Long range ferromagnetism in (Zn, Mn, Li)Se with competition between double exchange and p-d exchange

In this paper, we elucidate the mechanism for Li co-dopant induced enhancement of the ferromagnetism in 2×2×2 and 3×3×3 cubic (Zn, Mn)Se using density functional calculations. The doping atoms tend to congregate together according to the ferromagnetic (FM) energy. All configurations are strongly FM ones due to double exchange (DE) and p-d exchange (PE). DE and PE are shown in the partial density of states. The hole is uniformly distributed in the cubic (Zn, Mn, Li)Se, and it is the one and only parameter to decide the exchange energy, when impurity atoms stay further away from each other. The average exchange energy of these configurations is considered to be a function of the square root of the hole concentration. The fitting data to a polynomial function shows that DE and PE have roles of similar importance in the exchange energy.