The influence of the concentration of charge carriers on the ferromagnetic phase transition of the semimagnetic semiconductor Pb1-x-ySnyMnxTe for various compositions is reported. A critical density of carriers above which a ferromagnetic transition can take place, is observed. A simple modified Ruderman-Kittel-Kasuya-Yosida mechanism for semiconductors is proposed in which carriers from two valence bands located in different regions of the Brillouin zone contribute and a finite mean free path is implemented. An excellent quantitative agreement with the data is obtained.
Swagten, H. J. M., Jonge, de, W. J. M., Galazka, R. R., Warmenbol, P., & Devreese, J. T. (1988). Hole density and composition dependence of ferromagnetic ordering in lead tin manganese telluride. Physical Review B: Condensed Matter, 37(16), 9907-9910. https://doi.org/10.1103/PhysRevB.37.9907