Microscopic model for the semiconductor-to-ferromagnetic-metal transition in FeSi_1−xGe_x Alloys

The simplified band structure introduced by Mazurenko et al. to model FeSi is used to analyze the singlet semiconductor to ferromagnetic metal transition in the isoelectronic isostructural alloys, FeSi_1−xGe_x. The complex band structure of the alloy is replaced by an alternating chain of doubly and singly degenerate atoms to represent Fe and Si/Ge, respectively. The former (latter) form narrow (broad) bands with a substantial hybridization between them. A substantial onsite repulsion including Hund's rule coupling is introduced on the Fe sites. The mean-field phase diagram contains a first-order phase transition from the singlet semiconductor to a ferromagnetic metal with increasing temperature and interaction strength, similar to the alloys. The analysis also reproduces the rapid rise of the spin susceptibility in the semiconductor with a crossover to a Curie-Weiss form at higher temperatures. Good agreement is found at zero temperature between the mean-field and accurate DMRG calculations.