Generalization of a scattering theorem for plane-stratified gyrotropic media

A previously derived eigenmode scattering theorem for plane-stratified gyrotropic media established that the scattering matricesS andS′, defined, respectively, in terms of a given and a conjugate set of eigenmode amplitudes, are mutually transposed, i.e. , the theorem being valid specifically for the incoming and outgoing eigenmodes ofgyrotropic bounding media. In this paper the theorem is extended to include linearly and circularly polarized base-modes in theisotropic media which may bound the multilayered, gyrotropic structure. Transformation of the eigenmode scattering matrix leads to a generalization of the scattering theorem to include base modes which are not necessarily eigenmodes of the medium. In the important special case in which the ambient magnetic field is parallel to the plane of the stratification, the scattering matrix is shown to have a special symmetry whose form depends on the base modes chosen (eigenmodes, linear modes or circular modes).     

New intensity magneto-optical effect in materials exhibiting giant magnetoresistance

The change in the reflectivity of a metallic magnetic multilayer that exhibits giant magnetoresistance for a monochromatic electromagnetic plane wave with polarization along the magnetization (s polarization) in response to a change from the antiferromagnetic magnetic configuration of the multilayer to the ferromagnetic configuration is investigated. This magneto-optical effect is treated in the effective-medium approximation, in which the dielectric constant needed is found analytically with consideration of the interface roughness scattering of electrons. It is shown in the example of an Fe/Cu multilayer that the effect amounts to ∼0.7%. The representation found for the complex conductivity is convenient in a special case for investigating the magnetoresistive effect. Zh. éksp. Teor. Fiz. 114, 1101–1114 (September 1998)     

Reciprocity and equivalence in reciprocal and non-reciprocal media through reflection transformations of the current distributions

The electromagnetic wave fields generated by arbitrary electric and equivalent magnetic current distributions are expressed by means of a Maxwell operator in anisotropic, gyrotropic or bianisotropic media. Provided that the constitutive tensorK(r), (which relates the wave-field vectorsD andB toE andH), has in each case the appropriate symmetry in its spatial variation, Lorentz-type reciprocity relations are obtained connecting the given current distributions and their wave fields with a transformed (reflected) set of current distributions and their fields. Reflections are with respect to a plane, a line or a point, depending on the symmetry structure of the constitutive tensor. Modified Lorentz reciprocity appears as a special case of the reflection transformations. A related set of reflection transformations yields equivalence (rather than reciprocity) relationships, in which mirrored current distributions generate mirrored wave fields. Various applications are discussed.     

Plane and cylindrical shock waves in magnetogasdynamics

Summary The Chisnell-Chester-Whitham method has been used to study the propagation of diverging plane and cylindrical shock waves through an ideal gas in the presence of a magnetic field having only constant axial and azimuthal components, simultaneously for both weak and strong cases. By assuming an initial density distribution ϱ₀ = ϱ′r ^−W , where ϱ′ is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density and the particle velocity immediately behind the shock have been derived for both the cases.

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Riassunto Il metodo di Chisnell-Chester-Whitham è stato usato per studiare la propagazione di onde d’urto divergenti cilindriche e piane attraverso un gas ideale in presenza di un campo magnetico che ha solo componenti costanti assiali e azimutali, contemporaneamente per casi deboli e forti. Assumendo una distribuzione di densità iniziale ϱ₀ = ϱ′r ^−W , dove ϱ′ è la densità al piano/asse di simmetria ew è una costante, si sono ottenute le espressioni analitiche per la velocità d’urto e la forza d’urto. Le espressioni per la pressione, la densità e la velocità delle particelle immediatamente dopo l’urto sono state determinate per entrambi i casi.

     

New phase transition in an easy-axis “triangular” antiferromagnet

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear anti-ferromagnet CsMnI₃ is investigated at T=1.3 K in magnetic fields up to ∼80 kOe and angles between the field and C ₆ axis ϕ≈ 0.5° and ϕ=7°. A new reorientational magnetic phase transition is observed in a field H _c1≈39.0 kOe. The magnetic structure for H>H _c1 is determined. The average Mn²⁺ spins of the magnetic sublattices in the new phase are determined from an analysis of the NMR spectrum to be 〈 S _C 〉=1.63 and 〈S _D 〉=1.72. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 988–993 (25 June 1998)     

Superconducting current in hybrid structures with an antiferromagnetic interlayer

It is shown experimentally that the superconducting current density in Nb/Au/Ca_{1 − x} Sr _x CuO₂/YBa₂Cu₃O_{7 − δ} hybrid superconducting heterostructures with a Ca_{1 − x} Sr _x CuO₂ anti-ferromagnetic (AF) cuprate interlayer is anomalously high for interlayer thicknesses d _M = 10–50 nm and the characteristic damping length for superconducting correlations is on the order of 10 nm. The experimental results are explained on the basis of theoretical analysis of a junction of two superconductors (S′ and S) connected by a magnetic multilayer with the AF ordering of magnetization in the layers. It is shown that with such a magnetization ordering, anomalous proximity effect determined by the singlet component of the condensate wavefunction may take place. As a result, the critical currents in S′/I/AF/S and S′/I/N/S structures (I denotes an insulator, and N, the normal metal) may coincide in order of magnitude even when the thickness of the AF interlayer considerably exceeds the decay length of the condensate wavefunction in ferromagnetic layers.     

Magnetization of optically polarized gas atoms by an optical pulse train

The properties of the density matrix and the multipole moments arising in oriented and aligned atoms with zero nuclear spin through the interaction with strong resonant ultrashort pulses with wave vector k ₀ and circular or linear polarization have been found. Calculations have been made for the time-dependent light-induced magnetization μ(t′) of a gas of pre-oriented and prealigned atoms following the passage of a weak resonant elliptically polarized pulse with frequency ω and wave vector k collinear with k ₀. It is shown that for oriented atoms, μ(t′) is an even function of the detuning from resonance, ω-ω _ba, and can be split into two terms whose directions are a consequence of symmetry and are determined by the vectors k ₀ and k as well as by the direction of rotation of the electric fields corresponding to the pulses. For aligned atoms the vector μ(t′) is collinear with k, and the first term is an even function of ω-ω _ba. However, the second term is an odd function of ω-ω _ba and reverses direction when the sign of ω-ω _ba changes, as well as when the orientation of the axes of the polarization ellipse is changed. It is shown that if a series of weak linearly polarized pulses pass through the gas, the light-induced magnetization of the oriented and aligned gas atoms can be decomposed into three factors: the first determines the direction and is a consequence of the symmetry; the second (with the dimensions of magnetic moment) depends on the characteristics of the resonant transitions; and the third is a universal function of t′ and ω-ω _ba that does not depend on the underlying characteristics of the resonant transition. These vector factors and the universal functions are in principle different for oriented and aligned atoms. Zh. éksp. Teor. Fiz. 111, 63–92 (January 1997)     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.     

Angular dependence of the giant magnetoresistance for a current perpendicular to the plane of the layers in a magnetic sandwich

A quantum-statistical model using the Kubo formalism is proposed for describing the magnetoresistance of a multilayer structure with the current perpendicular to the plane of the layers. In particular, this model describes the case of noncollinear magnetization of consecutive ferromagnetic layers of the structure. Interference between electron wave functions with different directions of the spin projections onto the magnetization axis, which arises in the noncollinear configuration, is investigated along with the role of electron scattering, not only within the bulk of the layers, but also at their interfaces. Fiz. Tverd. Tela (St. Petersburg) 41, 1814–1818 (October 1999)     

Soliton-magnon scattering in a two-dimensional isotropic magnetic material

We use the generalized σ-model to analytically study the solution of the problem of magnon scattering in two-dimensional isotropic ferromagnets and antiferromagnets in the presence of a Belavin-Polyakov soliton. We obtain the exact analytical solution to this problem for the partial mode with the azimuthal quantum number m=1. The scattering amplitude for other values of m (i.e., values not equal to unity) are studied analytically in the long-and short-wavelength approximations and also numerically for an arbitrary value of the wave number. We establish the general laws governing the soliton-magnon interaction. For a magnetic material of finite dimensions we calculate the frequencies of the magnon modes. We also use the data on local modes to derive the equations of motion of the soliton. Finally, we calculate the low-temperature (long-wavelength) asymptotic behavior of the magnon density of states due to the soliton-magnon interaction. Zh. éksp. Teor. Fiz. 116, 1091–1114 (September 1999)     

Shaping dynamics and structure of large-scale surface plasma formations under single-pulse laser action on various materials

It is established that, in the case of laser action on materials in large illuminated spots in atmospheric-pressure air for a laser radiation power density q≤2 MW/cm² (λ=1.315 μm), an evaporative regime with plane scattering of the laser-produced erosion plasma is realized while, for q≈5–17 MW/cm², the plasma front is transferred to the air, leading to plasma screening of the target and shaping of a subsonic radiation wave in the air. As the duration of the laser pulses increases (τ∼160 μsec), in spite of the large illuminated spots (S∼150 cm²) the evaporative regime of the laser action with plane plasma scattering goes over into a regime with jet outlow and formation of a quasistationary shock wave. Deceased. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 2, pp. 261–268, March–April, 1998.     

Photocurrent in gyrotropic Weyl semimetals

Photocurrents in the Weyl semimetals belonging to the gyrotropic symmetry classes have been theoretically studied. It has been shown that the circular photocurrent transverse to the direction of light incidence appears in weakly gyrotropic crystals with the C _nv (n = 3, 4, 6) symmetry only when spin-dependent terms both linear and quadratic or cubic in the quasimomentum, as well as a spin-independent term resulting in the tilt of the cone dispersion, are taken into account in the electron effective Hamiltonian. A polarization-independent magnetic-field-induced photocurrent, which is allowed only in gyrotropic systems, has been predicted. For crystals with the C_2v symmetry, a microscopic mechanism of the photocurrent in a quantized magnetic field, which is generated in direct optical transitions between the ground and first excited magnetic subbands, has been considered. It has been shown that this photocurrent becomes nonzero in the presence of the anisotropic tilt of dispersion cones.     

Magnon-mediated binding between holes in an antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2 ϕ)/r ² where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry.     

Light scattering by axisymmetric multilayer particles

A new recursive algorithm for solving the problem of scattering a plane electromagnetic wave by axisymmetric dielectric multilayer particles is constructed. The approach that was proposed earlier and demonstrated for uniform axisymmetric particles is used. It has the following basic features: (1) the fields are represented in the form of a sum of two terms, one of which is independent of the azimuthal angle, whereas averaging of the second term over this angle gives zero; (2) the axisymmetric problem is solved by using the scalar potentials related to the azimuthal components of electromagnetic fields; and (3) the non-axisymmetric problem is solved by using the superposition of Debye potentials and vertical components of the magnetic and electric Hertz vectors. It is of principal importance for the solution proposed here that the scattering problem is formulated in the form of surface integral equations in these scalar potentials, which are represented in the form of expansions in wave spherical functions. Infinite systems of linear algebraic equations for unknown expansion coefficients are obtained, which are rather simple in structure. The reduced systems for multilayer particles have the same dimension as the systems for identical uniform particles. In the case of multilayer spherical particles, the algorithm gives an explicit solution to the problem, and the dependence on the radial spherical functions for the layers is specified in terms of the derivative of the logarithm (i.e., the ratio of the derivative to the function itself) and the ratio of the functions of neighboring layers. Numerical calculations demonstrated the high efficiency of the algorithm.     

A new type of local polariton at the interface of gyrotropic enantiomorphic crystals

It is shown that a new type of local polariton can propagate at the interface of enantiomorphic twins—gyrotropic crystals with left-handed and right-handed rotation of the polarization plane. The wave function of these local polaritons oscillates strongly, with changes of sign, over lengths of the order of the lattice constant near the interface, and the period of the spatial oscillations grows with increasing distance from the interface. The local polariton term is detached from the band of delocalized states toward higher frequencies. Calculations of the radiation broadening of this term show that, for a local polariton, the effect of a giant increase of the decay (“superradiance”) is possible. The magnitude of the polarization rotation due to a local polariton has been found. Fiz. Tverd. Tela (St. Petersburg) 41, 337–340 (February 1999)     

Dependence of nuclear diffraction on the azimuthal angle: (002)- and (0010)-reflections of YIG

Nuclear diffraction of synchrotron radiation has been investigated using YIG single crystals in different scattering geometries. Time resolved quantum beat spectra of pure nuclear (002) and (0010) Bragg reflections were observed in a set-up where the hyperfine interaction was kept constant, while the azimuthal angle in the (001) surface between the [100] axis and the scattering plane (k _in,k _out) was varied. The time spectra were analyzed by means of the dynamical theory for coherent nuclear scattering. The results revealed the high sensitivity of this experimental technique on the complete set of hyperfine interaction parameters and on the specific geometrical conditions for nuclear diffraction of polarized γ-rays.     

Brewster’s angle polarizer design based on a gyrotropic double-periodic perforated layer

This paper is devoted to the study of the features of artificial gyrotropic magneto-dielectric layer with two-dimensional periodicity. Such a layer can be used in the development of the polarizers operating in the microwave and optical ranges. Analytical solution of a plane wave scattering from a double-periodic gyrotropic layer is obtained by the Method of Integral Functionals in the quasi-static approximation. The numerical results allow to realize the TE- and TM-pass Brewster’s angle polarizers.     

Phase transitions in biperiodic stripe domain structures of uniaxial magnetic films with a positive anisotropy constant

New phase transitions induced by a magnetic field and accompanied by a change in the symmetry or the period of the distribution of the magnetization vector are observed in biperiodic stripe domain structures of iron garnet films with a positive anisotropy constant. A symmetry classification of the observed types of domain structures is derived, and the form of the state diagram of the films is determined in the H∥H⊥ plane, where H∥ and H⊥ are the components of the magnetic field vector perpendicular and parallel to the normal to the surface. Zh. éksp. Teor. Fiz. 114, 2089–2110 (December 1998)     

Power law distributions and dynamic behaviour of stock markets

A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t ^′ = 2Dδ t-t ^′ and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψϕ - ln G(ϕ)} where Ψϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ² - cϕ³ and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ≫ɛ, a distribution function with power law tails, viz: P ϕ = exp{2bϕ-cϕ² /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D≈ | J|. Received 25 July 2000     

On hydrogen localization in the β′ phase of VO0.2

The results of an investigation of the dynamics of hydrogen atoms in the body-centered tetragonal lattice of the interstitial β′ phase of vanadium-oxygen by the method of inelastic scattering of slow neutrons are reported. It is concluded on the basis of an analysis of the structure of the alloy investigated that hydrogen in the lattice is localized in tetrahedral interstices with the point symmetry of an almost ideal tetrahedron. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 326–328 (10 March 1998)