Effect of the intersite Coulomb interaction on chiral superconductivity at the noncollinear spin ordering

We investigate the effect of the intersite Coulomb interaction in a planar system with the triangular lattice on the structure of chiral order parameter Δ(p) in the phase of coexisting superconductivity and noncollinear 120° magnetic ordering. It has been established that the Coulomb correlations in this phase initiate the state where the quasi-momentum dependence Δ(p) can be presented as a superposition of the chiral invariants corresponding to the \({d_{{x^2} - {y^2}}} + i{d_{xy}}\) and p _x + ip _y symmetry types. It is demonstrated that the inclusion of the Coulomb interaction shifts the Δ(p) nodal point positions and, thereby, changes the conditions for a quantum topological transition.     

Spin-spin interaction and the EPR spectrum of KDy(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The EPR spectrum of a KDy(WO₄)₂ monoclinic crystal is investigated. It is found that the EPR spectrum of magnetically concentrated materials at a low frequency (9.2 GHz) undergoes a substantial transformation in addition to the well-known broadening of the EPR lines. At low Dy³⁺ concentrations (x<10^?2), the EPR spectrum of an isomorphic crystal, namely, KY_(1?x)Dy_x(WO₄)₂, is characterized by the parameters g_x=0, g_y=1.54, and g_z=14.6. For a magnetically concentrated crystal KDy(WO₄)₂, the g values are as follows: g_x=0, g_y=0.82, and g_z=2.52. It is demonstrated that the difference in the parameters is associated with the specific spin-spin interaction between Dy³⁺ ions, including the Dzyaloshinski interaction, which is not observed at high frequencies.     

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.     

Polar Phase of Superfluid <Superscript>3</Superscript>He: Dirac Lines in the Parameter and Momentum Spaces

The time reversal symmetric polar phase of the spin-triplet superfluid ³He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space (p _x , p _y , p _z ), the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters—the components of magnetic field (H _x ,H _y ,H _z ). The bosonic Dirac system lives on the border between the type-I and type-II.     

Ferroelectric phase transitions in ionic conductors based on bismuth vadanate

Ceramic solid solutions (Bi_{1 ? x} La _x )₄V₂O_{11 ? z} (I), Bi₄(V_{1 ? x} Fe _x )₂O_{11 ? y} (II), and (Bi_{1 ? x} La _x )₄(V_0.96Fe_0.04)₂O_{11 ? y} (III) (x = 0–0.3, step Δx = 0.02) are prepared using solid-phase synthesis. The concentration and temperature ranges of stabilization of different polymorphic modifications, including the ranges of concentrations x corresponding to the stabilization of the ferroelectric phase, are established. It is revealed that an increase in the concentration x in the region of existence of the pseudoorthorhombic phase α of the solid solutions studied leads to a decrease in the transition temperature, smearing of the transition, and an increase in the width of the thermal hysteresis of the ferroelectric phase transition. The effect of compressing of the domain walls by oxygen vacancies was revealed in the samples from the region of existence of the ferroelectric α phase, and the effect of dielectric relaxation was detected in the samples from the region of existence of the orthorhombic phase β.     

Studies of the defect structure from the calculations of optical and electron paramagnetic resonance spectra for Ni<Superscript>2+</Superscript> centre in <Emphasis Type="Italic">α</Emphasis>-LiIO<Subscript>3</Subscript> crystal

By calculating the optical spectrum band positions and EPR parameters (g factors, g‖, g⊥ and zero-field splitting D) by diagonalizing the complete energy matrix of 3d⁸ ions in trigonal symmetry, the defect structure of Ni²⁺ centre in α-LiIO₃ crystal is studied. It is found that to reach the good fits of optical and EPR data between calculation and experiment, the Ni²⁺ ion should shift by Δz ≈ 0.298 Å along C₃-axis and the O^2? ions between the Ni²⁺ ion and Li⁺ vacancy (V _Li) should be displaced away from the V _Li by Δx ≈ 0.097 Å because of the electrostatic interaction. The results are discussed.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

The analysis of the densities of <Emphasis Type="Italic">s</Emphasis>-wave neutron resonances separated with respect to spin

The density ratio of s-wave neutron resonances z=ρ(J₁)/ρ(J₂) was analyzed on the basis of the experimental data for 22 atomic nuclei and the Gilbert-Cameron formula for ρ(J). Here, J₁=I_x—1/2 and J₂=I_x+1/2, where I_x denotes the spin of the target nucleus in the ground state. Our aim was to verify whether the factor η(I_x), as a multiplier, can be applied in the expression describing ρ(J₁), with the assumption that ρ(J₂) values remain unchanged, or whether the factor 1η(I_x) can be applied, as a multiplier with ρ(J₂), while the ρ(J₁) values remain unchanged. The final conclusions, e.g., the confirmation or the negation of the fact that it may be necessary to apply the η(I_x) factor, depend on the values of “real” errors Δz of the z variable, which can be calculated if the optimal values of Δρ(J₁) and Δρ(J₂) are known.     

Electron paramagnetic resonance in mixed crystals (BaF<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>(LaF<Subscript>3</Subscript>)<Subscript>x</Subscript> activated by Ce<Superscript>3+</Superscript> ions

The electron paramagnetic resonance (EPR) spectra of mixed crystals (BaF₂)_{1?x? y}(LaF₃)_x(CeF₃)_y (y = 0.001 = 0.1%, x = 0–0.02) are investigated in a magnetic field H‖C₄ at a frequency of 9.5 GHz. The angular dependence of the EPR spectrum is measured for the sample with x = 0.02. The lines attributed to Ce³⁺ impurity centers with tetragonal symmetry and g factors (g_‖ = 0.75, g_⊥ = 2.4) close to those measured for the KY₃F₁₀: Ce³⁺ compound are separated in the complex EPR spectrum. The assumption is made that the aforementioned impurity centers are cubooctahedral clusters of the La₆F₃₇ type in which one of the La³⁺ ions is replaced by the Ce³⁺ ion.     

Effect of vibronically induced spin-orbit coupling of electronic ππ* states on nonradiative intersystem crossing: Naphthalene

The effect of (I) S ₁(¹ B _2u ) ? T ₁(³ B _1u ) and (II) S ₁ ? T ₂ (³ B _3g ) ? T ₁ transitions in naphthalene on the rate constant K _ST ^s of the S ₁ ? T ₁ nonradiative transitions to all triplet sublevels s = z, y, x of the T ₁ state has been investigated in the approximation of vibronically induced spin-orbit couplings, taking into account all out-of-plane vibrational modes. The shapes of the vibrational modes that are most active in these transitions are determined. The calculated values K _ST = (0.33–0.75) × 10⁷ s^?1, obtained with allowance for the I and I + II transitions, are consistent with the experimental values (K _ST)_exp found by different researchers. It is established in all calculation versions that K _ST > K _ST ^z > k _ST ^x . This relation is in qualitative agreement with the known magnetooptical data.     

Measuring entanglement-induced quantum correlations in the oscillatory motion of a trapped ion

The preparation of a wide class of entangled vibrational states involving two or three phononic modes of a three-dimensional trapped ion has been reported in the literature from both theoretical and experimental points of view. Here, the time evolution of such a system from an initial condition wherein two oscillatory modes (M _x, M _y) are reciprocally entangled and both are disentangled to the third mode (M _z) is studied. By coupling one of the entangled oscillators (M _x) with the third oscillator (M _z), a correlation between the two uncoupled modes (M _y, M _z) is induced, well visible when the mean value of a suitable operator is considered. A method of measuring the expectation value of a vibrational observable is briefly sketched and then exploited in order to reveal such nonclassical behavior.     

Extreme Electromechanical Characteristics and Microstructural Features of Ferro-Piezoceramics Based on Lead Titanate

Microstructural features and electrophysical parameters of a number of solid solutions based on PbTiO₃ are investigated. Solid solutions (Pb_{1–3/2x + z/2}Nd _x )(Ti_1–y–zMn _y Inz)O₃ and Pb_1–xCa _x Ti_1–y(W_1/2Co_1/2) _y O₃ with extreme values of the mechanical Q-factor and electromechanical anisotropy are chosen as the objects of investigation. The ferro-piezoceramic samples are obtained through conventional sintering and hot pressing. X-ray structural and microstructural studies are performed, and the complex elastic, dielectric, and piezoelectric parameters of experimental samples are measured. The frequency dependences of complex parameters of the experimental samples have been studied at frequencies of up to 40 MHz. It is established that the extreme values of the mechanical Q-factor and piezoelectric anisotropy of the investigated PbTiO₃-based solid solutions are due to microstructural features associated with the technological regimes of ferropiezoceramic fabrication.     

Parabolic Anderson Model in a Dynamic Random Environment: Random Conductances

The parabolic Anderson model is defined as the partial differential equation ? u(x, t)/? t = κ Δ u(x, t) + ξ(x, t)u(x, t), x ∈ ? ^d , t ≥ 0, where κ ∈ [0, ∞) is the diffusion constant, Δ is the discrete Laplacian, and ξ is a dynamic random environment that drives the equation. The initial condition u(x, 0) = u ₀(x), x ∈ ? ^d , is typically taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate 2d κ, split into two at rate ξ ∨ 0, and die at rate (?ξ) ∨ 0. In earlier work we looked at the Lyapunov exponents

$$ \lambda _{p}(\kappa ) = \lim\limits _{t\to \infty } \frac {1}{t} \log \mathbb {E} ([u(0,t)]^{p})^{1/p}, \quad p \in \mathbb{N} , \qquad \lambda _{0}(\kappa ) = \lim\limits _{t\to \infty } \frac {1}{t}\log u(0,t). $$

For the former we derived quantitative results on the κ-dependence for four choices of ξ : space-time white noise, independent simple random walks, the exclusion process and the voter model. For the latter we obtained qualitative results under certain space-time mixing conditions on ξ. In the present paper we investigate what happens when κΔ is replaced by Δ^??, where ?? = {??(x, y) : x, y ∈ ? _d , x ～ y} is a collection of random conductances between neighbouring sites replacing the constant conductances κ in the homogeneous model. We show that the associated annealed Lyapunov exponents λ _p (??), p ∈ ?, are given by the formula

$$ \lambda _{p}(\mathcal{K} ) = \text{sup} \{\lambda _{p}(\kappa ) : \, \kappa \in \text{Supp} (\mathcal{K} )\}, $$

where, for a fixed realisation of ??, Supp(??) is the set of values taken by the ??-field. We also show that for the associated quenched Lyapunov exponent λ ₀(??) this formula only provides a lower bound, and we conjecture that an upper bound holds when Supp(??) is replaced by its convex hull. Our proof is valid for three classes of reversible ξ, and for all ?? satisfying a certain clustering property, namely, there are arbitrarily large balls where ?? is almost constant and close to any value in Supp(??). What our result says is that the annealed Lyapunov exponents are controlled by those pockets of ?? where the conductances are close to the value that maximises the growth in the homogeneous setting. In contrast our conjecture says that the quenched Lyapunov exponent is controlled by a mixture of pockets of ?? where the conductances are nearly constant. Our proof is based on variational representations and confinement arguments.

     

How Far can the Anisotropy Deviate from Uniaxiality in a Dy-Based Single-Molecule Magnet? Dinuclear Dy(III) Complex Study

The Dy^III ions in the dimer [Dy₂(H₂tea)₂(O₂CPh)₄]·2H₂O (1) (H₃tea = triethanolamine) have the 9-coordinate monocapped square-antiprismatic ligand field environment. Compound 1 shows slow relaxation of magnetization which is observable only with applied magnetic fields. This is consistent with the idea that low-symmetry ligand fields allow for the quantum tunneling of magnetization. This is reflected by the fact that there are no observable maxima in the out-of-phase ac susceptibility above 1.8 K. The {g}-tensor of the Dy^III ions {g _x = 11, g _y = 8.2, g _z = 1} further underlying the reduced uniaxiality in this system was determined in electron paramagnetic resonance (X- and Q-band) studies of 1 at temperatures down to 4 K.     

Multicomponent <Emphasis Type="Italic">n</Emphasis>-(Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions with different atomic substitutions in the Bi and Te sublattices

The thermoelectric properties of n-Bi_{2 ? x} Sb _x Te_{3 ? y ? z} Se _y S _z solid solutions are studied in the temperature range 300–550 K. It is shown that an increase in the parameter β determining the figure-of-merit Z of the material is observed in compositions with the optimally related effective mass of the density of states m/m ₀, the carrier mobility μ₀, and the lattice thermal conductivity κ _L . Within the temperature range 300–350 K, the parameter β and the figure-of-merit Z are found to increase in solid solutions with substitutions in both bismuth telluride sublattices Bi → Sb and Te → Se, S (x = 0.16, y = z = 0.12) for optimum electron concentrations. An increase in the electron concentration and substitutions of atoms only in the tellurium sublattice bring about an increase in the β parameter and the value of Z at higher temperatures. Within the range 350–450 K, the parameters β and Z are observed to increase in a solid solution with a low content of substituted atoms in the tellurium sublattice Te → Se, S for y = z = 0.09 and, at higher temperatures up to 550 K, in compositions with tellurium substituted by selenium only, with increasing content of substituted atoms.     

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.     

Spectroscopy of optical centers of Eu<Superscript>3+</Superscript> ions in partially stabilized and stabilized zirconium crystals

The structure of the optical centers of Eu³⁺ ions in tetragonal (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 2.7–3.6; y = 0.1) and cubic (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 8–38; y = 0.1–0.5) crystals of solid solutions on the basis of zirconium dioxide is studied using the methods of optical and Raman-scattering spectroscopy. Characteristic optical centers of Eu³⁺ ions with different crystalline environments are revealed in the above compounds.     

Paramagnetische Resonanz von Er3+ in Y2O3

The paramagnetic resonance absorption of trivalent erbium in single crystals of Y₂O₃ on sites of crystal field symmetry C_3i and C₂ is investigated at 4.2°K and 9.2 kMc/s. The values of theg-tensors and those of the hyperfine structure parallel to the axes of crystalline fields are:g _‖=12.176,g _⊥=3.319,A=426.4·10^?4 cm^?1, andg _z =12.314,g _x =1.645,g _y =4.892, andA _z =433.2·10^?4 cm^?1 for the C_3i-ions and the C₂-ions, respectively. For ions on sites of symmetry C₂ the principal axes ofg in the plane perpendicular toz are found ± 2° beside the [100]-directions. This is different from the result on Yb³⁺ in Y₂O₃. The dependency ofg on the angle of rotation is determined for the (001)-, (110)-, and (111)-plane.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Phase Diagrams of Solid Solutions of Relaxor Ferroelectrics from the Dielectric Spectroscopy Data

The dielectric spectra of Pb(_1–z)Ba _z (Mg_1/3Nb_2/3) _m (Zn_1/3Nb_2/3) _y (Ni_1/3Nb_2/3) _n TixO₃ (x = 0.25–0.4, y = 0.1130–0.0842, m = 0.4844–0.1298, n = 0.1266–0.4726, z = 0–0.15) ceramics with substitution in both A and B crystallographic positions of the perovskite structure are studied. The system demonstrates a transition from the relaxor state to the normal ferroelectric state in both cases: when the concentration of lead titanate grows and the concentration of barium is reduced. On the basis of experimental results, the x–T and z–T phase diagrams are plotted. Despite different crystal chemical reasons of the relaxor state emergence in the investigated solid solutions, their diagrams demonstrate an evident similarity. We have revealed the disappearance of the temperature hysteresis at the transition to the relaxor state in both cases, which has allowed us to make an assumption of the existence of tricritical points on the corresponding diagrams.