Magnetic phases of magnetic polarons in diluted magnetic semiconductor nanocrystals

We present theoretical studies of magnetism in II-VI magnetic nanocrystals (NCs) containing single electron coupled to substitutional magnetic ions Mn ²⁺. By using exact diagonalization techniques, we explore the magnetic phases of magnetic polarons in NCs doped with few Mn²⁺ ions, as functions of NC size, Mn number and positions. We show that ferromagnetic magnetic polarons (MPs) are stably formed in small magnetic NCs due to strong quantum confinement. By contrast, magnetic polarons with short ranged Mn-clusters in larger NCs exhibit various distinct magnetic phases, from ferromagnetism (FM) to anti-ferromagnetism (AF), sensitively depending on NC size. The stability of magnetic polarons in NCs with arbitrary number of Mn ions are analyzed within a proposed solvable model, supported by the numerical results calculated by using local mean field theory (MFT).