  We consider the magnetic structure on the Fe(001) surface and theoretically
study the scanning tunneling spectroscopy using a spin-polarized tip (SP-STM).
We show that minority-spin surface states induce a strong bias dependence of
the tunneling differential conductance which largely depends on the orientation
of the magnetization in the SP-STM tip relative to the easy magnetization axis
in the Fe(001) surface. We propose to use this effect in order to determine the
spin character of the Fe(001) surface states. This technique can be applied
also to other magnetic surfaces in which surface states are observed.
