Recent experiments [1] suggest that the ferromagnetism (FM) in GaAs: Mn is determined by the impurity band rather than holes in the valence band. We discuss here the physical mechanism of FM mediated by the carriers in impurity band, where the Mn d-l
evel play a crucial role. The theory is based on the first principle approach.
The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Ham
iltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.
The state of art in the theoretical and experimental studies of transition metal doped oxides (dilute magnetic dielectrics) is reviewed. The available data show that the generic non-equilibrium state of oxide films doped with magnetic impurities may
either favor ferromagnetism with high Curie temperature or result in highly inhomogeneous state without long-range magnetic order. In both case concomitant defects (vacancies, interstitial ions play crucial part.
A theory of collective states in a magnetically quantized two-dimensional electron gas (2DEG) with half-filled Landau level (quantized Hall ferromagnet) in the presence of magnetic 3d impurities is developed. The spectrum of bound and delocalized spi
n-excitons as well as the renormalization of Zeeman splitting of the impurity 3d levels due to the indirect exchange interaction with the 2DEG are studied for the specific case of n-type GaAs doped with Mn where the Lande` g-factors of impurity and 2DEG have opposite signs. If the sign of the 2DEG g-factor is changed due to external influences, then impurity related transitions to new ground state phases, presenting various spin-flip and skyrmion-like textures, are possible. Conditions for existence of these phases are discussed. PACS: 73.43.Lp, 73.21.Fg, 72.15.Rn
We consider the Kondo tunneling induced by multiphonon emission/absorption processes in magnetic molecular complexes with low-energy singlet-triplet spin gap and show that the number of assisting phonons may be changed by varying the Zeeman splitting
of excited triplet state. As a result, the structure of multiphonon Kondo resonances may be scanned by means of magnetic field tuning.
