A Kerr effect study of microwave behaviour of partially magnetised ferrites

Magneto-microwave Kerr effect has been experimentally studied on three ferrite samples in the Polder-Smit loss region. Experimental data have been compared with the theoretical values which were calculated on the basis that the real part of the permeability tensor element μ′ is given by Green and Sandy's expressions (IEEE Trans. Microwave Theory Tech. MTT-22, 641 (1974)). This has a term given by Schlomann for μ′₀, the permeability for the demagnetised state. No agreement is found between theoretical and experimental values hence the above expression for ν′₀ has been substituted by another one given by Sandy (Raytheon Tech. Memor. T-815 (1969)) which involves the average demagnetisation factor N. It is found that there is a good agreement between the theory and the experiment provided N is assumed to depend linearly on the magnetisation of the sample.     

Excess entropy for a vacancy in a crystal

The following topics are discussed: (1) Within the harmonic theory a general expression is given for excess entropy of a localized detect in any crystal with cyclic boundary conditions and in the small perturbation limit. For a single vacancy defect Stripp and Kirkwood's formula is obtained, ΔS/k_B = d/2,d being the dimension of the space. For other localized defects the perturbation formula requires calculation of the unperturbed Green's matrix. (2) It is argued that the effect of free surface boundary conditions, as well as other surface changes, leaves ΔS effectively invariant. (3) Using the vacancy perturbation result for ΔS and Lawson's formula, a value for the vacancy formation volume is obtained only in terms of known measured parameters; this result is compared to experimental and other calculated values of ΔV_f. (4) If localized vibrational modes are present due to the vacancy, what effect these might have on ΔS, and, from this, what materials might be candidates for observing localized modes.     

Optical anisotropy of orthorhombic InS

The optical anisotropy of InS single crystals in the range of photon energy from 1.8 to 3.5 eV has been studied by absorption, electroreflectance and wavelength-derivative reflectance measurements. These systematic optical measurements for the polarizations, E//a and E//b, have revealed that the transition at the fundamental absorption edge of InS is allowed for E//b, and there exist three distinct doublet transitions having different selection rules in the photon energy region from 2 to 3.5 eV; Bo and B^'₀doublet allowed only for E//b, A₀ and A^'₀ allowed only for E//a, and E₁ and E^'₁ allowed for both polarizations. The observed results are discussed based on the anisotropic nature of two chemical bonds in InS, cation-cation and cation-anion.     

Polarization fluctuations in regions bounded by equi-potentials

It is shown that the integral of <{P(rτ), P(r')}>· n? as a function of r over a volume V_e bounded by an equi-potential is independent of r' and of V_e and is determined solely by [?(ω)?1] · n? provided the dielectric constant is local and that V_e is of macroscopic dimensions.     

Quantum-statistical conductance theory of nonideal plasmas by use of the force-force correlation function method

Using the formalism of force-force correlation functions developed recently, the Spitzer formula for the conductance is generalized by taking into account the following effects: (1) dynamical screening; (2) ion-ion correlations by the ion structure factor; (3) deviations from Coulomb's interaction law; (4) influence of the Debye-Onsager relaxation effect; (5) quantum effects.It is shown that all these effects decrease the conductance in comparison with the values predicted by the Spitzer theory and lead to a more reasonable agreement with the experimental data in the region μ = e²/r_DkT ? 1 (r_D - Debye radius).Electron-electron interactions are treated by a systematic perturbative expansion of the force-force correlation function with the help of the Matsubara Green's function technique.     

Determination of the Ni+-F- distance for square-planar and linear centers in LiF:Ni+ and NaF:Ni+

The distance R between Ni⁺ and the closest F^- anions for several square- planar and linear Ni⁺ centers observed in LiF and NaF has been derived from the isotropic superhyperfine constant A_s. R is smaller for linear than for square-planar centers according to Pauling's criteria. The knowledge of R for every square-planar center allows one to explain reasonably variations undergone by the experimental g_∥?g₀ values. Finally the present data reveal that the ionic radius of the unusual Ni⁺ ion is indeed quite close to that of Cu⁺.     

An AB initio analysis of the second-order elasticity effect on nematic configurations

The term k₁₃ div(n div n) introduced by Oseen and by Nehring and Saupe in the expression of the distortion energy of nematic liquid crystals is considered. It is shown that all the calculations previously made in order to take into account its effects must be revised. It is pointed out that such effects can be correctly evaluated only if Nehring and Saupe's theory is properly extended to take into account the expression of the free energy at the sample boundaries, a fact which requires a separate and specific analysis.     

Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.     

A study of the effective line width in lithium ferrites using magneto microwave Kerr effect

A new technique to determine the effective line width ΔH_eff using the dimensional resonance phenomenon observed in magneto-microwave Kerr-effect experiment is discussed. This effect depends on the Permeability tensor components and the damping parameter α. The components of permeability tensor μ have been calculated theoritically and the damping parameter α is determined from experimental data. The measurements have been made at 24 GHz on three samples of lithium ferrite and their effective line widths have been obtained both in the partially magnetised and the saturated states of magnetisation. It has been found that ΔH_eff for two states of magnetisation are different. Further, the value of ΔH_eff obtained are higher than expected at this frequency. This suggests the possibility of additional relaxation mechanisms at dimensional resonance.     

n-Dimensional complex riemann-einstein spaces with O(n−1, C) as the symmetry group

Working with a complex Riemannian space V_n, we determine the most general form of the metric which admits O(n?1, C) as a symmetry subgroup. The conformal curvature tensor, which is of type D for the real cross-section of signature (+---) with n = 4, has a very similar structure for n > 4 and complex V_n. Solutions of the empty space Einstein equations with the λ-term are then studied. There are two different static solutions which, with n = 4 and real cross-section of signature (+---), reduce to Schwarzschild-de Sitter metric, or to the Nariai's solution. A proof of a slight generalization of Birkhoff's theorem that every time-dependent solution of G_μv = λg_μv is reducible, by a coordinate transformation, to one of these two solutions, is given. The complete symmetry groups of the solutions obtained are examined. The techniques of embedding in a higher-dimensional flat space and of Kruskal's variables which exhibit the spurious nature of Schwarzschild's singularity are generalized to the case of (complex) n dimensions. General properties of geodesic lines for both solutions are examined and various real cross-sections of Nariai's solution for n = 4 are discussed. The last section studies some contractions of the two solutions.     

Core-level binding energy shifts in dilute alloys

Core level binding energy shifts for the element A of a large number of dilute alloys AB have been measured, where the concentration of the dilute component A is 10% or less. The experimental shifts are analysed in terms of alloy heat of formation data, for which we have used Miedema's semi-empirical scheme. Good overall agreement is obtained between the experimental data and the calculated values, encouraging the use of electron spectroscopy for evaluating solution energies of metallic systems.     

On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.     

Statistical mechanics of a bounded,ideal magnetofluid

A statistical model of a three-dimensional, incompressible, cylindrically bounded, current-bearing magnetofluid is presented for the purpose of gaining insight into the nonlinear relaxation process routinely observed in reversed-field-pinch experiments. An absolute equilibrium ensemble is utilized that incorporates energy, magnetic helicity, and magnetic flux constraints. Results are extracted only after an extensive mathematical treatment of the properties of poloidal and toroidal fields. The model predicts the presence of magnetic fluctuations about a cylindrically symmetric, Bessel-function-model, mean magnetic field, which satisfies ▽ × 〈B〉 = μ〈B〉. As Taylor's ∵-parameter approaches 1.56, the model predicts that the significant region of the fluctuation spectrum narrows down to a single (coherent) m = 1 mode. An analogy between the Debye length of an electrostatic plasma and μ^?1 suggests the physical validity of the model's prediction of the magnetic-field-fluctuation autocorrelation tensor 〈δB(r) δB(r′)〉, when |;r ? r′| ≥ μ^?1.     

Operator equivalents in general

We show that recent criticism of a formula for diagonal operator equivalents (OE's) is unfounded. We generalise this formula to derive off-diagonal OE's ^jT_l^m, as a finite polynomial in J_Z, and claim that this is a definitive formula for the ^jT_l^m.     

Collective excitations in the 1-D-ferromagnet CsFeCl3 with singlet ground state

By means of inalastic neutron scattering we have determined the dispersion relation of the magnetic excitations in CsFeCl₃ at different temperatures.The dispersion in c-direction, along the Fe-chains is typically ferromagnetic and in the hexagonal plane antiferromagnetic. Due to the lack of an applicable theory the data were parametrized by the simple heuristic formula:?ω = [2J[1 - cos πq_c] [A + 2J(1 - cos π)q_c)] + [C + J' (1.5 + γ(q))]²]^{$\text{1}\text{2}$}The gap was found to be C = 0.148 THz, the easy plane anisotropy A = 0.308 THz, the ferromagnetic interaction J = 0.148 THz and the antiferromagnetic interaction J' = -0.04 THz. At 1.25 K all excitations had a width smaller than the instrumental resolution ΔE = 0.025 THz. These results can be interpreted as follows: CsFeCl₃ is a singlet ground state system with strong ferromagnetic interaction J along the crystallographic c-axis and weak antiferromagnetic interaction J' in the plane perpendicular to c.In addition we have measured the influence of a magnetic field along the hexagonal c-axis. The splitting found agrees with the assumed level scheme yielding g = 2.5 for the first excited level.     

Determination of ionicity in zinc chalcogenides by X-ray absorption study

K-absorption edges and associated extended fine structure is recorded for zinc and zinc chalcogenides using a 40 cm, automatic scanning, Cauchois type X-ray spectrometer. It is observed that there is a correlation between the positive X-ray K-absorption edge chemical shift and Phillips' electronegativity difference C for zinc chalcogenides. The bond lengths for these compounds are determined using Lytle, Chivate et al. and Levy's methods. These bond lengths are observed to tally well with X-ray crystallographic data. The covalent energy gaps in Phillips' theory are determined using bond lengths determined by Chivate et al.'s method. Values of ionicities are obtained from X-ray spectroscopically determined values of C and E_h and are compared with Phillips' spectroscopically determined ionicities for zinc chalcogenides. It is shown that X-ray spectroscopically determined values of ionicities for these compounds show a more correct chemical trend.     

Particles of nonzero rest mass and spin algebras

We construct a family of parametrized spin-Z_α algebras from the (canonical) spin-S and (helicity)spin-Z ones in the case of irreducible unitary representations [m, s] of the Poincaré group. The parameter α refers to a rotation angle around the third axis. Equivalences of such constructions are given through a family of unitary transformations containing, for definite values of α, well established and very useful transformations. General formulas referring to the so-called Shirokov-Foldy form of the Poincaré generators and to typical Shirokov's operators are given explicitly.     

Meson exchange and the theory of finite fermi systems

The spin-dependent parameters g₀ and g'₀ in Migdal's theory of finite Fermi systems are studied. Assuming their values to be such as to reproduce the M1 states in ²⁰⁸Pb at 7 and 8 MeV, the origin of these (large) values in meson-exchange contributions to the nucleon-nucleon force is studied. Pion exchange contributes little, because of cancellation between matrix elements from the spin-spin and tensor components. The largest, nearly equal, contributions to g₀ and g'₀ come from p-meson exchange. In order to explain the large values needed for g₀ and g'₀, the tensor coupling of the ρ-meson must be substantially larger than the effective ones found in current phenomenological potentials, such as the Reid soft-core and Hamada-Johnston ones. The large value of the coupling needed follows from work analyzing nucleon form factors.     

The decays ψ';'→J/ψ+π0(η) and quark masses

We discuss the decays ψ';'→J/ψ+π⁰ and ψ';'→J/ψ+η. We obtain a reliable, model-independent theoretical prediction for the ratio of the decay rates based only on the QCD lagrangian and certain low-energy theorems. The theoretical formula, apart from kinematical factors, contains only the ratio of the current quark masses, m_d/m_u. Under a standard choice of m_d/m_u theory and experiment are in good agreement with each other.     

Thermodynamics of superconducting Nb3Sn

Shen's experimental data on α²(ω)F(ω) and μ¹ in superconducting Nb₃Sn is used to calculate its thermodynamic properties. It is found to exhibit the same size strong coupling corrections to BSC as does Pb. Comparison with experimental data shows satisfactory agreement.