Various atomic arrangements of the Mn-induced GaAs(001) surface, consisting of one Ga-As dimer and one Mn atom in the (2 x 2) unit, have been investigated by first-principles calculations. The most stable arrangement is reasonable in view of the classical electrostatic theory. It has been revealed that the topmost Ga-As dimers tend to be aligned along the [110] direction, while they are less ordered along the [110] direction. These anisotropic orderings, that is, anisotropic interactions, imply that the Mn atom, which is located between the Ga-As dimers, enhances the local electrostatic interaction between the dimers along the [110] direction, as a result of the dielectric anisotropy at the surface. (C) 2016 The Japan Society of Applied Physics.