High-frequency susceptibility of a multilayered ferromagnetic system with two-dimensional inhomogeneities

This paper reports on the results of the investigation of the high-frequency susceptibility of a layered ferromagnetic structure in which, apart from a periodic change in the magnetic anisotropy parameter from layer to layer, this parameter varies along layers according to a random law (the superlattice with two-dimensional phase inhomogeneities). The evolution of the frequency dependence of the imaginary part of the averaged Green’s function in the range of the energy gap (band gap) in the spectrum of waves propagating along the superlattice axis due to the change in the relative root-mean-square fluctuations of the phase γ2 has been studied at the boundaries of the odd Brillouin zones. It has been found that, for all odd Brillouin zones, the imaginary part of the Green’s function exhibits a universal behavior: the peak corresponding to the edge of the band gap with a lower frequency remains unchanged, and the peak corresponding to the edge of the band gap with a higher frequency is smoothed with an increase in the quantity γ₂. These effects, which were initially revealed at the boundary of the first Brillouin zone of the sinusoidal superlattice, have been explained, as before, by the specific features of the energy conservation laws for the incident and scattered waves in the lattice with two-dimensional inhomogeneities. It has been demonstrated that an increase in the Brillouin zone number leads to a decrease in the value of γ₂ at which the peak at the edge of the band gap with a higher frequency disappears.     

Effect of the correlation properties of one-and three-dimensional inhomogeneities on the high-frequency magnetic susceptibility of sinusoidal superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δν_m between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γ_i and the correlation wavenumbers η_i of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δν_m(γ₁, η₁) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ ₁ ² and η₁, whereas the function Δν_m(γ₃, η₃) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ ₂ ³ and η₃. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.     

Effects of cross correlations between 1D and 3D inhomogeneities on the high-frequency susceptibility of superlattices

Cross correlations between components of a mixture of one-dimensional (1D) and three-dimensional (3D) inhomogeneities are described by introducing a distribution function taking into account correlations between absolute values of two random variables in the absence of correlations between the variables themselves. This distribution function is used for derivation and analysis of the superlattice correlation function containing a mixture of cross-correlated 1D and 3D inhomogeneities. The effect of such inhomogeneities on the high-frequency susceptibility at the edge of the first Brillouin zone of the superlattice is investigated. It is shown that positive cross correlations partly suppress the effect of a mixture of 1D and 3D inhomogeneities on the wave spectrum: the gap at the boundary of the Brillouin zone increases, and wave damping decreases as compared to the effect produced by a mixture of 1D and 3D inhomogeneities in the absence of cross correlations. Negative cross correlations lead to the opposite effect: the gap decreases and wave damping increases. Cross correlations also lead to the emergence of new resonance effects: a narrow dip or a narrow peak at the center of the band gap (depending on the sign of the correlation factor).     

Spectral properties of waves in superlattices with 2D and 3D inhomogeneities

We investigate the dynamic susceptibility and one-dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough-nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inhomogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was discovered earlier [15] upon an increase in root-mean-square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio-spectroscopic and optical methods for identifying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.     

Spin-wave susceptibility of partially randomized ferromagnetic superlattices

This paper is a theoretical investigation of the effect of inhomogeneities in the period of a ferromagnetic superlattice on the high-frequency superlattice susceptibility. The calculations are done for a model in which the uniaxial magnetic anisotropy is taken as the physical parameter that characterizes both the ideal superlattice and a partially randomized superlattice. It is found that as the inhomogeneities become more intense, the two resonance peaks corresponding to the splitting of the spectrum at the edge of the Brillouin zone of the superlattice broaden, move closer to each other, and finally merge into one. The height of this peak increases and the peak width decreases as the intensity of the inhomogeneities increases further. The effect of inhomogeneities on the susceptibility differs dramatically in the two limits of short-and long-wave inhomogeneities: in the latter case (in contrast to the former) the dependence of the separation of the susceptibility peaks on the intensity and correlation properties of the inhomogeneities is nonmonotonic. The possibility of observing these effects in spin-wave resonance experiments involving multilayer magnetic films is also discussed. Zh. éksp. Teor. Fiz. 116, 1335–1345 (October 1999)     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k _c. For the limiting case of infinite correlation radius (k _c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k _c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k _c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k _c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k _c values), because it describes both the shape and width of peaks much better than the standard approximation.     

Crossing resonance of wave fields in a medium with an inhomogeneous coupling parameter

The dynamic susceptibilities (Green’s functions) of the system of two coupled wave fields of different physical natures in a medium with an arbitrary relation between the mean value ? and rms fluctuation Δ? of the coupling parameter have been examined. The self-consistent approximation involving all diagrams with noncrossing correlation lines has been developed for the case where the initial Green’s function of the homogeneous medium describes the system of coupled wave fields. The analysis has been performed for spin and elastic waves. Expressions have been obtained for the diagonal elements G _mm and G _uu of the matrix Green’s function, which describe spin and elastic waves in the case of magnetic and elastic excitations, and for the off-diagonal elements G _mu and G _um , which describe these waves in the case of cross excitation. Change in the forms of these elements has been numerically studied for the case of one-dimensional inhomogeneities with an increase in Δ? and with a decrease in ? under the condition that the sum of the squares of these quantities is conserved: two peaks in the frequency dependences of imaginary parts of G _mm and G _uu are broadened and then joined into one broad peak; a fine structure appears in the form of narrow resonance at the vertex of the Green’s function of one wave field and narrow antiresonance at the vertex of the Green’s function of the other field; peaks of the fine structure are broadened and then disappear with an increase in the correlation wavenumber of the inhomogeneities of the coupling parameter; and the amplitudes of the off-diagonal elements vanish in the limit ? → 0.     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Effects of the mixture of one-and three-dimensional inhomogeneities on the wave spectrum of superlattices

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on the dimensionality of inhomogeneities modulating the period of the superlattice are studied. The cases of one-and three-dimensional modulations, as well as modulation by a mixture of inhomogeneities of both of these dimensionalities, are considered. The correlation function of the superlattice K(r) has the form of a product of the same periodic function and a decreasing function that is significantly different for these different cases. The decreasing part of the correlation function for the mixture of inhomogeneities of different dimensionalities has the form of a product of the decreasing parts of the correlation functions of the components of the mixture. This leads to the nonadditivity of the contributions of the components of different dimensionalities to the resulting modification of the parameters of the wave spectrum that are due to the inhomogeneities (the damping of waves for the mixture of these components is smaller than the sum of the dampings of the components, the maximum gap in the spectrum corresponds to the simultaneous presence of both components of the mixture, not only of the three-dimensional inhomogeneities).     

Electronic exchanges between adsorbed Ni atoms and TiO2(1 1 0) surface evidenced by resonant photoemission

Nickel was deposited on stoichiometric TiO₂(1 1 0) surface in the 0.02–2.1 equivalent monolayer (eqML) range and analyzed by means of photoemission and resonant photoemission. In the case of very low coverage (lower than 0.1 eqML), deposited nickel reacts with the surface through an electronic transfer from nickel atoms towards titanium ions. This exchange caused the filling of unoccupied Ti3d states leading to the increase of a peak in the TiO₂ band gap. These states can be better characterized through resonant photoemission experiments at the Ti 3p → 3d absorption edge: for very low coverage, these states in the TiO₂ band gap have resonant behavior of Ti3d electrons rather than Ni3d ones, confirming the filling of Ti3d states and thus electron transfer between nickel and titanium. For coverage higher than 0.14 eqML, nickel peaks (both Ni3p core level and valence band) should be related to the presence of metallic nickel in small clusters.     

Hydrothermal growth of ZnO on annealed electrodeposited titanate film: Influence of zinc nitrate and methenamine

Hydrothermal growth of hexagonal ZnO nanorods on the annealed titanate nanotube films is reported as a function of molar ratio of Zn(NO₃)₂ and methenamine (1:1-1:4). The molar ratio of 1:4 results in a dense and thinner rod in comparison with other molar ratios. Corn-like structures of the rods are believed to be due to the higher amine concentration. Raman peaks at 437 and 331 cm⁻¹ are assigned to E₂ and E_2H-E_2L modes. Near band gap edge and green photoluminescence emission indicates the structural and oxygen vacancy. O 1s peak is found built-up of sub-peaks at 530.62, 531.8 and 532.84 eV corresponding to O²⁻ on normal wurtzite structure and OH and oxygen vacancies of ZnO, respectively.     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

First-principles investigation of armchair stanene nanoribbons

In this study, we systematically investigated the structural, electronic and optical properties of armchair stanene nanoribbons (ASNRs) by using the first-principles calculations. First, we performed full geometry optimization calculations on various finite width ASNRs where all the edge Sn atoms are saturated by hydrogen atoms. The buckled honeycomb structure of two dimensional (2D) stanene is preserved, however the bond length between the edge Sn atoms is shortened to 2.77 Å compared to the remaining bonds with 2.82 Å length. The electronic properties of these nanoribbons strongly depend on their ribbon width. In general, band gap opens and increases with decreasing nanoribbon width indicating the quantum confinement effect. Consequently, the band gap values vary from a few meV exhibiting low-gap semiconductor (quasi-metallic) behavior to ～0.4–0.5 eV showing moderate semiconductor character. Furthermore, the band gap values are categorized into three groups according to modulo 3 of integer ribbon width N which is the number of Sn atoms along the width. In order to investigate the optical properties, we calculated the complex dielectric function and absorption spectra of ASNRs, they are similar to the one of 2D stanene. For light polarized along ASNRs, in general, largest peaks appear around 0.5 eV and 4.0 eV in the imaginary part of dielectric functions, and there are several smaller peaks between them. These major peaks redshifts, slightly to the lower energies of incident light with increasing nanoribbon width. On the other hand, for light polarized perpendicular to the ribbon, there is a small peak around 1.6 eV, then, there is a band formed from several peaks from 5 eV to ～7.5 eV, and the second one from 8 eV to ～9.5 eV. Moreover, the peak positions hardly move with varying nanoribbon width, which indicates that quantum confinement effect is not playing an essential role on the optical properties of armchair stanene nanoribbons. In addition, our calculations of the optical properties indicate the anisotropy with respect to the type of light polarization. This anisotropy is due to the quasi-2D nature of the nanoribbons.     

Studies of electro-optical properties and band alignment of InGaPN/GaAs heterostructures by photoreflectance and photoluminescence

Photoreflectance (PR) and photoluminescence (PL) spectra are measured for a series of In_0.54Ga_0.46P_1−yN_y/GaAs heterostructures at temperatures ranging from 25 to 300 K. The redshifts of the PR and PL peaks indicate that the band gap of InGaPN is dramatically reduced as nitrogen is incorporated. The transition energies of the band edge at various temperatures are measured and least-squares fitted to the Varshni equation. With N incorporation, the PL peak energy exhibits a particular behavior with temperature, which is not observed in PR spectra. This is attributed to carrier localization at low temperatures resulting from N clusters in the samples. In addition, the emergence of additional peaks in PR spectra as N is incorporated implies that the band alignment switches from type I to type II, due to the lowering of the conduction band, thus forming a two-dimensional electron gas (2DEG) in the interface region between InGaPN and GaAs. The number of confined levels in the 2DEG is found to increase with N concentrations.     

第一原理研究Sn(O1-xNx)2材料的光电磁性质

基于第一原理的密度泛函理论, 以量子化学从头计算软件 为平台研究了Sn(O_1-xN_x)₂材料的光电磁性能, 分析了体系的态密度、 能带结构、 磁性、 介电虚部及折射率. 计算结果表明, N替代O后, 随着掺杂浓度的增加, 体系的带隙先减小后增大, 掺杂量为12.50%时带隙最窄. 由于N 2p轨道电子的贡献, 在0.55-1.05 eV范围内产生了浅受主能级, 价带和导带处的能级均出现了劈裂及轨道的重叠现象, Sn-O键的键强大于N-O键的键强. 从磁性来看, N原子决定了磁矩的大小. 从介电虚部可知, 掺杂后体系的光学吸收边增宽, 主跃迁峰发生红移, 反射率和介电谱相对应, 各峰值与电子的跃迁吸收有关.     

应变超晶格(ZnS)1/(ZnSe)1的光学性质

用linear mufin tin orbital能带方法，计算Si衬底上（ZnS）_n/（ZnSe）_n（001）超晶格的能带结构，计算中采用外加调整势进行带隙修正．在得到较准确的能带结构和波函数的基础上，计算该超晶格系统的光学介电函数虚部ε₂（ω）．结果表明，该超晶格系统的光学性质结合了ZnS和ZnSe体材料光学性质的特点，在相当宽的能量范围内有较好的光谱响应．并且该超晶格系统是直接带隙材料，在光电器件应用中有很大潜力． 关键词：     

Order-disorder phase transition in Ni4W alloy

The order-disorder phase transition in Ni₄W alloy with a D1 _a superlattice was studied experimentally by x-ray structural analysis and theoretically by the Green function method. An experimental temperature dependence was obtained for the equilibrium parameter of long-range order for Ni₄W alloy. It was established that the order-disorder phase transition in the alloy is a first-order transition; the transition occurs through the two-phase region D1_a + A1. The Green function technique, with account for the pair-correlation functions, was used to describe the order-disorder transition for the D1 _a superlattice. The theoretical temperature dependence obtained for the equilibrium parameter of long-range order is in satisfactory agreement with the experimental curve.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–97, April, 1978.     

Infrared modulated reflectance spectra of n and p type gallium antimonide and n type indium antimonide

We have observed the modulated reflectance spectra of n and p type GaSb at 300, 80, and 5 K from 0.56 to 2 eV. The modulated reflectance of intrinsic n type InSb was measured at 80 K from 0.2 to 2 eV. The “dry sandwich” vapor deposition technique was used to make the electroreflectance (ER) samples. The low-temperature spectrum of the undoped p type GaSb sample shows three peaks at the band edge that could be associated with transitions from the top of the valence band, the light (0.903 eV) and heavy (1.014eV) hole state Fermi levels to the conduction band. The energies of the observed peaks are in agreement with the Fermi level determination from Hall effect and Faraday rotation measurements. This modulation mechanism is based on band population effects. The ER signal of InSb under flatband condition at 80 K has five half oscillations at the direct band gap. The contribution of piezoelectric strain to ER is present since the dc bias required to achieve flatband condition is different at the band gap than at E₁. The ER signal corresponding to the direct gap energy E₀ and to the spin-orbit energy E₀ + Δ₀ was determined in the n and p type samples of GaSb at different temperatures. We have measured the intrinsic energy gap in GaSb at room temperature. E_g = 0.74 eV. The corresponding spin-orbit splitting was found to be Δ₀ = 0.733 ± 0.002 eV.