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Using a microscopic finite-cluster tight-binding model, we investigate thetrend of the magnetic anisotropy energy as a function of the cluster size foran individual Mn impurity positioned in the vicinity of the (110) GaAssurface,We present results of calculations for large cluster sizes, containingapproximately 104 atoms, which have not been investigated so far. Ourcalculations demonstrate that the anisotropy energy of a Mn dopant in bulk GaAsfound to be non-zero in previous tight-binding calculations, is purely a finitesize effect, and it vanishes as the inverse cluster size. In contrast to this,we find that the splitting of the three in-gap Mn acceptor energy levelsconverges to a finite value in the limit of infinite cluster size. For a Mn inbulk GaAs this feature is related to the nature of the mean-field treatment ofthe coupling between the impurity and its nearest neighbors atoms. Moreover, wecalculate the trend of the anisotropy energy in the sublayers, as the Mn dopantis moved away from the surface towards the center of the cluster. Here the useof large cluster sizes allows us to position the impurity in deeper sublayersbelow the surface, compared to previous calculations. In particular, we showthat the anisotropy energy increases up to the fifth sublayer and thendecreases as the impurity is moved further away from the surface, approachingits bulk value. The present study provides important insight for experimentalcontrol and manipulation of the electronic and magnetic properties ofindividual Mn dopants at the semiconductor surface by means of advancedscanning tunneling microscopy techniques.

Trend of the magnetic anisotropy for individual Mn dopants near the (110) GaAs surface