This dissertation focuses on the study of ferromagnetism in Dilute Magnetic Semiconductors. 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 (DMS) incorporates the strong spin-orbit couplings of the carrier holes as found in most III-V semiconductors doped with manganese such as Ga1-xMnxAs. 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. We show that non-local correlations, within the DCA, are responsible for magnetic frustration and magnetic reorientation of the DMS. The DMFA is employed to study ferromagnetism and transport in Ga1-xMnxAs, using the sp3 tight-binding Hamiltonian. Finally, employing the sp3 tight-binding Hamiltonian and the DMFA, ferromagnetism in a wide band gap Ga1-xMnxN is studied.
The magneto-optical properties of the ferromagnetic semiconductor Ga$_{1-x}$Mn$_{x}$As are studied within the dynamical mean-field approximation (DMFA). A material-specific multiband $sp^{3}$ tight-binding Hamiltonian is employed for the dispersion of the GaAs host. The calculated density of states shows an impurity band and a distorted valence band for large and moderate values of magnetic coupling, respectively. Upon using the more realistic band structure, the ferromagnetic transition temperature is significantly closer to the experimental results than the previous predictions of $k\cdot p$ models. The optical conductivity shows a Drude-like peak at low frequencies which is suppressed by increasing of the magnetic coupling.
The magnetic properties of the diluted magnetic semiconductor Ga_{1-x}Mn_{x}As are studied within the dynamical cluster approximation. We use the k-dot-p Hamiltonian to describe the electronic structure of GaAs with spin-orbit coupling and strain effects. We show that nonlocal effects are essential for explaining the experimentally observed transition temperature and saturation magnetization. We also demonstrate that the cluster anisotropy is very strong and induces rotational frustration and a cube-edge direction magnetic anisotropy at low temperature. With this, we explain the temperature-driven spin reorientation in this system.
We employ the dynamical mean-field approximation to study the magnetic properties of a model relevant for the dilute magnetic semiconductors. Our model includes the spin-orbit coupling on the hole bands, the exchange interaction, and the attractive Coulomb potential between the negatively charged magnetic ions and the itinerant holes. The inclusion of the Coulomb potential significantly renormalizes the exchange coupling and enhances the ferromagnetic transition temperature for a wide range of couplings. We also explore the effect of the spin-orbit interaction by using two different values of the ratio of the effective masses of the heavy and light holes. We show that in the regime of small $J_{c}$-$V$ the spin-orbit interaction enhances $T_{c}$, while for large enough values of $J_{c}$-$V$ magnetic frustration reduces $T_c$ to values comparable to the previously calculated strong coupling limit.