<Emphasis Type="Italic">Ab initio</Emphasis> theory of the electronic structure and spectra of impurity <Emphasis Type="Italic">nl</Emphasis> ions

The fundamentals of the theory of the electronic structure of impurity clusters and the results of numerical calculations for the iron-, lanthanum-, and actinium-group ions in Me⁺ⁿ: [L]_k clusters are presented. The effects of the interionic distance and ligands in the Me⁺ⁿ: [L]_k clusters on the electronic structure of the nl ^N and nl^N?1n′l′ configurations of the 3d, 4f, and 5f ions are considered. The correspondence between the optical and x-ray spectra of different impurity crystals is also analyzed.     

Intersubband cyclotron resonance of holes in strained Ge/GeSi(111) heterostructures with germanium wide quantum wells and cyclotron resonance of 1<Emphasis Type="Italic">L</Emphasis> electrons in GeSi layers

The submillimeter (?ω=0.5–5 meV) magnetoabsorption spectra of strained Ge/Ge_1?xSi_x(111) multilayer heterostructures with thick Ge layers (d_Ge=300–850 Å, d_GeSi≈200 Å, x≈0.1) are investigated at T=4.2 K upon band-gap optical excitation. It is revealed that the absorption spectra contain cyclotron resonance lines of 1L electrons localized in GeSi solid solution layers (unlike the previously studied structures with thin Ge layers as quantum wells for 3L electrons). The absorption spectra of the samples with thick Ge layers (d_Ge=800–850 Å) exhibit cyclotron resonance lines of holes due to transitions from the lower Landau levels in the first quantum-well subband to the Landau levels belonging to the third and fifth higher subbands.     

Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams

We consider random Schrödinger equations on \({\mathbb{R}^{d}}\) for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ _t the solution with initial data ψ₀. The space and time variables scale as \({x\sim \lambda^{-2 -\kappa/2}, t \sim \lambda^{-2 -\kappa}}\) with 0 < κ <  κ₀(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ _t converges weakly to the solution of a heat equation in the space variable x for arbitrary L ² initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i.e. the ladder diagrams with renormalized propagator, converge to the heat equation.     

Electronic energy structure and x-ray spectra of wide-gap AlN and BN crystals and B<Subscript>x</Subscript>Al<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solutions

The electronic energy structure of 2H and 3C AlN and BN crystals and B_xAl_1?xN solid solutions is calculated on the basis of the local coherent potential method using the cluster version of the MT approximation and the theory of multiple scattering. The features of the electronic structure of 2H-AlN crystals are compared with x-ray K and L absorption and emission spectra of aluminum and nitrogen. An interpretation of these features is given. The concentration dependences of the width of the upper subband of the valence band and the band gap in B_xAl_1?xN solid solutions (x = 0.25, 0.5, 0.75) are investigated. Charge transfer from aluminum to nitrogen atoms is shown to occur and increase with boron doping in both crystallographic modifications.     

Correlation between structural and giant magnetoresistance properties of Fe–Ag nanogranular films

Fe _x Ag_1?x granular thin-films, with the atomic Fe concentration, x, ranging from 0 up to 0.5, were deposited by dc magnetron co-sputtering. The giant magnetoresistance (GMR) intensity is maximum at x _I  = 0.32, while the maximum of GMR efficiency, γ, i.e., the change of GMR intensity for a unit change of reduced squared magnetization, is observed at x _γ = 0.26. Owing to the spin-dependent scattering features, the GMR intensity and γ depend on both the concentration and the arrangement of the magnetic material. Therefore, to explain the difference between x _I and x _γ and to understand how the structural properties affect the magnetoresistive behaviour, we performed magnetization, Mössbauer and X-ray diffraction measurements as a function of x. X-ray data indicate that the granular films exhibit three different regimes: for x < 0.2, they can be described as a Fe–Ag solid solution; for 0.2 < x < 0.32 the Fe–Ag solid solution is still observed and very small Fe precipitates are found; finally, for x > 0.32, a Fe–Ag saturated solid solution is detected, containing bcc Fe clusters whose size is about 10 nm. Differently, for all the concentrations, magnetization data show the presence of Fe precipitates, whose size increases with x, and the Mössbauer investigation confirms this picture. We find that the samples grown at x = x _γ display the finest Fe dispersion within the Ag matrix, as the Fe–Ag solid solution is nearly at saturation and the Fe cluster size is of the order of a few nanometers; this arrangement possibly maximizes the magnetic/non-magnetic interface extension thus enhancing the GMR efficiency. If x is slightly increased, the increase in total Fe content compensates the GMR efficiency reduction, so the GMR intensity maximum is observed.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

The theory of morphotropic phase transition in PbZr<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ti<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript>

The concept of the mechanism of formation of morphotropic boundaries in T?x phase diagrams of solid solutions of complex oxides with the perovskite structure has been formulated. This concept is illustrated by calculation of the conditions for existence of morphotropic phase transition in a quasy-binary solid solution of the PbZr_{1 ? x} Ti _x O₃ and (1 ? x)PbMg_1/3Nb_2/3O₃ + xPbTiO₃ compositions.     

Low-temperature plasticity and lattice dynamics of solid parahydrogen with an isotopic impurity

The low-temperature plasticity of solid polycrystalline parahydrogen doped with an isotopic impurity (deuterium) is studied. The dependences of the rate of steady-state creep in p-H₂ on the impurity concentration and stress are obtained. The deformation of p-H₂ is described with inclusion of the zero-point mean-square displacements 〈x²〉 of particles making up a crystal. The calculated and experimental values of 〈x²〉 are compared for two possible isotope molecules (HD and D₂) at three stress levels. A correlation between the 〈x²〉 values and an increase in the force constants of a p-H₂ crystal doped with the isotopic impurity is established. An increase in the mean-square displacements of p-H₂ with the tensile load is discussed. Deformation-induced purification of a p-H₂ crystal from the isotopic impurity is suggested to occur.     

Study of ferromagnetic correlations caused by impurities in nonmagnetic materials by the method of small-angle scattering of polarized neutrons

The possibility of the study of ferromagnetic correlations caused by d-metal impurities in nonmagnetic matrices is discussed. The polarization and magnetic-nuclear interference obtained by analyzing the small-angle scattering of polarized neutrons in a CuZn(20) alloy with Ni impurity (1 at %) are reported. It has been shown that Ni is clustered in the CuZn matrix with the characteristic correlation radius in the range 100 Å < R _c < 5000 Å depending on the thermal processing of the samples. The cross correlation function determining magnetic-nuclear interference is satisfactorily approximated by the exponential exp(?r/R _c), where r is the distance. It has been found that the nonmagnetic matrix CuZn(20) with an almost uniform distribution of 1% Ni impurity has metamagnetic properties in the field H ≈ 0.5 T at room temperature.     

Mechanism of charge transfer in <Emphasis Type="Italic">n</Emphasis>-CdS/<Emphasis Type="Italic">p</Emphasis>-CdTe heterojunctions

The capacitance-voltage and current-voltage characteristics of the n-CdS/p-CdTe heterosystem are investigated. Analysis of these characteristics demonstrates that the CdTe_1?x S _x solid solution formed at the n-CdS/p-CdTe heterointerface is inhomogeneous in both the conductivity and composition. The thickness of solid solutions is estimated from the capacitance-voltage characteristics. It is shown that, for the n-CdS/p-CdTe heterosystem, the current-voltage characteristic in the current density range 10^?8-10^?5 A cm^?2 is governed by the thermal electron emission, whereas the current in the heterostructure at current densities in the range 10^?4-10^?2 A cm^?2 is limited by recombination of charge carriers in the electroneutral region of the CdTe_1?x S _x solid solution. The lifetime and the diffusion length of minority charge carriers in the CdTe_1?x S _x solid solution and the surface recombination rate at the interface between the CdS layer and the CdTe_1?x S _x solid solution are determined. It is demonstrated that the n-CdS/p-CdTe heterostructure operates as a p-i-n structure in which CdTe is a p layer, CdTe_1?x S _x is an i layer, and CdS is an n layer.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.     

Charge state of a transition metal impurity in II–VI semiconductors

The results of calculating the electronic structure of semiconductor compounds A^IIB^VI: 3d(A = Zn; B = S, Se, Te; 3d = Sc-Cu) at a low content of 3d impurities are discussed. The excess charge of an impurity ion with respect to the charge of the zinc ion is determined for the whole series of 3d impurities. It is found that the excess charge gradually varies from +0.6|e| for the scandium impurity to ?0.2|e| for the copper impurity. Photoionization of an impurity ion is simulated by adding a hole or an electron to the impurity center. The added charge is redistributed between the impurity ion and its nearest neighbors, thus decreasing or increasing the total excess charge of the impurity center by a magnitude of ～ 0.2|e|.     

Effect of the composition of the solid solution on the high-temperature microhardness of SiGe heteroepitaxial layers grown on Ge and Si substrates

The effect of the composition of epitaxial layers (ELs) of the Si_xGe_1?x solid solution grown on Ge and Si substrates on their microhardness and the length of dislocation rosettes forming around indentations is studied at a homologous temperature 0.5T_melt for each composition. For the Si_xGe_1?x/Ge (0≤x<0.15) and Si_xGe_1?x/Si (0.85<x≤1) ELs, the dependences of the microhardness and the length of dislocation rosettes on the solid-solution composition are nonmonotonic. The nonmonotonic change in the plasticity of the ELs is most likely caused by hardening of the solid solutions in a certain composition range due to their spinodal decomposition with the formation of clusters and disperse precipitates.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.     

(Pr–Ca) Manganites That Display Multiferroic Properties: High-Temperature Magnetic,Resistive, and Dielectric Measurements

Complex magnetic, resistive, and dielectric studies of Pr_1–xCa_xMnO₃ (х = 0.15–0.30) manganites reveal multiferroic properties at T?T_C in these solid solutions. States with local magnetization in the form of ferromagnetic clusters (nucleation temperature T* ≈ 700 K) and high dielectric constants coexist in the temperature window T_C ≤ T ≤ T*. There is a correlation between the temperature dependences of specific resistance and specific magnetization.     

CARS study of deuterium clusters stabilized in solid helium

Solid deuterium clusters that for the first time have been isolated in a matrix of solid helium have been investigated at T=1.3 K and P=3 MPa by the coherent anti-Stokes Raman spectroscopy (CARS) technique. The vibronic Q₁((J=0) and Q₁(J=1) line intensity, shape, and positions have been studied as functions of ortho and para content in the solid, as well as of the size of clusters. The strong effect of Raman scattering cross-section sensitivity to the molecular environment nuclear spin state has been found in CARS: the ratio of probabilities for the scattering by para(J=1) and ortho(J=0) deuterium, which is equal to 1 in a gas, is as high as 10000 in nearly pure ortho deuterium, whereas it is about 50 in spontaneous Raman scattering. This effect has been shown to occur starting from a cluster size corresponding to the onset of the phonon band.     

Lattice instability induced by 3<Emphasis Type="Italic">d</Emphasis> impurities in II–VI compound semiconductors

Nickel-impurity-induced transverse displacements of ions in a Zn_1?xNi_xSe lattice (x = 0.0025) were detected. This type of displacement correlates with macroscopic distortions of a crystal associated with transverse ultrasonic waves that are propagated along the 〈110〉 direction. The shear instability is assumed to be due to the hybridization of the sp³ bonds with the 3d states of the impurity centers.     

A Raman study of lattice vibrations in II–VI semiconductors doped with 3<Emphasis Type="Italic">d</Emphasis> elements

Room-temperature Raman spectra were obtained for powder samples of Zn_1?xNixSe and Zn_1?yCr_ySe compounds and for a single-crystal Zn_1?xNi_xSe (x = 0.0025) sample in the temperature range 5–140 K. The results obtained are interpreted in terms of large-scale lattice shear strains induced by 3d elements in these solid solutions.     

Magnetic ordering in La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3−<Emphasis Type="Italic">x</Emphasis>/2</Subscript> anion-deficient manganites

The structural, magnetic, and electrotransport properties of La_1?xSr_xMnO_{3? x/2}(0≤x≤0.30) manganites with perovskite structure are investigated experimentally as a function of oxygen deficiency. In the solid solutions La_1?xSr_xMnO₃, a change in the type of symmetry of the unit cell is observed at x=0.125. Samples with x≤0.125 are characterized by an O′-orthorhombic unit cell, whereas samples with x>0.125 are characterized by a rhombohedral unit cell. The structural properties of the anion-deficient solid solutions La_1?xSr_xMnO_3?x/2 are analogous to those of the stoichiometric system. It is assumed that, as the oxygen content decreases, La_{1? x}Sr_xMnO_3?x/2 anion-deficient solid solutions experience a series of successive magnetic phase transformations in the ground state: from an A-type (x=0) antiferromagnet to a cluster spin-glass-type inhomogeneous magnetic state (0.175>x≤0.30) through a two-phase (antiferromagnetic and ferromagnetic) state (0>x≤0.175). The anion-deficient solid solution with x=0.175 has the maximal value of the ferromagnetic component. As the oxygen deficiency increases, the resistivity of La_{1? x}Sr_xMnO_3?x/2 samples first decreases (up to a value of x=0.175), acquiring an activation character, and then increases (up to a value of x=0.30). In this case, none of the anion-deficient solid solutions exhibits a metal-semiconductor transition in the whole range of concentrations considered. A peak of magnetoresistance at a temperature below the point of magnetic ordering is observed only in the sample with x=0.175. The results of experiments carried out with a series of La_1?xSr_xMnO_3?x/2 anion-deficient solid solutions are summarized in the concentration diagrams of the spontaneous magnetic moment and the critical temperature of magnetic phase transitions. Hypothetical magnetic phase states are pointed out. The experimental results obtained can be interpreted in terms of the phase-separation model and the competition between ferromagnetic and antiferromagnetic indirect superex-change interactions. It is assumed that Mn³⁺-O-Mn³⁺ indirect superexchange interactions in the orbitally disordered phase are positive in the case of octahedral coordination of manganese ions and are negative when the coordination of at least one Mn³⁺ ion is pentahedral.