  We employ a kinetic-exchange tight-binding model to calculate the magnetic
interaction and anisotropy energies of a pair of substitutional Mn atoms in
GaAs as a function of their separation distance and direction. We find that the
most energetically stable configuration is usually one in which the spins are
ferromagnetically aligned along the vector connecting the Mn atoms. The
ferromagnetic configuration is characterized by a splitting of the topmost
unoccupied acceptor levels, which is visible in scanning tunneling microscope
studies when the pair is close to the surface and is strongly dependent on pair
orientation. The largest acceptor splittings occur when the Mn pair is oriented
along the <110> symmetry direction, and the smallest when they are oriented
along <100>. We show explicitly that the acceptor splitting is not simply
related to the effective exchange interaction between the Mn local moments. The
exchange interaction constant is instead more directly related to the width of
the distribution of all impurity levels -- occupied and unoccupied. When the Mn
pair is at the (110) GaAs surface, both acceptor splitting and effective
exchange interaction are very small except for the smallest possible Mn
separation.
