  X-ray magnetic circular dichroism spectroscopy has been used to characterize
the electronic structure and magnetic moment of Cr$_2^+$. Our results indicate
that the removal of a single electron from the $4s\sigma_g$ bonding orbital of
Cr$_2$ drastically changes the preferred coupling of the $3d$ electronic spins.
While the neutral molecule has a zero-spin ground state with a very short bond
length, the molecular cation exhibits a ferromagnetically coupled ground state
with the highest possible spin of $S=11/2$, and almost twice the bond length of
the neutral molecule. This spin configuration can be interpreted as a result of
indirect exchange coupling between the $3d$ electrons of the two atoms that is
mediated by the single $4s$ electron through a strong intraatomic $3d$-$4s$
exchange interaction. Our finding allows an estimate of the relative energies
of two states that are often discussed as ground-state candidates, the
ferromagnetically coupled $^{12}\Sigma$ and the low-spin $^2\Sigma$ state.
