  Theoretical foundations and applications of the generalized spin-fermion
(sp-d) exchange lattice model to various magnetic systems, e.g. rare-earth
metals and compounds and magnetic semiconductors are discussed. The
capabilities of the model to describe spin quasi-particle spectra are
investigated. The main emphasis is made on the dynamical behavior of two
interacting subsystems, the localized spins and spin density of itinerant
carriers. A nonperturbative many-body approach, the Irreducible Green Functions
(IGF) method, is used to describe the quasi-particle dynamics.
  Scattering states are investigated and three branches of magnetic excitations
are calculated in the regime characteristic of a magnetic semiconductor. For a
simplified version of the model (Kondo lattice model) we study the spectra of
quasi-particle excitations with special attention given to diluted magnetic
semiconductors in simple approximation, to demonstrate the possibilities of the
IGF approach. For this, to include the effects of disorder, a modified mean
fields are determined self-consistently. The approach permits to investigate
and clarify the role of various interactions and disorder effects in unified
and coherent fashion.
