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We determine the effective total spin $J$ of local moments formed fromacceptor states bound to Mn ions in GaAs by evaluating their magnetic Chernnumbers. 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 theacceptor orbital moment. For Mn pairs in bulk, the total $J$ depends on thepair orientation in the GaAs lattice and on the separation between the Mnatoms. We point out that Berry curvature variation as a function of localmoment orientation can profoundly influence the quantum spin dynamics of thesemagnetic entities.

Chern number spins of Mn acceptor magnets in GaAs