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By using non-equilibrium Green's function (NEGF) method and tight-binding(TB) approximation, we investigated a perfect control on spin transport in azigzag $\alpha^{\prime}$-boron nanoribbon ($\alpha^{\prime}$-BNR) as the mustsemi-conducting structure of borophene. It has been found that when an$\alpha^{\prime}$-BNR is exposed to an out-of-plane exchange magnetic field,spin splitting occurs for both spin-up and spin-down states in specific rangesof energy. Therefore, the spin polarization of current could be controlled byadjusting the energy of incoming electrons by means of an external back-gatevoltage. We focus on the edge manipulation of $\alpha^{\prime}$-BNR byferro-magnetic (FM) or anti-ferromagnetic (AFM) exchange field which leads tothe emergence of a giant magneto resistance and a perfect spin filtering. Localcurrent provides the best picture of spin distribution of current in thenanoribbon. In order to observe the response of the system to the proximityeffect of magnetic strips, we calculate the magnetic moment of each site. Then,we show that applying a transverse or perpendicular electric field in thepresence of the exchange magnetic field gives another controlling tool on thespin polarization of current in a constant energy. Finally, by simultaneouseffect of in-plane and out-of-plane exchange magnetic field on the edges ofnanoribbon, we reach a control on spin rotation in the scattering region. Ourinvestigation guarantees the $\alpha^{\prime}$-BNR as a promising twodimensional (2D) structure for spintronic purposes.

Controllable giant magneto resistance and perfect spin filtering in $\alpha^{\prime}$-borophene nanoribbons