| This dissertation focuses on the study of ferromagnetism in Dilute Magnetic Semiconductors and Heavy Fermion Systems. To study these strongly correlated electronic systems, two non-perturbative techniques are used: the Dynamical Mean Field Approximation (DMFA) and the Dynamical Cluster Approximation (DCA).; The model used for Dilute Magnetic Semiconductors incorporates the strong spin-orbit couplings of the carrier holes as found in most III-V semiconductors doped with manganese such as Ga1-xMn xAs. Calculated within the DMFA, the spin-orbit coupling effects give rise to various interesting physics, primarily the anisotropic behavior of the impurity band that affect the charge transport properties in the ferromagnetic phase.; Heavy Fermion Systems are studied using the Periodic Anderson Model (PAM). In order to investigate the effects of spatial correlations, both the DCA and the DMFA techniques are used. Two different ferromagnetic mechanisms are found in these systems, one is driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interactions, and the other by the precursors of charge density wave (CDW) formation of the conduction electrons. We provide evidence for the existence of charge density wave (CDW) precursors within one- and two-particle levels, and the argument to explain how these CDW precursors lead the system to ferromagnetic phase. |
