Hole density and composition dependence of ferromagnetic ordering in lead tin manganese telluride

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