Spatial dispersion of the lattice polarizability and the properties of the large polaron

The polaron states are studied in crystals with optical phonon dispersion of the type ω²(k) = ω ₀ ² + u ² k ². The appearance and propagation of a local polarization in such a medium is treated as the evolution of a wave packet having a nonzero group velocity. This approach enables one to construct a consistent theory of moving self-trapped electron. The total energy and the effective mass of a slowly moving polaron are found and are shown to be strongly dependent on the dispersion parameter σ = u/ω₀.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.     

The vibrational spectrum of the OCS molecule based on the data on spectra of liquid and cryosolutions

The IR absorption spectra of liquid OCS (T = 135(1) K) and of the following solutions—OCS + Ar (T = 90 K), OCS + N₂ (T = 90 K), OCS + Kr (T = 130 K), and OCS + Xe (T = 163 K)—are measured in the range 800–7000 cm^?1. From 16 to 40 bands corresponding to transitions to vibrational states up to the third order inclusive are interpreted for basic isotope modification and for the isotopically substituted molecules ¹⁸O¹²C³²S, ¹⁶O¹³C³²S, and ¹⁶O¹²C³⁴S. In the spectra of the liquids, the spectral moments M(1) and M(2) of all the observed bands are determined. The harmonic frequencies ω _i and the anharmonicity constants x _ik are calculated for all the systems, including the liquid. The anharmonicity is found to be constant within the experimental error. A large shift Δω₃ is primarily determined by the dipole-induced dipole interaction.     

Critical current in S-FNF-S Josephson structures with the noncollinear magnetization vectors of ferromagnetic films

The critical current I _C of S-FNF-S Josephson junctions, which are ferromagnet (F)-normal metal (N)-ferromagnet multilayer structures whose ends are in contact with the superconducting (S) electrodes, has been calculated. It has been shown that both the magnitude and sign of I _C depends significantly on the misorientation angle α of the magnetization vectors M _{1, 2} of the ferromagnetic films and the distance L between the superconducting electrodes. The effect of the triplet superconducting component ～〈ψ↑ψ↑〉 ～〈ψ↓ψ↓〉 appearing in the structure on I _C(α) has been analyzed. It has been proven that a new type of the π junction exists, appearing due to the superposition of two contributions to I _C that decrease monotonically with L and are damped at lengths about the coherence length of the normal metal. It has been shown that the effective control over the magnitude and sign of I _C of the structure is achieved at a small deflection of the vectors M _{1, 2} from the antiferromagnetic (M ₁ ↑↓ M ₂) configuration.     

Spin-orbit interactions in heterocyclic analogues of fluorene

For carbazole, dibenzofuran, and dibenzothiophene—heterocyclic analogues of fluorene containing N-H, O, and S groups, respectively—the transition dipole moments P ₀₀ ⁱ for the transitions ³ B ₂→S ₀ and ³ A ₁→S ₀ from the sublevels i=z, y, x of the triplet electronic ππ* states, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The effect that the SO coupling between the S ₀ state and highest triplet states has on the calculation results is considered. The effects exerted on the value of P ₀₀ ⁱ by such specific features of the molecular structure as the position of a heteroatom on the symmetry axis, its valence, and different constants of SO coupling in heteroatoms are discussed. The reason for the weak influence of the quantity ?_HA on the rate constant of radiative deactivation of the lowest T state is ascertained.     

High-frequency susceptibility and ferromagnetic resonance in multidomain thin films of the yttrium-iron garnet type

The field dependence of the high-frequency susceptibility and the ferromagnetic resonance were experimentally studied in a thin (d≈0.1 µm) (111)-oriented single-crystal film of substituted yttrium-iron garnet with the factor q?1. It was shown that the anomaly in the high-frequency susceptibility observed in a magnetic field H parallel to the normal to the film surface in the magnetization saturation region (H≈H_s) has a dual nature; more specifically, this anomaly is associated with an abrupt collapse of the stripe domain structure and a ferromagnetic resonance in the experimental configuration H ∥ [111] and h ⊥ H. In this case, the film transition from the inhomogeneous multidomain state to the homogeneous (single-domain) state at the point H≈H_s has no indications of a second-order phase transition. The experimental frequency-field dependence of ferromagnetic resonance (FMR) in the sample under study, having a characteristic minimum at the point ω₀=5 MHz and H_FMR=H_s, agrees qualitatively and quantitatively with calculations. The influence of the cubic magnetic anisotropy and the film thickness on the FMR spectrum and the orientation of the spontaneous magnetization in domains with respect to the film plane in the zero field H was theoretically studied.     

Formation of the incommensurate ordered phase in TaC<Subscript>y</Subscript> carbide

Structural neutron diffraction studies indicate that only one ordered phase arises after the disorder-order transition in nonstoichiometric cubic tantalum carbide TaC_y. This phase arises in the composition range y = 0.79–0.89 due to long-term annealing with a decrease in temperature from 1600 to 300 K. It is incommensurate in the [1–11]_B1 direction, but it is close to commensurate M₆C₅ structures (C2/m and P3₁ space groups) in mutual arrangement of atoms and vacancies in nonmetallic (1–11)_B1 planes. The disorder-order transition channel that is associated with the formation of the incommensurate superstructure in TaC_y carbide includes two arms k ₅ ⁽⁶⁾ ≈ 0.473b₂ and k ₅ ⁽⁵⁾ = ?k ₅ ⁽⁶⁾ of the {k₅} star and arms of the {k₄} and {k₃} stars. The translation period of the incommensurate phase in the [1–11]_B1 direction is 8.9–9.1 nm, which is larger than that in the commensurate phase M₆C₅ by a factor of about 18.     

Anomalies in the Magnetic Susceptibility in the Second-Order Phase Transitions beyond the Curie Point

Taking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field H_C at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C₄, the magnetic susceptibility becomes infinite at H → H_C. It is shown that as the magnetic field direction deviates from the C₄ axis, the magnetic susceptibility in the critical field H_C proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C₄ axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

Synthesis,structural, and spectroscopic (FT-IR,NMR, and UV) Characterization of 1-(Cyclohexylmethyl)-2-(pyridin-2-yl)-1<Emphasis Type="Italic">H</Emphasis>-benzo[<Emphasis Type="Italic">d</Emphasis>]imidazole by experimental techniques and quantum chemical calculations

The title compound (II), 1-(cyclohexylmethyl)-2-(pyridin-2-yl)-1H-benzo[d]imidazole (C₁₉H₂₁N₃), was synthesized via N-alkylation of 2-(pyridin-2-yl)-1H-benzo[d]imidazole (I). Both compounds I and II were characterized by IR, NMR and UV-vis spectroscopy. Solid-state structure of compound II was determined by single-crystal X-ray diffraction technique. Furthermore, quantum chemical calculations employing density functional theory (DFT/B3LYP) method with the 6–311++G(d, p) basis set were performed for the theoretical characterization of the molecular and spectroscopic features of the compounds. Using the TD-DFT method, electronic absorption spectra of the compounds have been predicted at same level. When the obtained results were compared with the experimental findings, it is seen that theoretical results support the experimental data and a good agreement exists between them.     

Role of critical fluctuations in the formation of a skyrmion lattice in MnSi

The region in the H–T phase diagram near the critical temperature (T _c ) of the cubic helicoidal MnSi magnet is comprehensively studied by small-angle neutron diffraction. Magnetic field H is applied along the [111] axis. The experimental geometry is chosen to simultaneously observe the following three different magnetic states of the system: (a) critical fluctuations of a spin spiral with randomly orientated wavevector k _f , (b) conical structure with k _c ∥ H, and (c) hexagonal skyrmion lattice with k_sk ⊥ H. Both states (conical structure, and skyrmion lattice) are shown to exist above critical temperature T _c = 29 K against the background of the critical fluctuations of a spin spiral. The conical lattice is present up to the temperatures where fluctuation correlation length ξ becomes comparable with pitch of spiral d _s . The skyrmion lattice is localized near T _c and is related to the fluctuations of a spiral with correlation length ξ ≈ 2d _s , and the propagation vector is normal to the field (k_sk ⊥ H). These spiral fluctuations are assumed to be the defects that stabilize the skyrmion lattice and promote its formation.     

Pseudogap in the spin-polaron approach for the carrier spectrum of a two-dimensional doped antiferromagnet

In the Kondo model of the two-dimensional lattice with a strong spin-hole antiferromagnetic exchange, the pseudogap behavior of the carrier spectral function A(k, ω) is considered in the optimal and almost dielectric doping limits. A distinctive feature of the analysis is the introduction of the spin polaron even in the mean-field approximation that leads to the formation of two bands (the analogs of the upper and lower Hubbard bands) and makes it possible to immediately take into account the main rearrangement of A(k, ω). The inclusion of the scattering of the mean-field polaron (within the irreducible Green’s functions) describes the further rearrangement of A(k, ω), in particular, the unusual appearance of the pseudogap near the points N = (±π/2, ±π/2).     

First- and second-order Raman scattering from MoTe<Subscript>2</Subscript> single crystal

We report on Raman experiments performed on a MoTe₂ single crystal. The system belongs to the wide family of transition metal dichalcogenides which includes several of the most interesting two-dimensional materials for both basic and applied physics. Measurements were performed in the standard basal plane configuration, by placing the ab plane of the crystal perpendicular to the wave vector k _i of the incident beam to explore the in-plane vibrational modes, and in the edge plane configuration with k _i perpendicular to the crystal c axis, thus mainly exciting out-of-plane modes. For both configurations we performed a polarization-dependent study of the first-order Raman components and detailed computation of the corresponding selection rules. We were thus able to provide a complete assignment of the observed first-order Raman peaks, in agreement with previous literature results. A thorough analysis of the second-order Raman bands, as observed in both basal and edge plane configurations, provides new information and allows a precise assignment of these spectral structures. In particular, we have observed and assigned Raman active modes of the M point of the Brillouin zone previously predicted by ab initio calculations but never previously measured.     

Spin-frustrated antiferromagnets based on <Emphasis Type="Italic">BEDT-TTF</Emphasis> and manganese dicyanamide complexes

The magnetic properties of new radical cation salts (BEDT-TTF)₂[CuMn(dca)₄] (I) and (BEDT-TTF)₂[Mn(dca)₃] (II) [where BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene and dca = N(CN₂)] are investigated using superconducting quantum interference device (SQUID) magnetometry and electron paramagnetic resonance (EPR) spectroscopy. It is established that, at temperatures below 25 K, both salts are characterized by antiferromagnetic deviations from the paramagnetic behavior. The Weiss constants for compounds I and II are determined to be ?5 and ?10 K, respectively. The corresponding correlations in the structure of compound I are short-range correlations and do not lead to a change in the effective spin equal to 5/2. It is found that the widths of the EPR lines attributed to the BEDT-TTF conducting sublattice correlate with the widths of the EPR lines associated with the magnetic sublattice of the Mn(dca) ₃ ^? counterion in the structure of salt II. This correlation suggests that the antiferromagnetic ordering in the magnetic sublattice of compound II affects the spin-lattice relaxation in the BEDT-TTF sublattice. The dependence of the magnetic moment on the magnetic field for compound II at a temperature of 2 K is typical of weakly frustrated uniaxial antiferromagnets and exhibits a kink in a magnetic field of 20 kOe, which corresponds to spin-flop transitions.     

Thermodynamics of the frustrated J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green’s function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of the frustratedspin-S J ₁-J ₂ Heisenbergmagnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighborbonds J ₁<0 and antiferromagnetic next-nearest-neighbor bonds J ₂ ≥ 0 andarbitrary spin S. We find that the transition point\hbox{$J_2^c$}J2cbetween the ferromagnetic ground state and theantiferromagnetic one is nearly independent of the spin S, i.e., it is very closeto the classical transition point\hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$}J2c,clas=23|J1|. At finite temperatures we focus on the parameterregime\hbox{$J_2<J_2^c$}J2<J2cwith a ferromagnetic ground-state. We calculate theCurie temperature T _C (S, J ₂)and derive an empirical formula describing the influence of the frustration parameterJ ₂ and spin S on T _C . We find that theCurie temperature monotonically decreases with increasing frustration J ₂, where veryclose to\hbox{$J_2^{c,{\rm clas}}$}J2c,clasthe T _C (J ₂)-curveexhibits a fast decay which is well described by a logarithmic term\hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$}1/log(23|J1|?J2). To characterize the magnetic ordering below and aboveT _C , we calculate thespin-spin correlation functions ?S ₀ S _R ?, the spontaneous magnetization, the uniform static susceptibilityχ ₀ as well as the correlation lengthξ.Moreover, we discuss the specific heat C _V and the temperaturedependence of the excitation spectrum. As approaching the transition point\hbox{$J_2^c$}J2csome unusual features were found, such as negativespin-spin correlations at temperatures above T _C even though theground state is ferromagnetic or an increase of the spin stiffness with growingtemperature.     

Ternary generalization of Pauli’s principle and the <Emphasis Type="Italic">Z</Emphasis><Subscript>6</Subscript>-graded algebras

We show how the discrete symmetries Z ₂ and Z ₃ combined with the superposition principle result in the SL(2,C) symmetry of quantum states. The role of Pauli’s exclusion principle in the derivation of the SL(2,C) symmetry is put forward as the source of the macroscopically observed Lorentz symmetry; then it is generalized for the case of the Z ₃ grading replacing the usual Z ₂ grading, leading to ternary commutation relations. We discuss the cubic and ternary generalizations of Grassmann algebra. Invariant cubic forms on such algebras are introduced, and it is shown how the SL(2,C) group arises naturally in the case of two generators only, as the symmetry group preserving these forms. The wave equation generalizing the Dirac operator to the Z ₃-graded case is introduced, whose diagonalization leads to a sixthorder equation. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.     

Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Specific Heat Anomalies in Solids Described by a Multilevel Model

In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C(T)/T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ_i = (E_i?E₀) and the degeneracy of each energy level g_i, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of \({\Delta }_{2}/{\Delta }_{1}\thickapprox \) 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.