Magnetic field dependence of vibrational excitations in a two-dimensional triangular Wigner crystal

It is shown that a static magnetic field applied perpendicular to a quasi twodimensional Wigner crystal lifts the degeneracy, e.g., of transverse and longitudinal vibrational frequencies and modifies their dispersion. The dependence of the effect on the magnitude of the applied field, on the electron surface concentration, and its relevance for observing a two-dimensional Wigner crystal are investigated quantitatively for a triangular lattice of a three-layer structure in harmonic approximation.     

Magnetic properties of the HoMn2Ge2 intermetallic compound

The magnetic properties of a tetragonal intermetallic compound, namely, HoMn₂Ge₂, are investigated experimentally and theoretically. The experimental temperature dependences of the initial magnetic susceptibility and the lattice parameters are obtained in alternating and static magnetic fields. The magnetization curves are measured in strong magnetic fields up to 50 T. The parameters of the crystal field and Ho-Mn and Mn-Mn exchange interactions are determined, and the temperature dependence of the magnetic field of the phase transition from an antiferromagnetic phase to a ferromagnetic phase in a magnetic field aligned along the tetragonal axis is calculated.     

Impurity effects on the magnetization and magnetic susceptibility of an electron confined in a quantum ring under the presence of an external magnetic field

The magnetization and the magnetic susceptibility of a single electron confined in a two-dimensional (2D) parabolic quantum ring under the effect of external uniform magnetic field and in the presence of an acceptor impurity have been studied. The shifted 1/N expansion method was used to solve the Hamiltonian quantum ring within the effective mass approximation. The computed energy spectra, the magnetization and magnetic susceptibility have been displayed as a function of the quantum ring parameters: confinement strength ω₀, magnetic field strength (ω_c), and temperature (T). The obtained energy results show level-crossings, in the absence and presence of acceptor impurity, which are manifested as oscillations in the magnetization and magnetic susceptibility curves.     

Dispersion characteristics of two-dimensional unmagnetized dielectric plasma photonic crystal

This paper studies dispersion characteristics of the transverse magnetic (TM) mode for two-dimensional unmagnetized dielectric plasma photonic crystal by a modified plane wave method. First, the cutoff behaviour is made clear by using the Maxwell--Garnett effective medium theory, and the influences of dielectric filling factor and dielectric constant on effective plasma frequency are analysed. Moreover, the occurence of large gaps in dielectric plasma photonic crystal is demonstrated by comparing the skin depth with the lattice constant, and the influence of plasma frequency on the first three gaps is also studied. Finally, by using the particle-in-cell simulation method, a transmission curve in the \Gamma -X direction is obtained in dielectric plasma photonic crystal, which is in accordance with the dispersion curves calculated by the modified plane wave method, and the large gap between the transmission points of 27~GHz and 47~GHz is explained by comparing the electric field patterns in particle-in-cell simulation.     

Effective dielectric constant of two-dimensional photonic crystals in optical bands

By using the Fourier expansion method, we have developed an approach to calculate the effective dielectric index of a two-dimensional photonic crystal. The approach is very general: it can take into account various Bravais lattice structure as well as arbitrary spatial variation of the dielectric index. It has been found that near a nondegenerate frequency ω_n(Γ) at Γ point, the transverse magnetic (TM) mode is ordinary, as it is independent of the propagation direction, whereas in general the transverse electric (TE) mode depends on the propagation direction, it is extraordinary. Therefore, a two-dimensional photonic crystal can always be described by an effective dielectric index for TM mode near the nondegenerate frequency ω_n(Γ). However, the TE mode is much more complicated unless the lattice structure is highly symmetric. Moreover, a two-dimensional square photonic crystal has been identified as an effective birefringent crystal having two negative refractive indexes from the perspective of Snell's law.     

Structural and phonon dynamical properties of perovskite manganites: (Tb, Dy, Ho)MnO3

A shell model has been used to study the structure, phonon dynamics and phase coexistence of perovskite manganites RMnO₃ (R=Tb, Dy, Ho). The calculated crystal structure, Raman and IR frequencies and specific heats are found to be in good agreement with the available experimental data. The phonon density of states, elastic constants, elastic stiffness, shear constants and phonon dispersion curves have been computed for these manganites. A zone center imaginary A_u mode is revealed in these phonon dispersion curves, which indicates the occurrence of the metastability of the perovskite phase. The Gibbs free energy values calculated as a function of temperature and pressure for RMnO₃ in the orthorhombic phase, when compared with those of the hexagonal phase, reveal the possibility of coexistence of these two phases in the present multiferroic manganites under ambient conditions.     

Ground-state properties of jellium metals with low electron densities

The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew–Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r_s has an intermediate value. At r_s=60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.     

Magnons and phonons in antiferromagnetic CeMg compound

The magnon dispersion curves in the antiferromagnetic phase and the acoustic phonon dispersion in the paramagnetic phase of CeMg compound have been investigated. The magnetic moment and the tetragonal distortion are measured versus temperature. Their variations are consistent with the occurrence of a highly magnetostrictive first-order transition at T_N = 19.5 K. Transverse magnetic excitations associated to transitions between two sublevels of the Г₈ crystal field ground state were measured along the main lines of the Brillouin zone. There is a large anisotropy of the dispersion depending whether the wavevector is parallel or perpendicular to the fourfold axis of the tetragonal cell. This dispersion can be well described by means of a dynamical susceptibility model in which only a few interactions occur.     

Green’s function approach to the low temperature properties of Cs<Subscript>2</Subscript>CuCl<Subscript>4</Subscript>: anisotropy effects

We have studied the effect of both axial and transverse anisotropy on the critical field and thermodynamic properties of the field induced three dimensional antiferromagnetic Heisenberg model on the frustrated hexagonal lattice for Cs₂CuCl₄ compound. The spin model is mapped to a bosonic one with the hard core repulsion constraint and the Green’s function approach has been implemented to get the low energy spectrum and the corresponding thermodynamic properties. To find the critical field (B _c ) we have looked for the Bose-Einstein condensation of quasi-particles (magnons) which takes place when the magnon spectrum vanishes at the ordering spiral wave vector. We have also obtained the dispersion of magnon spectrum in the critical magnetic field for each anisotropy parameter to find the spiral wave vector where the spectrum gets its minimum. The magnon energies show a linear dispersion relation close to the quantum critical point. The effect of hard core boson interaction on the single particle excitation energies leads to a temperature dependence of the magnon spectrum versus magnetic field. We have also studied the behavior of specific heat and static structure factor versus temperature and magnetic field.     

Magnetic field dependent dielectric function for zero-gap semiconductors

Using the random phase approximation and the Yafet wave functions the inter and intraband static dielectric functions of degenerate zero-gap semiconductors placed in a magnetic field are calculated in the long wavelength limit. It is shown that the values of the dielectric function for gapless semiconductors differ considerably from the result obtained previously for the one-band model with parabolic energy dispersion ands-type wave functions. Finally the dielectric function is used to find the static screening of a point impurity charge.     

Magnetic ordering in GdI2

GdI₂ powder samples have been investigated by means of a.c. susceptibility and magnetisation measurements indicating magnetic ordering below T_C = 313 K. The structure consists of strongly coupled ferromagnetic layers of Gd³⁺ moments aligned perpendicular to the hexagonal crystal axis. The inter-layer coupling is much weaker and probably antiferromagnetic suggesting that GdI₂ is to a very good approximation a two-dimensional Heisenberg system.     

Magnetic properties of paramagnetically doped crystals Fe3+, Nd3+ and Ho3+ in various compounds

In this work we calculate the energy levels, wave functions and transition probabilities for a number of compounds whose crystal field parameters have been determined. We introduce a convergence criterion in the diagonalization of the Hamilton matrices dependent upon a self consistency test on the eigenvectors. This assures us of numerically accurate wave functions.First we calculated energy level and susceptibility differences in (Nd³⁺)PbMoO₄ dependent on the multiplicative constants θ_n, used with the published A_l^m to determine the crystal field parameters B_l^m, (B_l^m = θ_nA_l^M). Calculated energy levels as a function of external magnetic field strength and orientation are compared with experimental results for three different sets of published crystal field parameters, B_l^m, for (Fe³⁺)TiO₂. The ground state energy levels, and wave functions, have been calculated for the non-Kramers Ho³⁺ ion in the crystals PbMoO₄, LaCl₃ and HoCl₃. Easily distinguishable variations in the temperature dependence of the X_zz component of the susceptibility are found as a function of the host crystal. It is pointed out that susceptibility calculations, based upon measured crystal field parameters, in conjunction with subsequent susceptibility measurements, provide a good check on the validity of the crystal field parameters.     

Lattice dynamics and specific heat of the manganese antimonide Mn2Sb

Manganese cation binding energy, dispersion curves, total phonon spectrum, and temperature dependence of the lattice and magnetic contributions to specific heat of Mn₂Sb have been calculated. Fiz. Tverd. Tela (St. Petersburg) 40, 128–131 (January 1998)     

Magnetic properties of the bond and crystal field dilution Blume-Emery-Griffiths model in the presence of magnetic field

The magnetic properties of the spin-1 bond and crystal field dilution Blume-Emery-Griffiths (BEG) model in the presence of magnetic field are investigated on a simple cubic lattice by using effective field theory (EFT). In the M-H plane, the common action of bond and crystal field dilution leads to the exhibition of an irregular initial magnetization curve and slows down the magnetization process. The peak of the susceptibility curve has an explicit decline and shows a distinct shift toward the direction of increase of magnetic field. On the other hand, in the M-T plane, the magnetization curves show a discontinuity and a vertical leap in the small range of magnetic field when the negative crystal field is larger and the ratio of biquadratic and exchange interaction is positive (α>0). These results have not been revealed in previous works.     

Universal scaling of plateau width in the quantum Hall effect

The plateau width in the quantum Hall effect follows a general scaling rule with ΔB/B₀² being a constant for all the filling factors of integer intervals. This scaling rule can be derived based on the energy spectrum of two-dimensional electrons forming a crystal lattice in the presence of a strong magnetic field.     

A minimisation procedure for the calculation of lattice energies of tetragonal,hexagonal and trigonal crystals

This paper generalises the minimisation procedure for the calculation of lattice energies of cubic crystals to the cases of tetragonal, hexagonal, and trigonal crystals. If the repulsion energy is described within the simple Born-Mayer scheme minimisation of the lattice energy with respect to the lattice parameters a and c yields the repulsion parameters. The linear compressibilities obtained either by direct measurement or from the elastic constants of the crystal allow the repulsion exponent ? to be calculated. The application of this method to the tetragonal MgF₂ crystal is demonstrated.     

Anomalous behavior of the dielectric response of quantum paraelectric CaTiO3 with iron impurities

We report on the studies of lattice dynamics and crystal structure of natural perovskite with the general formula CaTiO₃:0.01Fe by dielectric spectroscopy and X-ray diffraction in a wide temperature range. In contrast to the “chemically pure” synthetic perovskite, the lattice dynamics of the Fe-containing natural sample exhibits a structural instability in the vicinity of 240 K. Our studies of the behavior of magnetic moment of CaTiO₃:0.01Fe demonstrate that in the temperature region from 4.3 to 300 K this material is paramagnetic. No changes in the crystal symmetry have been observed in the structural studies, which can be explained by the small degree of lattice distortions, as has been observed previously for isotopically substituted SrTiO ₃ ¹⁸ . Conductivity measurements and analysis of the dielectric response dispersion of CaTiO₃:0.01Fe have shown that the dispersion is due to the Maxwell–Wagner mechanism and can be attributed to oxygen vacancies present in the mineral.     

Dynamical fluctuation spectra of two-dimensional classical electron liquids in magnetic fields

Dynamical fluctuation spectra of a two-dimensional classical system of electrons in a magnetic field are obtained by numerical experiments in the domain of a strongly coupled liquid. Excitations in these systems have dispersion relations similar to those in the Wigner lattice of the same number density.     

Studies on the optical and dielectric properties of a zinc thiourea chloride NLO single crystal

Single crystals of a nonlinear optical material, zinc thiourea chloride were grown by the slow evaporation technique. The crystal structure and lattice parameters of the grown crystal were determined by the single crystal X-ray diffraction studies. The single crystal XRD revealed that the material crystallized in a orthorhombic crystal system. Optical studies were carried out and it was found that the tendency of transmission observed from the specimen, with respect to the wavelength of light, is practically more suitable for opto-electronic applications. The optical band gap is found to be 4.30 eV. Optical constants such as the band gap, refractive index, reflectance, extinction coefficient and real (?_r) and imaginary (?_i) components of the dielectric constant and electric susceptibility were determined from the UV–vis–NIR spectrum. The dielectric constant and dielectric loss of zinc thiourea chloride were measured in the different frequency range from 50 Hz to 5 MHz at different temperatures. Further, electronic properties, such as valence electron plasma energy, Penn gap, Fermi energy and electronic polarizability of the grown crystal have been estimated.