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We study the ferromagnetism of Ga1-xMnxAs by using a model Hamiltonian, based on an impurity band and the anti-ferromagnetic exchange interaction between the spins of Mn atoms and the charge carriers in the impurity band. Based on the mean field approach we calculate the spontaneous magnetization as a function of temperature and the ferromagnetic transition temperature as a function of the Mn concentration. The random distribution of Mn impurities is taken into account by Matsubara and Toyozawa theory of impurities in semiconductors. We compare our results with experiments and other theoretical findings.
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Role of localized magnetic moments in metal-insulator transitions lies at the heart of modern condensed matter physics, for example, the mechanism of high T$_{c}$ superconductivity, the nature of non-Fermi liquid physics near heavy fermion quantum criticality, the problem of metal-insulator transitions in doped semiconductors, and etc. Dilute magnetic semiconductors have been studied for more than twenty years, achieving spin polarized electric currents in spite of low Curie temperatures. Replacing semiconductors with topological insulators, we propose the problem of dilute magnetic topological semiconductors. Increasing disorder strength which corresponds to the size distribution of ferromagnetic clusters, we suggest a novel disordered metallic state, where Weyl metallic islands appear to form inhomogeneous mixtures with topological insulating phases. Performing the renormalization group analysis combined with experimental results, we propose a phase diagram in $(lambda_{so},Gamma,T)$, where the spin-orbit coupling $lambda_{so}$ controls a topological phase transition from a topological semiconductor to a semiconductor with temperature $T$ and the distribution for ferromagnetic clusters $Gamma$ gives rise to a novel insulator-metal transition from either a topological insulating or band insulating phase to an inhomogeneously distributed Weyl metallic state with such insulating islands. Since electromagnetic properties in Weyl metal are described by axion electrodynamics, the role of random axion electrodynamics in transport phenomena casts an interesting problem beyond the physics of percolation in conventional disorder-driven metal-insulator transitions. We also discuss how to verify such inhomogeneous mixtures based on atomic force microscopy.
Magnetic properties of Ga$_{1-x}$Mn$_x$N are studied theoretically by employing a tight binding approach to determine exchange integrals $J_{ij}$ characterizing the coupling between Mn spin pairs located at distances $R_{ij}$ up to the 16th cation coordination sphere in zinc-blende GaN. It is shown that for a set of experimentally determined input parameters there are no itinerant carriers and the coupling between localized Mn$^{3+}$ spins in GaN proceeds via superexchange that is ferromagnetic for all explored $R_{ij}$ values. Extensive Monte Carlo simulations serve to evaluate the magnitudes of Curie temperature $T_mathrm{C}$ by the cumulant crossing method. The theoretical values of $T_mathrm{C}(x)$ are in quantitative agreement with the experimental data that are available for Ga$_{1-x}$Mn$_x$N with randomly distributed Mn$^{3+}$ ions with the concentrations $0.01 leq x leq 0.1$.
In a recent Letter, Berciu and Bhatt have presented a mean-field theory of ferromagnetism in III-V semiconductors doped with manganese, starting from an impurity band model. We show that this approach gives an unphysically broad impurity band and is thus not appropriate for (Ga,Mn)As containing 1-5% Mn. We also point out a microscopically unmotivated sign change in the overlap integrals in the Letter. Without this sign change, stable ferromagnetism is not obtained.
The author reviews the present understanding of the hole-mediated ferromagnetism in magnetically doped semiconductors and oxides as well as the origin of high temperature ferromagnetism in materials containing no valence band holes. It is argued that in these systems spinodal decomposition into regions with a large and a small concentration of magnetic component takes place. This self-organized assembling of magnetic nanocrystals can be controlled by co-doping and growth conditions. Functionalities of these multicomponent systems are described together with prospects for their applications in spintronics, nanoelectronics, photonics, plasmonics, and thermoelectrics.
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Yu.G.Semenov (Groupe dEtude des Semi-Conducteurs
, Universiten Montpellier 2
, Montpellier Cedex
2001
We suggest an approach to account for spatial (composition) and thermal fluctuations in disordered magnetic models (e.g. Heisenberg, Ising) with given spatial dependence of magnetic spin-spin interaction. Our approach is based on introduction of fluctuating molecular field (rather than mean field) acting between the spins. The distribution function of the above field is derived self-consistently. In general case this function is not Gaussian, latter asymptotics occurs only at sufficiently large spins (magnetic ions) concentrations $n_i$. Our approach permits to derive the equation for a critical temperature $T_c$ of ferromagnetic phase transition with respect to the above fluctuations. We apply our theory to the analysis of influence of composition fluctuations on $T_c$ in diluted magnetic semiconductors (DMS) with RKKY indirect spin-spin interaction.
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