2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18189Starting from microscopic and symmetry considerations, we derive the Hamiltonian describing the exchange interaction between the localized Mn spins and the valence band holes in $Ga_{1-x}Mn_x As$. We find that due to the strong spin-orbit coupling in the valence band, this exchange interaction has a rather complex structure and generates a highly anisotropic effective interaction between the Mn spins. The corresponding ground state has a finite ferromagnetic magnetization but is intrinsically spin-disordered even at zero temperature.4 pages RevTEx 3.0, 2 EPS figuresStrongly Correlated Electronstext