  The electronic transport properties of a point-contact system formed by a
single Co atom adsorbed on Cu (100) and contacted by a copper tip is evaluated
in the presence of intra-atomic Coulomb interactions and spin-orbit coupling.
The calculations are performed using equilibrium Green's functions evaluated
within density functional theory completed with a Hubbard $U$ term and
spin-orbit interaction, as implemented in the Gollum package. We show that the
contribution to the transmission between electrodes of spin-flip components is
negative and scaling as $\lambda^2/\Gamma^2$ where $\lambda$ is the SOC and
$\Gamma$ the Co atom-electrode coupling. Hence, due to this unfavorable ratio,
SOC effects in transport in this system are small. However, we show that the
spin-flip transmission component can increase by two orders of magnitude
depending on the value of the Hubbard $U$ term. These effects are particularly
important in the contact regime because of the prevalence of $d$-electron
transport, while in the tunneling regime, transport is controlled by the
$sp$-electron transmission and results are less dependent on the values of $U$
and SOC. Using our electronic structure and the elastic transmission
calculations, we discuss the effect of $U$ and SOC on the well-known Kondo
effect of this system.
