  Circulating orbital currents produced by the spin-orbit interaction for a
single electron spin in a quantum dot are explicitly evaluated at zero magnetic
field, along with their effect on the total magnetic moment (spin and orbital)
of the electron spin. The currents are dominated by coherent superpositions of
the conduction and valence envelope functions of the electronic state, are
smoothly varying within the quantum dot, and are peaked roughly halfway between
the dot center and edge. Thus the spatial structure of the spin contribution to
the magnetic moment (which is peaked at the dot center) differs greatly from
the spatial structure of the orbital contribution. Even when the spin and
orbital magnetic moments cancel (for $g=0$) the spin can interact strongly with
local magnetic fields, e.g. from other spins, which has implications for spin
lifetimes and spin manipulation.
