Raman scattering in a ferroelectric sodium nitrite crystal

Raman spectra of the ferroelectric sodium nitrite are recorded over a wide spectral range at different temperatures, including the ferroelectric phase transition interval. The room-temperature Raman spectrum reveals the overdamped А₁(z) soft mode which is attributed to the ferroelectric phase transition.     

Raman Scattering on the Effective Soft Mode for Lithium Niobate Crystals

The evolution of Raman spectra in a wide range of temperatures that includes the ferroelectric transition point in lithium niobate single crystals is studied for polarization geometry X(ZZ)Y. In this geometry, the soft mode responsible for the phase transition distinguished by 1A₁(TO)-type symmetry should appear in the spectra. Experimental studies show that the 1A₁(TO) mode interacts resonantly with nonfundamental modes in the low-frequency region of the spectrum. Near the ferroelectric phase transition point, an isofrequency opalescence effect is observed that consists of an abrupt increase in Raman signal intensity at fixed frequencies near the excitation line.     

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.     

High-pressure behavior of the bond-bending mode of AIN

Lattice vibrations of the wurtzite-type AIN have been studied by Raman spectroscopy under high-pressure up to the phase transition to the rock salt structure at 20 GPa. Five fundamental bands E ₂ ² , A₁(TO), E₁(TO), A₁(LO), and E₁(LO) have a strong, positive pressure shift, whereas the shift of the low-frequency E ₂ ¹ band is weakly positive. We have found that the bond-bending mode has a positive mode Grüneisen parameter γ_i = 0.04, which is qualitatively consistent with the recently reported value γ_i = 0.12 [21]. Thus, we confirm that AIN remains stable with respect to the bond-bending mode, while in most tetrahedral semiconductors, bond-bending modes soften on compression. Experimental results are compared with the first-principle calculations.     

Optical properties of lithium niobate and lithium tantalate crystals with impurities and defects

The photoinduced and Raman scattering in lithium niobate and lithium tantalate crystals with impurities and defects have been studied. An exciting laser beam propagated either along the ferroelectric Z axis or perpendicular to it. The conditions for exciting transverse and longitudinal polar optical modes in Raman spectra are established. The regularities of the excitation of Raman spectra in several polarization geometries (X(ZZ)Y, Z(XX, Y Y)Z, Z(XX, Y Y)Z, X(ZX)Y, X(ZX)X and X(ZX)X) have been investigated. Additional (extra) spectral lines are interpreted as a manifestation of a biphonon enhanced by the Fermi resonance and the result of violation of selection rules for pseudoscalar modes of the A ₂ type due to the reduction of the point symmetry group caused by the presence of impurities and defects in real crystals. The conditions for exciting coherent longitudinal and transverse modes in lithium niobate and lithium tantalate single crystals upon stimulated Raman scattering are analyzed. The temperature evolution of the spectra recorded in the X(ZZ)Y geometry near the ferroelectric phase transition point is explained based on the concept of effective soft mode and analysis of the isofrequency opalescence effect. Strong photoluminescence is found in copper-doped lithium niobate crystals.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Raman light scattering in sodium nitrite crystals

Raman light scattering spectra of a ferroelectric sodium nitrite crystal is studied in the lattice mode region as the temperature is lowered from room temperature to 123 K. The existence of a Raman satellite corresponding to the soft lattice mode, i.e., transverse polar vibration responsible for the ferroelectric phase transition, is established for the first time. It is found that the intensity of the Raman scattering by the pseudo-scalar low-frequency A ₂ mode exceeds the intensity of other lattice variations by an order of magnitude.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Antiferromagnetic Resonance in GdB<Subscript>6</Subscript>

The electron spin resonance has been measured for the first time both in the paramagnetic phase of the metallic GdB₆ antiferromagnet (T_N = 15.5K) and in the antiferromagnetic state (T < T_N). In the paramagnetic phase below T* ~ 70 K, the material is found to exhibit a pronounced increase in the resonance linewidth and a shift in the g-factor, which is proportional to the linewidth Δg(T) ~ ΔH(T). Such behavior is not characteristic of antiferromagnetic metals and seems to be due to the effects related to displacements of Gd³⁺ ions from the centrosymmetric positions in the boron cage. The transition to the antiferromagnetic phase is accompanied by an abrupt change in the position of resonance (from μ₀H₀ ≈ 1.9 T to μ₀H₀ ≈ 3.9 T at ν = 60 GHz), after which a smooth evolution of the spectrum occurs, resulting eventually in the formation of the spectrum consisting of four resonance lines. The magnetic field dependence of the frequency of the resonant modes ω₀(H₀) obtained in the range of 28–69 GHz is well interpreted within the model of ESR in an antiferromagnet with the easy anisotropy axis ω/γ = (H ₀ ² +2H_AH_E)^1/2, where H_E is the exchange field and H_A is the anisotropy field. This provides an estimate for the anisotropy field, H_A ≈ 800 Oe. This value can result from the dipole?dipole interaction related to the mutual displacement of Gd³⁺ ions, which occurs at the antiferromagnetic transition.     

Features of the low-frequency polarization response in the region of the ferroelectric phase transition in multiferroic TbMnO<Subscript>3</Subscript>

The unusual behavior of the low-frequency (10 Hz–1 MHz) permittivity in single crystals of ferroelectric multiferroic TbMnO₃ has been experimentally and theoretically studied in detail in the region of the narrow temperature peak of the permittivity, associated with the ferroelectric phase transition (T_C ~ 27.4 K). It has been found that the ε_c^′(ω, T) maximum sharply decreases with increasing measured field frequency, while the temperature position of the maximum is independent of frequency. It has been shown that the observed features of the polarization response can be satisfactorily described within the Landau–Khalatnikov polarization relaxation theory.     

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.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Symmetries of the pseudo-diffusion equation and related topics

We show in details how to determine and identify the algebra g = {A_i} of the infinitesimal symmetry operators of the following pseudo-diffusion equation (PSDE) LQ ≡ \(\left[ {\frac{\partial }{{\partial t}} - \frac{1}{4}\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} - \frac{1}{{{t^2}}}\frac{{{\partial ^2}}}{{\partial {p^2}}}} \right)} \right]\) Q(x, p, t) = 0. This equation describes the behavior of the Q functions in the (x, p) phase space as a function of a squeeze parameter y, where t = e ^2y. We illustrate how G _i(λ) ≡ exp[λA _i] can be used to obtain interesting solutions. We show that one of the symmetry generators, A ₄, acts in the (x, p) plane like the Lorentz boost in (x, t) plane. We construct the Anti-de-Sitter algebra so(3, 2) from quadratic products of 4 of the A _i, which makes it the invariance algebra of the PSDE. We also discuss the unusual contraction of so(3, 1) to so(1, 1)? h². We show that the spherical Bessel functions I ₀(z) and K ₀(z) yield solutions of the PSDE, where z is scaling and “twist” invariant.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

Correlation between raman spectra and structural properties of Zn<Subscript>2 − 2<Emphasis Type="Italic">x</Emphasis></Subscript>Cu<Subscript>x</Subscript>In<Subscript>x</Subscript>Se<Subscript>2</Subscript> films

The Raman spectra of Zn_{2 ? 2x} Cu_xIn_xSe₂ (ZCIS) semiconductor films designed for use as optically active layers in thin-film solar cells have been investigated. The Raman spectra of ZCIS films are characterized by the presence of the dominant mode A ₁, which is observed in A^IB^IIIC ₂ ^VI compounds with chalcopyrite structure. The spectra of CuInSe₂ films (x = 1) obtained at low temperatures (T ≤ 400°C) contain and additional mode at 258 cm^?1, which is due to the presence of the impurity Cu_xSe phase. All modes observed in the spectra of ZCIS films with a Zn concentration ≤20 at % obtained under optimal conditions (520–540°C) correspond to the symmetry of vibrations in the chalcopyrite structure. The broadening and blue shift of the A ₁ mode occurring with an increase in the Zn concentration are indicative of degradation of the chalcopyrite crystal structure and the chalcopyrite → sphalerite phase transition at Zn concentrations exceeding 20 at %.     

Spin-selective low temperature spectroscopy on single molecules with a triplet-triplet optical transition: Application to the NV defect center in diamond

The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T ₀–T ₁, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g ⁽²⁾(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T ₁→S→T ₀ to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T ₀) state sublevels can be obtained from the spectra and g ⁽²⁾(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet ³ A-³ E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m _S =0 sublevel of the excited ³ E state to the singlet ¹ A state (~1 kHz) is much slower than the rates from the m _S =±1 substates, while the rates of ISC transitions to different m _S substates of the ground ³ A state are close to each other (~1 Hz). As a result, only the optical transition between m _S =0 sublevels in the ³ A-³ E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g ⁽²⁾(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T ₀(m _S )=0) transition and (ii) the S→T ⁰(m _S =±1) transitions followed by the slow spin-lattice relaxation T ₀(m _S =±1)→T ₀(m _S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.     

Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Geometrical effects in nanodimensional epitaxial films of barium strontium titanate

The effect of the thickness of 6- to 950-nm-thick Ba_0.8Sr_0.2TiO₃ films epitaxially grown on (001)MgO on their ferroelectric properties is investigated. Raman scattering and X-ray diffraction data indicate a structural phase transition taking place at a film thickness of ≈70 nm, which changes drastically the lattice parameters of the film. Raman spectra taken of the films confirm that they are in the ferroelectric state and that their symmetry changes in going over a critical thickness, as revealed by a sharp displacement of the peaks corresponding to the A ₁(TO) and E(TO) components of the soft mode. At film thicknesses of <100 nm, the permittivity versus thickness dependence exhibits two peaks at thicknesses of ～18 and ～36 nm. Near the first peak, the dielectric nonlinearity is considerably higher than near the second one.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Excitons in monoclinic zinc diphosphide: The <Emphasis Type="Italic">A</Emphasis>-exciton series and Fano effect

The A-exciton series in the absorption spectra of β-ZnP₂ monoclinic zinc diphosphide samples is investigated at different directions of the wave vector and different polarization states of radiation. It is shown that the oscillator strengths determined for the observed transitions are adequately described by the relationship F _n ∝n^?3 characteristic of S-type exciton states. The assumption is made that the A-exciton series is associated with the partially allowed dipole transitions to nS states of the orthoexciton with Γ ₂ ^? (x) symmetry at m _s =0. These states are mixed, to a first approximation, with nS states of the Γ ₂ ^? (z) singlet exciton due to the spin-orbit 2 interaction and are split off by the long-range (nonanalytical) part of the exchange interaction. The Fano antiresonances arise in the absorption spectra at resonances of the A-exciton series when the radiation vector E (or the induction vector D) has a component along the crystallographic axis c. These antiresonances are induced by the configurational interaction of discrete exciton states of the A series with the continuum of the exciton-phonon spectrum due to indirect transitions to the 1S band of the singlet exciton with phonon emission.