Symmetry of Ground State in a Dilute Magnetic Metal Alloy

It is proved that the spin of the ground state of a magnetic atom having exchange interaction with a nonmagnetic host metal is $s\mp \frac{1}{2}$, where $s=\mathrm{spin}\mathrm{of}\mathrm{noninteracting}\mathrm{magnetic}\mathrm{atom}$, the upper sign is appropriate to antiferromagnetic coupling, and the lower, to ferromagnetic coupling. This result is generalized to any number of conduction bands and to nonpointlike impurities, provided that the exchange interactions with the number of conduction bands, or with the various partial waves, are all of the same sign. For $p$ such bands or partial waves, the result is that the ground-state $\mathrm{spin}=|s\mp \frac{1}{2}p|$.