Competing long-range and short-range interactions in ferromagnetic semiconductors: Evidence from first principle calculations

Based on ab-initio calculations, we have investigated the structural, electronic, and magnetic properties of diluted magnetic semiconductors ( B a 1 − y K y ) F ( Z n 1 − x M n x ) t A s with (K, Mn) substitution in the parent compounds, BaFZnAs and BaFMnAs. The coexistence of two types of magnetic exchange coupling interactions was detected via the calculation of the distance-resolved and the individual exchange parameters J ( d M n 0 − M n i ) ≡ J i , where i runs over the i th nearest neighbor atom ( i N N ) of the reference one M n 0 distanced by d M n 0 − M n i . The short-range interactions (SRI), at J 1 and J 2 , are strongly influenced by hole doping and substitutional disorder of both hole and spin co-doping. The long-range interaction (LRI), at distances beyond the 2 N N , of a ferromagnetic nature, is less sensitive to hole doping, although these holes are the reason for their appearance. The results analysis showed that the dependence of the LRI on y / x doping ratio, in the co-doping system, is more systematic than on the y or x doping separately. In (BaK)F(ZnMn)As system, a peak appears in the LRI at around 1.5 of y / x doping ratio. Therefore, an estimation of the optimal hole doping for each spin doping concentration was given, where it is important to obtain the maximal ferromagnetic coupling, therefore the highest ferromagnetic ordering temperature, T C . Our findings are consistent with experiments, manifested, especially, in the saturation of the ordering temperature at large hole doping, as was obtained for the experimental T C of ( B a K ) ( Z n M n ) 2 A s 2 system. The results also show a doubling of the T C when the spin doping is doubled at high hole doping. Finally, we demonstrated via a proposed model that the SRI has the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction nature.