Fractional-dimension approach to bound magnetic polarons in quantum structures of diluted magnetic semiconductors

We use the concept of fractional dimensionality to investigate properties of donor-bound magnetic polarons in quantum wells and quantum wires composed of the diluted magnetic semiconductor system Cd(Mn,Mg)Te. The polaron binding energy was found by solving numerically the nonlinear Schrödinger equation in noninteger dimensions. The calculations were performed at several temperatures for magnetically uniform structures (quantum wells and quantum wires) as well as for magnetic wells (or wires) with nonmagnetic barriers and for nonmagnetic wells with magnetic barriers. In all cases we observe a significant enhancement of the polaron binding energy compared to its value in the bulk material. The dependence of the binding energy on the quantum well (wire) width is discussed.