The origin of ferromagnetic interaction between bound magnetic polarons in diluted magnetic semiconductors: A minimal model

Abstract We present a detailed analysis of the role of various interaction mechanisms contributing to the bound magnetic polaron (BMP) molecule Hamiltonian with the purpose of gaining an insight into the origin of the ferromagnetic interaction between BMPs. Explicitly, it appears that the BMP molecule Hamiltonian without interatomic direct exchange interaction does not lead to appearance of the parallel alignment of polaronic clouds in the lowest energy state even for large magnitudes of the polaronic exchange fields (up to ~65 meV in Cd 0.95 Mn 0.05 Se). Also, it appears that for the range of moderate values of polaronic exchange fields (16–25 meV in Cd 0.95 Mn 0.05 Se), the regular Hubbard BMP pair Hamiltonian must be supplemented with the direct interatomic (Heisenberg) exchange interaction to form a minimal model Hamiltonian of BMP molecule with the parallel alignment of the polaronic clouds in the lowest energy state.