  The spin-polarized scanning tunnelling microscope (STM) can in principle
resolve not only the electronic, but also the magnetic surface structure. We
model recent STM measurements achieving magnetic resolution on the atomic scale
by a first-principles method. It is shown that the signature of a specific
magnetic or non-magnetic STM tip can unambiguously be identified. It is also
established that the model of Tersoff and Hamann would yield an electronic as
well as magnetic contrast of the surface which is well below STM resolution.
