  We report numerical simulation result of a recently proposed \{P. Bruno,
Phys. Rev. Lett {\bf 79}, 4593, (1997)\} approach to perform magnetic scanning
tunneling microscopy with a two terminal non-magnetic tip. It is based upon the
spin asymmetry effect of the tunneling current between a ferromagnetic surface
and a two-terminal non-magnetic tip. The spin asymmetry effect is due to the
spin-orbit scattering in the tip. The effect can be viewed as a Mott scattering
of tunneling electrons within the tip. To obtain quantitative results we
perform numerical simulation within the single band tight binding model, using
recursive Green function method and Landauer-B\"uttiker formula for
conductance. A new model has been developed to take into account the spin-orbit
scattering off the impurities within the single-band tight-binding model. We
show that the spin-asymmetry effect is most prominent when the device is in
quasi-ballistic regime and the typical value of spin asymmetry is about 5%.
