  We present the magnetic phase diagram of artificial H$_2$ molecule in lateral
quantum dots doped with magnetic impurities as a function of external magnetic
field and plunger gate voltage. The onset of Mn-Mn
antiferromagnetic-ferromagnetic transition follows the electron spin
singlet-triplet transition. We deploy a configuration-interaction method to
exactly diagonalize the electron-Mn Hamiltonian and map it to an effective
Mn-Mn Heisenberg Hamiltonian. We find that Mn-Mn exchange coupling can be
described by RKKY-interaction/magnetic-polaron in weak/strong electron-Mn
coupling at low/high magnetic fields.
