  The zero-bias anomaly in conductance spectra of single Co atoms on Cu(111)
observed at $\approx$ 4 K, which has been interpreted as being due to a Kondo
resonance, is strongly modified when the Co atoms are attached to monatomic Cu
chains. Scanning tunneling spectra measured at 340 mK in magnetic fields
exhibit all characteristics of spin-flip excitations. Their dependence on the
magnetic field reveals a magnetic anisotropy and suggests a non-collinear spin
state. This indicates that spin-orbit coupling (SOC), which has so far been
neglected in theoretical studies of Co/Cu(111), has to be taken into account.
According to our density functional theory and multi-orbital quantum Monte
Carlo calculations SOC suppresses the Kondo effect for all studied geometries.
