Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when E _C ??ω_c (ω_c is the cyclotron frequency and E_C is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δ_S = δ_Sz = ?2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit N_Φ → ∞ (_N? is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δ_S = δ_Sz = ?1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of ?3/2, the energy is found to be lower than the energy (e²/εl _B )√π/2 required for exciting an electron-hole pair in the strictly 2D case (l_B is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e²/εl _B )√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δS _z |?1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ S_z =?3. The energy of a spin biexciton is calculated for values of the wavevector such that ql _B ?1.     

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s ₁ x ₁ + s ₂ x ₂ + ? + s _N x _N is proposed. Here x = (x ₁, … , x _N ), x _j ∈ R and the coefficients s = (s ₁, … , s _N ), s _j ∈ N. Given the interpolation values \((f(1), f(2),...,f(N))=\vec {y}\), the unknown coefficients \(s = (s_{1}(\vec {y}),\dots , s_{N}(\vec {y}))\) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.     

Effect of cation substitution in Cs<Subscript>1–2<Emphasis Type="Italic">x</Emphasis></Subscript>Ba<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>H<Subscript>2</Subscript>PO<Subscript>4</Subscript> on structural properties and proton conductivity

We synthesized compounds with partial substitution of Cs⁺ cations in CsH₂PO₄ by Ba²⁺ cations. The structural, electron transport and thermodynamic properties of Cs_1–2x Ba _x H₂PO₄ (x = 0–0.15) were studied for the first time with the help of a set of physicochemical methods: infrared and impedance spectroscopy, X-ray diffraction and synchronous thermal analysis. The proton conductivity of Cs_1–2x Ba _x H₂PO₄ at 50–230°C was investigated in detail by impedance measurements. The formation of solid substitution solutions isostructural with CsH₂PO₄ (P2₁/m) is observed in the range of substitution degrees of x = 0–0.1, with a slight decrease in the unit cell parameters and some salt amorphization. The conductivity of disordered Cs_1–2x Ba _x H₂PO₄ in the low-temperature region increases by two orders of magnitude at x = 0.02 and increases with an increasing fraction of barium cations by three or four orders of magnitude at x = 0.05–0.1; the superionic phase transition practically disappears. At x = 0.15, heterophase systems based on salts are formed, showing high conductivity and a further decrease in the activation energy of conductivity to 0.63 eV. The conductivity of the high-temperature phase of Cs_1–2x Ba _x H₂PO₄ does not change with increasing fraction of the substituent.     

Photoluminescence of Ca(Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>S<Subscript>4</Subscript>:Eu<Superscript>2+</Superscript> compounds

Photoluminescence (PL) observed in solid solutions of Ca(Al _x Ga_1–x )₂S₄:Eu²⁺ (x = 0.1–0.3) is studied. It is shown that the increase in emission intensity by 18% is caused by changes in the x values and electronic 5d → 4 f transitions in Eu²⁺ ions. A change in the position of the emission spectrum or its partial shift toward shorter wavelengths is due to an increase in the aluminum concentration and a decrease in the crystal field energy. The energy of the zero phonon line E ₀, redshift D, and the Stokes shift ΔS are determined. A decrease in the photoluminescence intensity maximum and an increase in the half-width of the spectrum are found in the temperature range of 10–300 K. The efficiency of emission at temperatures of 20 and 300 K is almost independent of the excitation power density of up to ~10⁴ W/cm². The luminescence lifetime of Eu²⁺ ions was 383, 357, 346, and 333 ns for x = 0, 0.1, 0.2, and 0.3, respectively.     

Electrical conductivity and thermopower in Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Mn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript> S sulfides

This paper reports on the results of investigations into the structural, electrical, and thermoelectrical properties of sulfides Co _x Mn_{1 ? x} S (0 ≤ x ≤ 0.4) in the temperature range 80–950 K. It is established that the thermopower coefficient α decreases significantly with an increase in the cobalt concentration in the lattice of the α-MnS compound. The Co _x Mn_{1 ? x} S compounds with cobalt concentrations in the range 0 ≤ x ≤ 0.3 are semiconductors with hole conduction (α > 0), whereas the compound with x = 0.4 exhibits metallic conduction (α < 0). It is found that the band gap E _g of the compounds under investigation varies in the range from 1.46 eV for α-MnS (x = 0) to 0.26 eV for Co _x Mn_{1 ? x} S (x = 0.4).     

Optical properties of Ni<Subscript>3</Subscript>Al<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> alloys with various degrees of localization of magnetic moments

The optical properties of Ni₃Al_{1 ? x} Mn _x (x = 0–1) ferromagnetic alloys have been studied in the spectral range 0.22–15 μm by the ellipsometry method. The substitution of manganese for aluminum is shown to substantially change the optical conductivity spectra. The concentration dependences of the plasma and relaxation frequencies of electrons have been found. The behavior of the optical characteristics of the alloys under study with varying x has been analyzed with allowance for the structure of the energy spectrum of electrons and the influence of a transition from the band magnetism to the spin-localized magnetism.     

Crystal-structure and magnetic phase transformations in solid solutions of BiFeO<Subscript>3</Subscript>-AFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (A = Ca,Sr, Ba,Pb)

Solid solutions of Bi_{1 ? x} A _x (Fe_{1 ? x/2}Nb _x/2)O₃, where A = Ca, Ba, and Pb, are obtained and their crystal structure and magnetic properties are investigated. It is shown that for A = Ca and x ≈ 0.15, the symmetry of the unit cell changes from rhombohedral (space group R3c) to orthorhombic (Pbnm). The transformation leads to the emergence of spontaneous magnetization due to the Dzyaloshinskii-Moriya interaction. Solid solutions with A = Pb remain rhombohedral up to a concentration of x = 0.3. Spontaneous magnetization sharply increases in the compound with x ≈ 1 at low temperatures and is due to the formation of the spin-glass component.     

Magnetic properties of cobaltites doped with chromium,gallium, and iron ions

The magnetic and magnetotransport properties of cobaltites La_0.5Sr_0.5Co_1–xMe_xO₃ (Me = Cr, Ga, Fe) have been studied. The initial compound (x = 0) is a ferromagnet with T_C = 247 K and a saturation magnetization close to 2μ_B per formula unit. It has ben shown that chromium substitution (x = 0.2) decreases the spontaneous magnetization to 0.3μ_B, while the iron substitution (x = 0.2) does not change the magnetization. The obtained data have been interpreted in a model of positive superexchange interactions between cobalt and iron and negative superexchange interactions between cobalt and chromium.     

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.     

Growth of (GaAs)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(ZnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution films and investigation of their structural and some photoelectric properties

Single-crystal films of the substitutional solid solution (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) on GaAs substrates have been grown using liquid phase epitaxy. The X-ray diffraction patterns, photoluminescence spectra, and current-voltage characteristics of the n-(GaAs)-p-(GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) heterostructures prepared have been investigated. The lattice parameters of the film a _f = 5.6544 Å and the substrate a _s = 5.6465 Å have been determined, and the profile of the molecular distribution of the solid solution components has been obtained. The photoluminescence spectrum of the (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) films exhibits a narrow peak (against the background of the broad luminescence band) with a maximum in the luminescence intensity at a photon energy of 2.67 eV due to the presence of Zn-Se bonds in the structure (ZnSe is covalently bonded to the tetrahedral lattice of the GaAs matrix). It has been shown that the direct branch of the current-voltage characteristics of the structures under investigation is described by an exponential dependence I = I ₀exp(qV/ckT) at low voltages (V > 0.3 V) and by a power-law dependence I ～ V ^α with exponents α = 4 at V = 0.4–0.8 V, α = 2 at V = 0.8–1.4 V, and α = 1.5 at V > 2 V. The experimental results have been explained in the framework of the double-injection model for the n-p-p ⁺ structure under the condition that the concentration distribution of nonequilibrium charge carriers has a minimum.     

Metal-insulator transition in Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>S crystals

Results of an experimental study of MnS, FeS, and Fe _x Mn_1?x S single crystals are presented. The phase composition, the lattice parameters, and the state of paramagnetic ions in Fe _x Mn_1?x S have been determined by x-ray diffraction analysis and Mössbauer spectroscopy. A sequence of transitions have been found in iron manganese sulfide with x = 0.29 at temperatures T ₁ ≈ 25–50 K, T ₂ ≈ 125 K, and T ₃ ≈ 190 K with a change in kinetic properties and the formation of a metallic state at low temperatures T ≈ 2 K. The possibility of a Mott-Hubbard transition in Fe _x Mn_1?x S sulfides with variation of the composition and the temperature is discussed.     

A statistical model of a metallic inclusion in semiconducting media

The atomic dynamics of the binary Al_100–xCu_x system is simulated at a temperature T = 973 K, a pressure p = 1.0 bar, and various copper concentrations x. These conditions (temperature, pressure) make it possible to cover the equilibrium liquid Al_100–xCu_x phase at copper concentrations 0 ≤ x ≤ 40% and the supercooled melt in the concentration range 40% ≤ x ≤ 100%. The calculated spectral densities of the time correlation functions of the longitudinal \({\tilde C_L}\)(k, ω) and transverse \({\tilde C_T}\)(k, ω) currents in the Al_100–xCu_x melt at a temperature T = 973 K reveal propagating collective excitations of longitudinal and transverse polarizations in a wide wavenumber range. It is shown that the maximum sound velocity in the v_L(x) concentration dependence takes place for the equilibrium melt at an atomic copper concentration x = 10 ± 5%, whereas the supercooled Al_100–xCu_x melt saturated with copper atoms (x ≥ 40%) is characterized by the minimum sound velocity. In the case of the supercooled melt, the concentration dependence of the kinematic viscosity ν(x) is found to be interpolated by a linear dependence, and a deviation from the linear dependence is observed in the case of equilibrium melt at x < 40%. An insignificant shoulder in the ν(x) dependence is observed at low copper concentrations (x < 20%), and it is supported by the experimental data. This shoulder is caused by the specific features in the concentration dependence of the density ρ(x).     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.     

Crystal structure and magnetic susceptibility of (CuInSe<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(2MnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The crystal structure of samples in the (CuInSe₂)_{1 ? x} (2MnSe) _x system at room temperature and their magnetic susceptibility in the temperature range 77–1000 K are investigated. It is established that compositions with concentrations 0≤ x ≤ 0.2 form solid solutions with a tetragonal structure, space group I \(\bar 4\)2d (122). The specific magnetic susceptibility χ of samples with 0.1 ≤ x ≤ 0.4 at 77 K lies in the range 9 × 10^?4?1.6 × 10^t-3cm³/g. The temperature dependence of the inverse magnetic susceptibility of the sample with x = 0.4 suggests the presence of a component with antiferromagnetic ordering and a reliably measured Néel temperature that is characteristic of MnSe. The dependences χ = f(T) of the compositions with x = 0.1, 0.2, 0.3, and 0.4 indicate the occurrence of magnetic phase transitions with a change in the spin state.     

Structure and dielectric properties of solid solutions Bi7Ti4 + x W x Ta1–2x O21 (x = 0–0.5)

A number of solid solutions Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) have been synthesized from oxides by solid-phase reaction. The crystal structure, the electrophysical characteristics, and the microstructure of the prepared ceramic samples have been studied. According to X-ray powder diffraction, all the compounds are single-phase with the structure of mixed-layer Aurivillius phases (m = 2.5) with the orthorhombic crystal lattice (space group I2cm, Z = 2). Temperature dependences of the relative permittivity ε(T) of the compound have been measured, from which it has been found that the Curie temperature T _C of perovskite-like oxides Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) decreases linearly as substitution parameter x decreases. The activation energies of charge carriers have been found in different temperature ranges.     

Hall effect in the Ce(Al<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript> heavy-fermion system

The influence of substitution on the binding energy of many-body states and the formation of the magnetically ordered state in a heavy-fermion compound (CeAl₂) have been studied by measuring the transport characteristics (Hall effect, resistivity) in intermetallic compounds of the Ce(Al_1?x M _x )₂ system (M = Ni, Co; x ≤ 0.08). It is established that the Hall coefficient R _H in Ce(Al_1?x Co _x )₂ intermetallides with x = 0.05 and 0.08 grows by more than an order of magnitude as the temperature decreases from 1.8 to 300 K. The experimental data are used to estimate the effective mass of charge carriers, the relaxation time, and the localization radius of many-body states.     

Anomalous magnetocaloric effect in van vleck paramagnet HoVO<Subscript>4</Subscript> near energy level crossing

The anomalous magnetocaloric effect in singlet rare-earth paramagnets near energy level crossing has been experimentally observed for the first time. The magnetization and differential magnetic susceptibility of Ho_{1 ? x} Y _x VO₄ crystals (x = 0, 0.5) measured along the tetragonal axis in a pulsed magnetic field with various change rates near the crossover field, dH/dt, from 3 × 10³ to 2.5 × 10² T/s are compared to the data in static magnetic fields down to 0.1 K. These data indicate the large negative magnetocaloric effect in the pulsed magnetic field, so that the crystal with the initial temperature T ₀ = 4.2 K is cooled much lower than 1 K. The experimental data are qualitatively described in the crystal field model with various interactions including hyperfine interactions and with the known interaction parameters.     

Symmetry and lattice parameters of SrTiO<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> solid solutions

The lattice parameters of ceramic samples of (1 ? x)SrTiO₃-xPbTiO₃ solid solutions are measured at room temperature. It is found that the samples have cubic symmetry in the concentration range x = 0?0.3 and tetragonal symmetry for x > 0.3. The lattice parameter a is virtually independent of temperature for x < 0.8 and slightly decreases in the range x = 0.8?1.0, while the lattice parameter c increases with increasing x. The reduced cubic parameter varies nonlinearly and deviates from Vegard’s linear law as the concentration x increases.     

Neutron-diffraction study of the crystal structure of BaTiO<Subscript>3</Subscript> ferroelectric doped with iron

The crystal structure of iron-doped barium titanate BaTi_1–x Fe _x O₃ is studied by neutron diffraction in the range of 0 ≤ x ≤ 0.12. At low concentrations of iron, x < 0.01, and at room temperature, these compounds have a polar structure with tetragonal symmetry with space group P4mm. The temperature of the transition of the tetragonal ferroelectric phase into the cubic paraelectric phase with space group Pm \(\bar 3\) m for an iron concentration of x = 0.01 is 390 K (for pure BaTiO₃, it is 410 K). At an iron concentration of x = 0.07, the crystal structure of the studied compounds varies, and it is described by the centrosymmetric hexagonal space group P6₃/mmc. The structural parameters of various phases of compound BaTi_1–x Fe _x O₃ are determined from the experimental data.     

Stabilization of Ferromagnetism in BiFeO<Subscript>3</Subscript>:Ho at Hydrostatic Pressure

The isothermal magnetization of the Bi_{1 – x}Ho _x FeO₃ (x = 0?0.2) multiferroic has been studied at a hydrostatic pressure up to 9 GPa in the range of room temperatures. A new anomaly at P_C ≈ 3.81 GPa related to intermediate phases between the structural transition R3c → Pnma has been found against the background of the pressure-induced antiferromagnetic ordering in BiFeO₃ (BFO) at P ≈ 2.59 GPa. It is established that the ferromagnetic behavior under pressure depends on the Ho impurity concentration: P_C decreases at 0.05 ≤ x ≤ 0.1 because of the decrease in R3c bond lengths in the structure, and the stabilization of ferromagnetism is implemented at 0.1 ≤ x ≤ 0.2 probably because of the coexistence of the R3c and Pnma phases. The results of studies indicate that, in Bi_{1 – x}Ho _x FeO₃ with x = 0.2, the transition pressure P_C = 3.7 GPa exceeds the values for BFO doped with other 4f elements (Eu, Y, Sm) in the region R3c → Pnma of the transition.