Magnetic field dependence of the many-electron states in a magnetic quantum dot: The ferromagnetic-antiferromagnetic transition

The electron-electron correlations in a many-electron $({N}_{e}=1,2,\dots{},5)$ quantum dot confined by a parabolic potential is investigated in the presence of a single magnetic ion and a perpendicular magnetic field. We obtained the energy spectrum and calculated the addition energy which exhibits cusps as a function of the magnetic field. The vortex properties of the many-particle wave function of the ground state are studied and for large magnetic fields are related to composite fermions. The position of the impurity influences strongly the spin-pair-correlation function when the external field is large. In a small applied magnetic field, the spin-exchange energy together with the Zeeman terms leads to a ferromagnetic-antiferromagnetic (FM-AFM) transition. When the magnetic ion is shifted away from the center of the quantum dot, a remarkable re-entrant AFM-FM-AFM transition is found as a function of the strength of the Coulomb interaction. Thermodynamic quantities such as the heat capacity, the magnetization, and the susceptibility are also studied. The cusps in the energy levels show up as peaks in the heat capacity and the susceptibility.