Ge_(1-x)Sn_x alloys have proved difficult to form at large x, contrary to what happens with other group IV semiconductor combinations. However, at low x they are typical examples of well-behaved substitutional compounds, which is desirable for harnes
sing the electronic properties of narrow band semiconductors. In this paper, we propose the appearance of another kind of single-site defect ($beta-Sn$), consisting of a single Sn atom in the center of a Ge divacancy, that may account for these facts. Accordingly, we examine the electronic and structural properties of these alloys by performing extensive numerical ab-initio calculations around local defects. The results show that the environment of the $beta$ defect relaxes towards a cubic octahedral configuration, facilitating the nucleation of metallic white tin and its segregation, as found in amorphous samples. Using the information stemming from these local defect calculations, we built a simple statistical model to investigate at which concentration these $beta$ defects can be formed in thermal equilibrium. These results agree remarkably well with experimental findings, concerning the critical concentration above which the homogeneous alloys cannot be formed at room temperature. Our model also predicts the observed fact that at lower temperature the critical concentration increases. We also performed single site effective-field calculations of the electronic structure, which further support our hypothesis.
Recent inelastic neutron scattering experiments in CeIn$_{3}$ and CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong compet
ition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Neel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, used before for studies of the non-magnetic phase. The model includes the correlated Ce-$4 f$ electrons hybridized with the conduction band, where we also allow for correlations, and we consider competing RKKY (Heisenberg-like $J_{H} $) and Kondo ($J_{K}$) antiferromagnetic couplings. Carrying on a series of unitary transformations, we perturbatively derive a second-order effective Hamiltonian which, projected onto the antiferromagnetic electron ground state, describes the spin wave excitations, renormalized by their interaction with correlated itinerant electrons. We numerically study how the different parameters of the model influence the renormalization of the magnons, yielding useful information for the analysis of inelastic neutron scattering experiments in antiferromagnetic heavy fermion compounds. We also compare our results with the available experimental data, finding good agreement with the spin wave measurements in cubic CeIn$_3$.
Recent inelastic neutron scattering experiments in CeIn3 and CePd2Si2 single crystals, measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between
the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Neel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model as introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, used before for studies of the non-magnetic phase. The model includes the correlated Ce-4f electrons hybridized with the conduction band, and we consider competing RKKY (Heisenberg-like J_{H}) and Kondo (J_{K}) antiferromagnetic couplings. Carrying on a series of unitary transformations, we perturbatively derive a second-order effective Hamiltonian which, projected onto the antiferromagnetic electron ground state, describes the spin wave excitations, renormalized by their interaction with correlated itinerant electrons. We numerically study how the different parameters of the model influence the renormalization of the magnons, yielding useful information for the analysis of inelastic neutron scattering experiments in antiferromagnetic heavy fermion compounds. We also compare our results with available experimental data, finding good agreement with the spin wave measurements in cubic CeIn3.
