The broken symmetry at surfaces can give rise to a nonzero spin-orbit split
ting of valence bands. We observe such a splitting of the d-derived surface
state on W(110) and, to a lesser extent, on Mo(110), and follow the evolut
ion of the splitting as monovalent atoms an adsorbed. The observed evolutio
n is directly relevant to recent observations of altered orbital magnetic s
tructure versus adsorbate coverage in magnetic materials. We propose a spin
ordering for the associated Fermi contours which has important implication
s for spin excitations at surfaces.