Density-functional approach to doped magnetic semiconductors: Evolution of bound states of electrons as the donor concentration increases.

Abstract

We present a simple method for calculating dense bound states of electrons coupled with localized spins in doped magnetic semiconductors within the density-functional formalism. This paper deals with the case in which the defect in antiferromagnetic semiconductors behaves as a trapped center with an effective charge +\ensuremath{\Vert}e\ensuremath{\Vert}. We apply our method to clarify the evolution of the magnetic impurity state (MIS) and the bound magnetic polaron (BMP) as the donor concentration increases on a pseudocrystal approximation for defect sites, using the physical parameters relevant to an antiferromagnetic semiconductor EuTe. In the single MIS the localized spins around the defect are canted in the antiferromagnetic matrix by the exchange interaction between impurity electrons and localized spins, while in the single BMP, the localized spins around the defect are aligned completely ferromagnetically in the matrix. The evolution obtained for the MIS is substantially different from that for the BMP in both the electronic state of impurity electrons and the magnetic ordering of localized spins.In the MIS the evolution in the electronic state is qualitatively similar to that in doped nonmagnetic semiconductors, and a nonmetal-metal transition occurs at the donor concentration where the ferromagnetic moment of localized spins, induced by MIS, starts to decrease. The induced ferromagnetic moment, thus, seems like an obstruction for the metallic state. On the other hand, in the BMP, the strong exchange interaction favors the completely ferromagnetic polarization of electron spins; so the transition to a metallic state occurs when the ferromagnetic ordering of localized spins, produced by BMP, is established over a large part of the crystal. The comparison with the experiment strongly suggests that the doped EuTe, such as ${\mathrm{Eu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Gd}}_{\mathrm{x}}$Te and ${\mathrm{EuTe}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{I}}_{\mathrm{x}}$, is a typical material for the BMP, but not for the MIS. The effect of the random distribution of defect sites on the magnetic ordering is also studied in a conventional way, which implies that the heavily doped EuTe shows a complex magnetic structure involving the randomly distributed large ferromagnetic clusters and the remainder of the material more or less antiferromagnetic.