for both spin-up and spin-down so that the spindirection of transmitted electrons could be controlled by adjusting the energyof incoming electrons with the help of an external backgate voltage. It isfound that an armchair BNR (ABNR) in the simultaneous presence of a transverseelectric field and a nonlocal exchange field indicates a half-metallic naturewhich is electrically controllable. Moreover, the influence of local exchangefield fields is evaluated by exposing the edges of ABNR to ferromagnetic stripswith parallel and antiparallel configurations. Our findings show that the edgemanipulations in ABNRs lead to the emergence of a giant magnetoresistance and aperfect spin filter. Finally, we studied the effects of edge vacancies andAnderson disorder on the spin-dependent conductance of an ABNR and find thatthe perfect spin polarization is not destroyed in the presence of Andersondisorder and various single vacancies. Our results reveal the outstanding spintransport properties of ABNRs for future spintronic devices.

Controllable spin filtering and half metallicity in $\beta_{12}$-borophene nanoribbons