  We propose a computationally efficient atom-superposition-based method for
simulating spin-polarized scanning tunneling spectroscopy (SP-STS) on complex
magnetic surfaces based on the sample and tip electronic structures obtained
from first principles. We go beyond the commonly used local density of states
(LDOS) approximation for the differential conductance, dI/dV. The capabilities
of our approach are illustrated for a Cr monolayer on a Ag(111) surface in a
noncollinear magnetic state. We find evidence that the simulated tunneling
spectra and magnetic asymmetries are sensitive to the tip electronic structure,
and we analyze the contributing terms. Related to SP-STS experiments, we show a
way to simulate two-dimensional differential conductance maps and qualitatively
correct effective spin polarization maps on a constant current contour above a
magnetic surface.
