Enhanced backscattering in a magnetic field

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ξ(x₁), where the surface profile function ξ(x₁) is a stationary stochastic Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k₊(ω) for a surface polariton of frequency ω propagating in the +x₁-direction is unequal to the (magnitude of the) wavenumber k_-(ω) for a surface polariton of the same frequency propagating in the -x₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x₁-direction but not in the -x₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

Field induced flux pinning in Nd1+xBa2−xCu3O7−δ single crystal

The flux pinning behavior of a Nd_1+xBa_2−xCu₃O_7−δ (Nd123) single crystal, which exhibited a peak effect, has been studied by monitoring the time decay of the magnetic moment. The apparent pinning energy (U₀^*) was deduced from flux creep data on the basis of the Anderson-Kim model. The magnetic field dependence of U₀^* showed maxima at peak fields which depended on the temperatures, in a similar manner to those of critical current densities. In addition, the temperature dependence of U₀^* showed several features. To explain the increase in U₀^* with the field as well as its temperature and field dependence, we made a numerical calculation by introducing an additional pinning energy which increased with increasing field. The results are in good agreement with the experimental data, especially at temperatures above 60 K, where the contribution of field induced pinning centers is believed to be dominant.     

On the “quantum rainbow” in surface scattering

In this letter we propose a new method to compute the scattering amplitudes of atoms from a corrugated wall model of a crystal surface. The method method requires reasonable computing time and converges rapidly to the solution of the scattering amplitudes (within 0.01% in each beam and satisfying unitarity) for any corrugation such that kζ₀ < 4.5 and ζ₀ < 0.35 Å, where k is the magnitude of the incident wave vector and ζ₀ the amplitude of the corrugation. These conditions for kζ₀ and ζ₀ are satisfied for any crystal surface and light scattering atoms (H and He) at thermal energies which makes the method appropriate for the system He, LiF for which results are presented comparing them with recent experimental data.     

Very strong interlayer exchange coupling in epitaxial Fe/Fe1−xSix/Fe trilayers (x=0.4–1.0)

Fe/Fe_1−xSi_x/Fe (x=0.4–1.0) wedge-type epitaxial trilayers with improved homogeneity are grown by co-evaporation from two electron-beam sources. The coupling strengths of the bilinear (J₁) and biquadratic (J₂) coupling terms are derived from Brillouin light scattering (BLS) spectra and longitudinal MOKE hysteresis loops. The total coupling strength J=J₁+J₂ increases dramatically with increasing x and reaches values in excess of 6 mJ/m².     

Preparation and magnetic properties of the Sb-doped Bi---Pb---Sr---Ca---Cu---O superconductors

Two groups of samples were prepared by the wet method with nominal composition Bi_x1Pb_x2Sb_x3Sr₂Ca₃Cu₄O_z. In the first group x₁ + x₂ + x₃ = 2. Here x₁ ranges from 1.2 to 1.6 with x₂ varying from 0.72 to 0.12. The second group is characterized by x₁ + x₂ = 2. Here x₁ was chosen to be 1.4 and 1.6 while x₃ ranges from 0.08 to 0.16. The results show: (i) high Sb content reduces the transition temperature; (ii) for small Sb contents the transition temperature is relatively constant but the transition becomes sharper, (iii) the best sample (with x₁ = 1.4, x₂ = 0.48 and x₃ = 0.12) exhibits a very sharp transition with a peak in the imaginary component of the ac susceptibility at 108.4 K; abd (iv) the transition of lightly Sb-doped material is strongly influenced by small external magnetic fields.     

Quenching of spin fluctuations by high magnetic fields

The quenching of spin fluctuations by magnetic fields has been observed in heat capacity and electrical resistivity measurements at low temperatures for a series of highly exchange enhanced magnetic materials. These include: the weak itinerant electron ferromagnets Sc₃In, Zr_1−xHf_xZn₂ (0 x 0.2) and Ni₃Al; the strong Pauli paramagnets RCo₂ (R = Sc, Y and Lu), TiBe₂ and Pd_1−xNi_x (0 x 0.01); and the heavy fermion systems CeSn₃, CeSi_x (x ≈ 1.85) an d UAl₂. The reported quenching of spin fluctuations in scandium and palladium by magnetic fields is reviewed, and it appears that the initial observations and conclusions are incorrect, and that fields greater than 10 and 40 T, respectively, will be necessary to quench spin fluctuations in these metals. The behaviors of these spin fluctuators have been grouped into six classes.     

Normal state magnetism of the high Tc cuprate superconductors

Magnetic measurements of various types have played an essential role in establishing the novel normal state characteristics of high transition temperature (T_c) superconductors with T_c > 23 K. Among these materials, the highest T_c's ( 125 K) are exhibited by the layered cuprates. In this paper, the normal state magnetic susceptibilities of the cuprates are reviewed and interpreted in the context of magnetic neutron scattering and other magnetic measurements, using the La_2−xM_xCuO₄-type and YBa₂Cu₃O_6+x-type materials as prototypical examples. The evolution of the magnetism upon doping the insulating antiferromagnetic “parent” compounds with x = 0 to form the high temperature superconductors is described. A recurrent property which differentiates these materials from conventional superconductors is the existence of strong antiferromagnetic correlations in the metallic state on the same sublattice of the structure in which the itinerant carriers reside.     

Magnetic properties and percolation threshold in diluted B-spinel ZnCr2xAl2−2xS4: a study through high-temperature expansions

By making use of high-temperature series expansions (HTSE) of the correlation functions, we study the thermal and disorder variation of the short-range order (SRO) in the particular B-spinel ZnCr_2xAl_2−2xS₄. We developed the HTSE for the q-dependent static structure factor S(q) to the order 6 in reciprocal temperature including both the nearest- and next-nearest-neighbour interactions J₁ and J₂, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector q₀=[0 0 0.79] and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J₁ and J₂ in the case of the pure compound.

The bond percolation threshold x_p of the ZnCr_2xAl_2−2xS₄ is determined by studying the disorder variation of the correlation length ξ. The x_p is considered as the concentration at which ξ vanishes. The obtained values are x_p=0.27 when only J₁ is considered and 0.23 when both J₁ and J₂ are taken into account.     

Magnetic properties and composition range of non-stoichiometric m-type hexagonal ferrites prepared by ion exchange

Single crystals of Ba, Sr M-type hexagonal ferrites were prepared by ion exchange in Ba, Sr containing molten salts from single crystals of β″ -ferrites. A fast diffusion of the divalent Ba²⁺, Sr²⁺ is observed leading to a non-stoichiometric M-type ferrite with chemical formula: Ba_1+xFe_10.5Co_0.25O_17+x (0 ≤ x ≤ 0.25). x depending on the exchange reaction time. Saturation magnetization ranges from 19 to 64 emu/g depending on exchange conditions. The Curie temperature is (470 ± 5)°C. An easy axis direction (M_s c) has been determined in all cases. The observed anisotropy is considerably lower than that of M ferrite. The calculated anisotropy constants are, in 10⁶ erg/cm³, K₁ = 0.8 and K₂ = 1.0 at room temperature.     

Surface roughness dependence of the first-order probability density function for integrated speckle

The surface roughness dependence of the first-order probability density function (PDF) of an integrated speckle pattern, produced in the condition of circular detection aperture and gaussian scattering spot, was theoretically investigated. The mutual intensity J_A(x₁, y₁; x₂, y₂) containing two roughness parameters, dispersion of surface height ø² lateral correlation length x_c, was calculated. The exact first-order probability density function was analytically derived and numerically calculated by means of the Karhunen-Loeve expansion and fast Fourier transform (FFT). As a diffuse object became smooth, the first order probability density function was changed from negative exponential to sharp peak gaussian centered around mean intensity.     

Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces

A review is made of theoretical and experimental work on retroreflection enhancements in the diffuse component of light elastically reflected from randomly rough surfaces. These effects are seen as a narrow peak in the angular distribution of the intensity of diffusely reflected light which is centered about the direction for reflected light motion antiparallel to the original incident beam. This peak is observed in the scattering of light from many different types of rough surfaces and has been studied in fields as diverse as solid state physics, astronomy, geophysics, meterology and radar. Work covering all of these fields will be presented in this review.

Retroreflection enhancements arise both from shadow casting properties of surface irregularities and from the phase coherence of retroreflected light. These mechanisms can act to create retroreflection enhancements from rough surfaces of dielectric and/or metallic compositions and of surface disorders characterizable on length scales which are large, comparable to or small compared to the wavelength of the scattered light.

Specific discussions will be presented of three types of enhanced retroreflectance: (1) A treatment of the optical glory and Heiligenschein phenomena which are concerned with the meterological and geophysical study of light reflected from clouds and terraine will be given. (2) The theory of the opposition effect, encountered in astronomy as an enhanced retroreflection in the light scattered from atmosphereless planets and space debris, will be used to provide a theoretical basis to understand shadowing effects. (3) A recently discovered phenomenon of enhanced retroreflection from weakly rough metallic mirrors, associated with the Anderson localization of surface waves, is also presented. This last phenomenon and its relationship to the study of the Anderson localization of surface waves will be emphasized throughout our discussions.

Similar enhancement effects in the scattering of acoustic waves from rough surfaces and a brief outline of some recent work on optical backscattering enhancements due to the Anderson localization of bulk polariton modes, is also presented.     

Effect of Pr and Ca substitution on superconductivity in Y(1−x−yPrxCay)Ba2Cu3O7−δ

Pr substituted at constant Ca concentration for Y in (Y_1−x−yPr_xCa_y)Ba₂Cu₃O_7−δ superconductors have been prepared under identical conditions and the temperature dependence of the electrical resistivity of these samples are measured. The resistively determined values of T_c decrease linearly with increasing x (0 ≤ x ≤ 0.2) for constant y = 0.10 and 0.15 which provides convincing evidence that the suppression of superconductivity by Pr is mainly due to magnetic pair breaking. The suppression of superconductivity can also be correlated to the observed changes in oxygen content determined by iodometric analysis and to the average Cu-valences. However, it is found that the observed suppression of T_c cannot be compensated by appropriate hole doping with Ca.     

Enhanced backscattering in a magnetic field

Abstract

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x ₃=ξ(x ₁), where the surface profile function ξ(x ₁) is a stationary stochastic Gaussian process. The plane of incidence is the x ₁ x ₃ plane, and the magnetic field is directed along the x ₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k ₊(ω) for a surface polariton of frequency ω propagating in the +x ₁-direction is unequal to the (magnitude of the) wavenumber k _?(ω) for a surface polariton of the same frequency propagating in the ?x ₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x ₁-direction but not in the ?x ₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

Current-induced step bunching at vicinal surfaces during crystal sublimation

The limits of the applicability of the generalized BCF model of electromigration-affected sublimation are discussed in detail. Only in surface-diffusion limited sublimation are the steps boundaries, effectively separating the transport processes at neighbouring terraces. In the opposite case of high surface mobility and slow exchange between the 2D gas of mobile adatoms and the crystal, many atoms simply cross the steps, spending some time in an intermediate state of adsorption at the step edge, but never becoming “crystal atoms”. In this regime of sublimation the steps are no longer boundaries. Therefore, one cannot analyze diffusion and desorption on one separate terrace (as in the generalized BCF model) since the coupling between the adatom concentration fields on neighbouring terraces cannot be neglected. A relevant model for this regime of electromigration-affected sublimation is proposed in this paper. This model manifests step buching at the step-up direction of the adatom electromigration. The central result of the mathematical treatment is the formula (x₂−x₁)^{n + 2}=(4kT/F) l^{n + 1}₀, relating the interstep distance x₂−x₁ in a stable pair of steps with the electromigration inducing force F. Here n and l₀ determine the form and the magnitude of the step-step interaction. The formula obtained for x₂−x₁ provides a gound to evaluate n and l₀ from a set of experimental data on sublimation by combined DC and radiative heating.     

Magnetic anisotropy in the paramagnetic phase of TbAl2

The magnetic anisotropy of a single crystal of TbAl₂ has been measured by torque magnetometry from below the Curie point up to 170 K, well into the paramagnetic phase. Within a (110) plane the torque can be described by the expression L(θ) = {P sin 2θ} H² + {Q sin 2θ + S sin 4θ} H⁴ + {T sin 4θ} H⁶, where θ is the an gle formed by the magnetization vector with a [001] axis. The first term (in H²) is interpreted as produced by arrays of defects with axial symmetry. The second (in H⁴) and third (in H⁶) terms arise from anisotropic fourth and sixth rank tensor paramagnetic susceptibilities. On the other hand if the anisotropy is described in terms of effective conventional anisotropy constants K₁ and K₂ within the temperature range 90–170 K it is found that both constants change continuously across the Curie temperature and furthermore the [111] direction remains the easy direction in the paramagnetic range. Anisotropy measurements reveal themselves as a sensitive indicator of the level of macroscopic defects in magnetic crystals.     

Ferromagnetic Zr1−xMnxCo2 laves phase compounds

Structure and magnetic properties of the Zr_1−xMn_xCo_2+δ alloys were studied for 0 x <0.7, δ=0, 0.45. The cubic C15 Laves phase structure shows Mn solubility up to x≈0.4. The other Laves phase with the hexagonal C36 structure found for x0.5 apparently has a small region of Mn solubility in the vicinity of Zr_0.4Mn_0.6Co₂. Though the parent Mn-free compounds are known to be paramagnetic, the Mn-substituted alloys show ferromagnetic behavior with the Curie temperatures up to 625 K and the room-temperature saturation magnetization of about 100 emu/g. The onset of ferromagnetism with the Mn substitution for Zr may be caused by polarization of itinerant 3d electrons, like it was earlier supposed for the off-stoichiometric ZrCo_2+δ. The universal composition dependencies of the intrinsic magnetic properties for different δ can be obtained, if plotted against the amount of zirconium atoms missing in its sublattice. The room-temperature anisotropy with the noticeable anisotropy field of 24 kOe and the 1 1 0 easy magnetization direction laying in a basal plane was found in the hexagonal Zr_0.5Mn_0.5Co₂.     

A new type oscillatory phenomenon in the magnetotransport of θ-(BEDT-TTF)2I3

A new type oscillatory magnetotransport phenomenon has been observed in θ-type crystals of (BEDT-TTF)₂I₃ at temperatures below 6 K and in the magnetic field above 3 T. The oscillation appears when the magnetic field of a fixed strength is rotated from the direction normal to the conductive two dimensional plane to a direction parallel to the plane. The period of the oscillation is described by an equation tan (θ_min)=sN (s=0.39, N=0, 1, 2, 3,…), where θ_min is the angle giving the position of the trough of the oscillation. The amplitude of the oscillation is primarily determined by the magnetic field component normal to the conductive plane. It is related to the temperature through the change in the resistivity ₀.     

Disruption of antiferromagnetic order in Zn-doped La2CuO4

The magnetic phase diagram of La₂(Cu_1−xZn_x)O₄ has been determined from zero-field muon-spin-rotation (ZF-μSR) data taken at LAMPF for 0 ≤ x ≤ 0.10. Antiferromagnetic onset temperatures follow T_N(x) from susceptibility measurements on the same samples. However, the order becomes long range, as evidenced by a well-defined internal magnetic field, only at temperatures well below T_N. Extrapolation of our results yields T_N → 0 K at x = 0.11 for a single (Cu_1−xZn_x)O₂ plane, and comparison with YBa₂(Cu_1−xZn_x)₃O₆ implies identical disruption of magnetism by Zn doping in the single- and double-plane systems.     

A piecewise linear model for the zones of instability of an area-preserving map

In this note we study the global behavior of the piecewise linear area-preserving transformation x₁ = 1 − y₀ + |x₀|, y₁ = x₀, of the plane. We show that there are infinitely many invariant polygons surrounding an elliptic fixed point. The regions between these invariant polygons serve as models for the “zones of instability” in the corresponding smooth case. For our model we show that some of these annular zones contain only finitely many elliptic islands. The map is hyperbolic on the complement of these islands and hence exhibits stochastic behavior in this region. Unstable periodic points are dense in this region.