Disordered Electronic Models and Impurity Spin Dynamics. I: Ferromagnetic Ensemble and Mott Transition in an Exactly Solved Limit

Local gauge invariant n orbital models for elastic scattering of electrons in random potentials are extended to include local exchange interactions between electrons and magnetic impurities. The cooperation between local exchange interaction and electron hopping leads to ferromagnetic order in a low temperature phase for both the electronic and ionic subsystems. The critical temperature is proportional to the ensemble averaged exchange coupling. Ferromagnetic order implies spin split impurity bands in the electronic density of states. This as well as dc conductivity, internal energy, and magnetization is calculated exactly in the large n limit. The quasielectron states at EF, wherever EF comes to lie within the bands, can be classified as extended, i.e., conducting, in this limit. In the ferromagnetic phase, the proper variation of interaction parameters generates a Mott transition. The temperature- and magnetic field-dependence of the electronic magnetization is shown to be mean field like by using a high temperature expansion. It is also shown that an antiferromagnetic ensemble is always unstable and a spin glass phase is suppressed in the present models. The exact large n limit solutions render possible a future joint study in O(1/n) of both the Kondo effect in the nonmagnetic phase of a disordered system and of the Anderson metal insulator transition.