  We determine the effective total spin $J$ of local moments formed from
acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern
numbers. We find that when individual Mn atoms are close to the sample surface,
the total spin changes from $J = 1$ to $J = 2$, due to quenching of the
acceptor orbital moment. For Mn pairs in bulk, the total $J$ depends on the
pair orientation in the GaAs lattice and on the separation between the Mn
atoms. We point out that Berry curvature variation as a function of local
moment orientation can profoundly influence the quantum spin dynamics of these
magnetic entities.
