  The experimental observation of the Dirac fermion states in
$\beta_{12}$-borophene sheets and the discovery of their novel topological
properties properties have made them a promising candidate for spintronic
applications. Here, by combining non-equilibrium Green's function (NEGF) and
tight-binding (TB) approximation, we study the charge and spin transport
properties through a $\beta_{12}$-borophene nanoribbon (BNR) with the different
edge 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 spin
direction of transmitted electrons could be controlled by adjusting the energy
of incoming electrons with the help of an external backgate voltage. It is
found that an armchair BNR (ABNR) in the simultaneous presence of a transverse
electric field and a nonlocal exchange field indicates a half-metallic nature
which is electrically controllable. Moreover, the influence of local exchange
field fields is evaluated by exposing the edges of ABNR to ferromagnetic strips
with parallel and antiparallel configurations. Our findings show that the edge
manipulations in ABNRs lead to the emergence of a giant magnetoresistance and a
perfect spin filter. Finally, we studied the effects of edge vacancies and
Anderson disorder on the spin-dependent conductance of an ABNR and find that
the perfect spin polarization is not destroyed in the presence of Anderson
disorder and various single vacancies. Our results reveal the outstanding spin
transport properties of ABNRs for future spintronic devices.
