  The size dependent electronic structure and separate spin and orbital
magnetic moments of free Co$_n^+$ ($n = 4\;\textrm{-}\;9$) cluster ions have
been investigated by x-ray absorption and x-ray magnetic circular dichroism
spectroscopy in a cryogenic ion trap. A very large orbital magnetic moment of
$1.4\pm0.1\;\mu_{\mathrm B}$ per atom was determined for Co$_5^+$, which is one
order of magnitude larger than in the bulk metal. Large orbital magnetic
moments per atom of $\approx 1\;\mu_B$ were also determined for Co$_4^+$,
Co$_6^+$, and Co$_8^+$. The orbital contribution to the total magnetic moment
shows a non-monotonic cluster size dependence: The orbital contribution
increases from a local minimum at $n = 2$ to a local maximum at $n = 5$ and
then decreases with increasing cluster size. The $3d$ spin magnetic moment per
atom is nearly constant and is solely defined by the number of $3d$ holes which
shows that the $3d$ majority spin states are fully occupied, that is, $3d$ hole
spin polarization is 100%.
