  Ab initio calculations of surface-state mediated interactions between Cu
adatoms on transition metal surfaces are presented. We concentrate on
Co/Cu(111) and Co(0001) substrates and compare results with our calculations
for Cu(111). Our studies show that surface states of Co/Cu(111) and Co(0001)
are spin-polarized. We reveal that long-range interactions between adatoms are
mainly determined by sp-majority states. In contrast to Cu(111) and Co/Cu(111),
the interaction between adatoms on Co(0001) is strongly suppressed at large
adsorbate separations.
