Energy spectrum of the low-lying states in Sr<Subscript>2</Subscript>FeSi<Subscript>2</Subscript>O<Subscript>7</Subscript> and the nature of the magnetoelectric effect

A mechanism underlying the magnetoelectric effect is discussed. This mechanism is related to the combined action of an odd crystal field, spin?orbit coupling, and the interaction of the orbital angular momentum with an applied magnetic field. The effective operator describing the spin states of Fe²⁺ ions is obtained. Such operator allows one to interpret the terahertz spectroscopy data and to calculate both the electric field effect on the magnetization and the magnetic field effect on the electric polarization of the sample. It is demonstrated that the magnetoelectric effect is enhanced with a decrease in the energy corresponding to the tetragonal distortion of ligand tetrahedra.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

On the nature of the KH<Subscript>2</Subscript>PO<Subscript>4</Subscript> high-temperature transformation

For over two decades, the high-temperature phase transition (HTPT) at around T _p = 180 °C on KH₂PO₄ (KDP), which involves an ionic conductivity increase, constitutes a controversial subject; while most authors ratify a physical transformation (tetragonal → monoclinic phase transition), others defend the chemical transformation. A careful high-temperature phase behavior examination of this acid salt by means of modulated and conventional differential scanning calorimetry, thermogravimetric analysis, simultaneous thermogravimetric and differential scanning calorimetry, impedance spectroscopy, and temperature evolution of X-ray diffraction was performed to provide a possible solution to this long-standing issue. We found that the structural phase transition does not take place. Instead, a chemical transformation occurs at T _p. When KDP is heated through this temperature, the sample initially corresponding to a single phase (tetragonal) transforms to a sample composed of two solid phases: tetragonal KDP, located at its bulk, and monoclinic potassium metaphosphate (KPO₃), located at its surface. Most of the water produced evaporates, but a small portion of liquid water bonds to KPO₃. Because this is of polymeric nature, it takes the role of a host matrix that contains liquid water regions. Consequently, given that part of the water dissolves a portion of surface salt (providing protons), the surface sample system behaves in a similar manner to a polymer electrolyte membrane where the proton transport mechanism includes the vehicle type, using hydronium (H₃O⁺) as a charge carrier. On further heating, the bulk tetragonal KDP phase reduced to its total decomposition. The metastability of the high-temperature phase below T _p is also explained.     

Topological invariants for phase transition points of one-dimensional Z<Subscript>2</Subscript> topological systems

We study topological properties of phase transition points of two topologicallynon-trivial Z₂ classes (D and DIII) in one dimension byassigning a Berry phase defined on closed circles around the gap closing points in theparameter space of momentum and a transition driving parameter. While the topologicalproperty of the Z₂ system is generally characterized by aZ₂topological invariant, we identify that it has a correspondence to the quantized Berryphase protected by the particle-hole symmetry, and then give a proper definition of Berryphase to the phase transition point. By applying our scheme to some specific models ofclass D and DIII, we demonstrate that the topological phase transition can be wellcharacterized by the Berry phase of the transition point, which reflects the change ofBerry phases of topologically different phases across the phase transition point.     

Magnetic state of intercalation compounds in the Cr<Subscript>x</Subscript>TiTe<Subscript>2</Subscript> system

The temperature and field dependences of the magnetic characteristics of chromium-intercalated titanium ditelluride compounds are investigated over a wide range of chromium concentrations. The Cr_0.5TiTe₂ compound is studied by neutron diffraction. It is revealed that the system under investigation can occur in different magnetic states depending on the chromium concentration. An analysis of the experimental results demonstrates that the interaction between magnetic moments of chromium ions is predominantly ferromagnetic in character. An increase in the chromium concentration leads to ferromagnetic behavior with a pronounced magnetic hysteresis. The magnetic moments of chromium ions in these compounds are estimated.     

Charge dynamics of the spin-density-wave state in BaFe<Subscript>2</Subscript>As<Subscript>2</Subscript>

We report on a thorough optical investigation of BaFe₂As₂ over a broad spectral range and as a function of temperature, focusing our attention on its spin-density-wave (SDW) phase transition at T_SDW = 135 K. While BaFe₂As₂ remains metallic at all temperatures, we observe a depletion in the far infrared energy interval of the optical conductivity below T_SDW, ascribed to the formation of a pseudogap-like feature in the excitation spectrum. This is accompanied by the narrowing of the Drude term consistent with the dc transport results and suggestive of suppression of scattering channels in the SDW state. About 20% of the spectral weight in the far infrared energy interval is affected by the SDW phase transition.     

Magnetic state of the structural separated anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The results of neutron diffraction studies of the La_0.70Sr_0.30MnO_2.85 compound and its behavior in an external magnetic field are stated. It is established that in the 4–300 K temperature range, two structural perovskite phases coexist in the sample, which differ in symmetry (groups R[`3]cR\bar 3c and I4/mcm). The reason for the phase separation is the clustering of oxygen vacancies. The temperature (4–300 K) and field (0–140 kOe) dependences of the specific magnetic moment are measured. It is found that in zero external field, the magnetic state of La_0.70Sr_0.30MnO_2.85 is a cluster spin glass, which is the result of frustration of Mn³⁺-O-Mn³⁺ exchange interactions. An increase in external magnetic field up to 10 kOe leads to fragmentation of ferromagnetic clusters and then to an increase in the degree of polarization of local spins of manganese and the emergence of long-range ferromagnetic order. With increasing magnetic field up to 140 kOe, the magnetic ordering temperature reaches 160 K. The causes of the structural and magnetic phase separation of this composition and formation mechanism of its spin-glass magnetic state are analyzed.     

Specific features of structural states in the BiFeO<Subscript>3</Subscript>-YMnO<Subscript>3</Subscript> solid solutions

The (1 − x)BiFeO_3−x YMnO₃ solid solutions have been found to undergo the following sequence of phase transformations with increasing x: R3c → Pbnm → C2 → Pnma → P6₃ cm. It has been established that the Pbnm and Pnma phases have different orientations of atomic displacements and can exhibit antiferroelectric properties.     

Solid state synthesis of nonstoichiometric Bi<Subscript>2</Subscript>WO<Subscript>6</Subscript>/Bi<Subscript>2</Subscript>O<Subscript>3</Subscript> composites as visible-light photocatalyst

Nonstoichiometric Bi₂WO₆ photocatalyst with the composition of Bi_2?+?x WO_6?+?1.5x (?0.25 ≤ x ≤ 1) wa synthesized by a facile solid state reaction method. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and UV-vis absorption spectrum. The Bi_2.5WO_6.75 photocatalyst showed excellent visible-light-driven photocatalytic performance; nearly 100 % of RhB (10 ppm, pH?=?3?~?4) was decomposed within 25 min, which demonstrated that nonstoichiometric semiconductors could be an efficient visible-light-driven photocatalyst.     

Magnetic and valence states of iron ions in the Perovskite Bi<Subscript>0.9</Subscript>Sr<Subscript>0.1</Subscript>FeO<Subscript>3</Subscript>

Single-phase rhombohedral perovskites (Bi_0.9Sr_0.1)FeO₃ were studied by Mössbauer spectroscopy at temperatures of 293, 87, and 680 K. The Neel temperature T _N = 652 ± 2 K of the magnetic transition was measured. Three states of trivalent iron ions in the octahedral states were discovered. Substitution of Sr²⁺ for 0.1 mol % Bi³⁺ breaks the spatially spin-modulated structure.     

New magnetic states in copper metaborate CuB<Subscript>2</Subscript>O<Subscript>4</Subscript>

The static and resonance properties of copper metaborate CuB₂O₄ were experimentally studied in a magnetic field applied in the crystal tetragonal plane. The field-induced second-order phase transition to a weakly ferromagnetic state was observed in the temperature range 10–20 K. The low-field state is characterized by the absence of spontaneous moment, and it represents, presumably, a long-period helicoid. At temperatures below 2 K, two sequential first-order phase transitions were observed. They were accompanied by jumps in resonance absorption with a hysteresis upon changing field-scan direction. These transitions can be caused by the transformation of the incommensurate spin structure into the helicoidal states with periods commensurate with the lattice translation period.     

Low-temperature formation of thermal and electrodynamic states in Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8</Subscript>

The formation of thermal and electrodynamic states in Bi₂Sr₂CaCu₂O₈ under the condition of current input is studied. The analysis is carried out for partial and complete current penetration under the assumption that the superconductor is cooled down to liquid helium temperature at the zero time. When the current input is continuous, the temperature dependence of the Bi₂Sr₂CaCu₂O₈ specific heat influences the form of the I-V and I-T characteristics of the superconductor. This effect is observed at high electric fields when both stable and unstable states form. As a result, the nonstationary I-V characteristic of Bi₂Sr₂CaCu₂O₈ has the only branch the slope of which is positive and decreases with increasing temperature. Therefore, the higher the rate of current input, the more pronounced the decrease in the slope. It is concluded that one cannot find the current above which instability develops from the Bi₂Sr₂CaCu₂O₈ I-V characteristic if the current input is continuous.     

NMR study of the paramagnetic state of low-dimensional magnets LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript>

A comprehensive NMR study of the magnetic properties of single crystal LiCu₂O₂ (LCO) and NaCu₂O₂ (NCO) is carried out in the paramagnetic region of the compounds for various orientations of single crystals in an external magnetic field. The values of the electric-field gradient (EFG) tensor, as well as the dipole and transferred hyperfine magnetic fields for ^63,65Cu, ⁷Li, and ²³Na nuclei are determined. The results are compared with the data obtained in previous NMR studies of the magnetically ordered state of LCO/NCO cuprates.     

Valence and magnetic states of impurity iron ions in the La<Subscript>0.75</Subscript>Sr<Subscript>0.25</Subscript>Co<Subscript>0.98</Subscript>Fe<Subscript>0.02</Subscript>O<Subscript>3</Subscript> perovskite

The local magnetic and valence states of impurity iron ions in the rhombohedral La_0.75Sr_0.25Co_0.98 ⁵⁷Fe_0.02O₃ perovskite were studied using Mössbauer spectroscopy in the temperature range 87–293 K. The Mössbauer spectra are described by a single doublet at 215–293 K. The spectra contained a paramagnetic and a ferromagnetic component at 180–212 K and only a broad ferromagnetic sextet at T < 180 K. The results of the studies showed that, over the temperature range 87–295 K, the iron ions are in a single (tetrahedral) state with a valence of +3. In the temperature range 180–212 K, two magnetic states of Fe³⁺ ions were observed, one of which is in magnetically ordered microregions and the other, in paramagnetic microregions; these states are due to atomic heterogeneity. In the magnetically ordered microregions in the temperature range 87–212 K, the magnetic state of the iron ions is described well by a single state with an average spin S = 1.4 ± 0.2 and a magnetic moment μ(Fe) = 2.6 ± 0.4μ _B .     

Conduction through localized states in a single crystal of the TlGa<Subscript>0.5</Subscript>Fe<Subscript>0.5</Subscript>Se<Subscript>2</Subscript> alloy

Layered single crystals of the TlGa_0.5Fe_0.5Se₂ alloy in a dc electric field at temperatures ranging from 128 to 178 K are found to possess variable-range-hopping conduction along natural crystal layers through states localized in the vicinity of the Fermi level. The parameters characterizing the electrical conduction in the TlGa_0.5Fe_0.5Se₂ crystals are estimated as follows: the density of states near the Fermi level N_F = 2.8 × 10¹⁷ eV^?1 cm^?3, the spread in energy of these states ΔE = 0.13 eV, the average hopping length R_av = 233 Å, and the concentration of deep-lying traps N _t = 3.6 × 10¹⁶ cm^?3.     

On the nature of state with a charge-density wave in TiSe<Subscript>2</Subscript> from data of scanning tunneling microscopy

The surface of a fresh cleavage of TiS₂, TiSe₂, and TiTe₂ crystals has been investigated using scanning tunneling microscopy with atomic resolution. All materials are characterized by triangular defects coinciding in shape with those supposedly formed as a result of the local change in the titanium atom coordination from octahedral to trigonal-prismatic by the chalcogen due to the Jahn-Teller effect. The conclusion has been drawn that the Jahn-Teller effect exists in these materials, but it is responsible for the formation of nanodefects rather than for the transition to a charge-density wave state. It has been shown that this interpretation of defects allows one to understand the evolution of the stability boundary of a charge-density wave upon donor and acceptor doping.     

Multistable and excitable behavior in semiconductor ring lasers with broken Z<Subscript>2</Subscript>-symmetry

We study the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken. We show how a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser. The theoretical predictions and insights in these different dynamical regimes of the asymmetric semiconductor ring laser are confirmed and further explored experimentally in a semiconductor ring laser set-up that allows to controllably break the Z₂-symmetry of the laser.     

Two-phase paramagnetic-ferromagnetic state of La<Subscript>0.7</Subscript>Pb<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> single-crystal lanthanum manganite

Two phases, paramagnetic and ferromagnetic, were shown by the magnetic resonance method to coexist below the temperature T _C in La_0.7Pb_0.3MnO₃ single crystals exhibiting colossal magnetoresistance. The magnetic resonance spectra were studied in the frequency range 10–78 GHz. The specific features in the behavior of the spectral parameters were observed to be the strongest at the temperatures corresponding to the maximum magnetoresistance in the crystals. The concentration ratios of the paramagnetic and ferromagnetic phases in the samples were found to be sensitive to variations in temperature and external magnetic field. This behavior suggests realization of the electronic phase separation mechanism in the system under study.     

Zeeman effect and stark splitting of the electronic states of the rare-earth ion in the paramagnetic terbium garnets Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> and Tb<Subscript>3</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript>

The Zeeman effect in the ⁷ F ₆ → ⁵ D ₄ absorption band of the Tb³⁺ ion in the paramagnetic garnets Tb₃Ga₅O₁₂ and Tb₃Al₅O₁₂ was studied. The field dependences of the Zeeman splitting of some absorption lines are found to exhibit unusual behavior: as the magnetic field increases, the band splitting decreases rather than increases. Symmetry analysis relates these lines to 4f → 4f electron transitions of the doublet-quasi-doublet or quasi-doublet-doublet type, for which the field dependences of the splitting differ radically from the well-known field dependences of the Zeeman splitting for quasi-doublet-quasi-doublet or quasi-doublet-singlet transitions in a longitudinal magnetic field.     

Magnetic ground state and the spin-state transitions in YBaCo<Subscript>2</Subscript>O<Subscript>5.5</Subscript>

The crystal and magnetic structure of the perovskite-like, oxygen deficient cobalt oxide YBaCo₂O_5.5 has been studied by means of neutron and X-ray diffraction in the 10–300 K temperature range. The magnetic ground state is characterized by a coexistence of two distinct antiferromagnetic phases. In the first one, the ionic moments of high-spin Co³⁺ ions in the pyramidal sites are ordered in a spiral arrangement, while octahedral sites are non-magnetic due to presence of low-spin Co³⁺ ions. The arrangement in the second phase is collinear of the G-type, with non-zero moments both in pyramidal (high-spin Co³⁺ ions) and octahedral sites (presumably a mixture of the low- and high-spin states). With increasing temperature, at 260–300 K, the system develops a gradual structural transformation, which is associated with appearance of spontaneous magnetic moment. This process is related to a thermally induced reversion of low- and high-spin states at the octahedral sites to the intermediate-spin Co³⁺ states, resulting in an insulator-metal transition at T_C ≈ T_IM ≈ 295 K.