Competition between Zener's double exchange and p–d exchange in δ-(Zn, Mn, Li)Se with shape deformation: LDA + U calculations

• Systematic research on competition between double, p–d and super exchange in DMS.
• Double exchange and p–d exchange plays a major role in PBE and LDA + U respectively.
• The main peak of Mn d states is compatible with experimental results with LDA + U.
• All configurations under shape deformation are strong FM ones in LDA + U.

By local-density approximation plus U (LDA + U) calculations, diluted magnetic semiconductors (DMS) δ-(Zn, Mn, Li)Se are dominated by Zener's p–d exchange, which is different from Zener's double exchange mechanism by PBE calculations. The main peak of Mn d states is shifted to lower energy −3.9 eV versus Fermi energy. All configurations under shape deformation are strong ferromagnetic (FM) ones due to the large splitting of Mn d states. Because of the two-dimensional (2D) ordered Mn atoms with hole and long ranged effect of p–d exchange coupling, exchange energy of the supercell with crystal constant is much larger with p–d exchange than that with double exchange. The largest exchange energy is around the crystal constant. Fermi level across the valley of FM Mn d states makes the FM state much stable. Comparing with pure ZnSe, p-type co-doping of Li in δ-(Zn, Mn, Li)Se has a significant effect on the atomic structure. These results are useful in the research of DMS with shape deformation and p-type co-doping for spintronic applications.