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The simplified bandstructure introduced by Mazurenko et al to model FeSi isused to analyze the singlet semiconductor to ferromagnetic metal transition inthe isoelectronic isostructural alloys, FeSi$_{1-x}$Ge$_x$. The complexbandstructure of the alloy is replaced by an alternating chain of doubly andsingly degenerate atoms to represent Fe and Si/Ge respectively. Theformer(latter) form narrow(broad) bands with a substantial hybridizationbetween them. A substantial onsite repulsion including a Hund's rule couplingis introduced on the Fe sites. The mean field phase diagram contains a firstorder phase transition from the singlet semiconductor to a ferromagnetic metalwith increasing temperature and interaction strength similar to the alloys. Theanalysis also reproduces the rapid rise of the spin susceptibility in thesemiconductor with a crossover to a Curie-Weiss form at higher temperatures.Good agreement is found at zero temperature between the mean field and accurateDMRG calculations.

Microscopic model for the semiconductor-to-ferromagnetic-metal transition in FeSi$_{1-x}$Ge$_{x}$ Alloys