Controllable spin filtering and half-metallicity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>?</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math> -borophene nanoribbons

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