Energetics of acceptor-bound magnetic polarons in diluted magnetic semiconductors.

Abstract

We present a theory of the bound magnetic polaron (BMP) in diluted magnetic semiconductors, valid for large ${\mathrm{Mn}}^{2+}$ magnetic ion concentrations x, and investigate the formation of acceptor-BMP in ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te as a function of x and of the temperature T. Experimentally determined magnetization up to 40 T is used to derive a self-consistent potential expressed in terms of the magnetization in order to investigate the BMP binding energy for x up to 0.5. The nonlinear Schr\"odinger equation obeyed by the BMP is solved numerically to obtain the BMP wave function. This permits the separate estimation of the binding due to the Coulomb potential and that due to the self-consistent exchange potential, including fluctuation effects. The antiferromagnetic Mn-Mn interaction leads to a lowering of the effective value of x. With increasing x, the BMP binding energy saturates. It is proposed that stannite structures containing ${\mathrm{Mn}}^{2+}$, with their absence of nearest-neighbor Mn-Mn interactions, be investigated in order to observe larger BMP binding energy due to an increase in the effective value of x to 0.25. Theoretical estimates for the binding energy of BMP in such structures, due to the exchange interaction alone are found to be about 5 times that in ${\mathrm{Cd}}_{0.75}$${\mathrm{Mn}}_{0.25}$Te. The formation of free polarons, formed by free carriers lowering their energy and localizing in the exchange potential, is also investigated. In stannite structures, with their large effective Mn concentration, it is found that free-hole--polaron formation is favored at temperatures below 15 K.