  The local density of states of Mn-Mn pairs in GaAs is mapped with
cross-sectional scanning tunneling microscopy and compared with theoretical
calculations based on envelope-function and tight-binding models. These
measurements and calculations show that the crosslike shape of the Mn-acceptor
wavefunction in GaAs persists even at very short Mn-Mn spatial separations. The
resilience of the Mn-acceptor wave-function to high doping levels suggests that
ferromagnetism in GaMnAs is strongly influenced by impurity-band formation. The
envelope-function and tight-binding models predict similarly anisotropic
overlaps of the Mn wave-functions for Mn-Mn pairs. This anisotropy implies
differing Curie temperatures for Mn $\delta$-doped layers grown on differently
oriented substrates.
