Angular Dependent Terms Research Articles

Unconventional angular dependence of spin-orbit torque-induced harmonic Hall resistance in Pt/YIG bilayers

Spin-orbit torque (SOT), arising from spin-orbit coupling-induced spin currents, provides efficient control of magnetization. SOT characterization involving harmonic Hall resistances is typically done in low-current regimes, distinct from high-current regimes, where SOT-induced magnetization switching occurs. In this study, we investigate azimuthal angle (ϕ)-dependent harmonic Hall resistances of a Pt/yttrium iron garnet (YIG) layer across a wide range of measurement currents. Under low-current conditions, conventional ϕ-dependent Hall resistances are observed; the first harmonic Hall resistance exhibits sin 2ϕ behavior and the second harmonic Hall resistance comprises cos ϕ and cos 3ϕ terms. Interestingly, with increasing current, higher-order angular-dependent terms become non-negligible, referring to the sin 4ϕ and sin 6ϕ terms for the first harmonic and the cos 5ϕ and cos 7ϕ terms for the second harmonic Hall resistances. We attribute this unconventional angular dependence to the nonlinear response of magnetization direction to SOT, emphasizing its relevance to understanding the magnetization dynamics during SOT-induced switching under large currents.

Four-parameter model of thin surface layer contribution to reflectance-absorbance spectroscopy and ellipsometry.

The contribution of the surface layer to the reflection coefficients is shown to be determined by four surface integral values, which can be interpreted as real and imaginary parts of two complex permittivity excesses. The reflectance-absorbance spectra are determined by the spectra of these parameters. The spectra of the surface excess integrals cannot be found with the angular measurements of reflection-absorption spectra, which are determined by only three angular dependent terms. To determine these four surface excess integrals, it is necessary to involve the experimental data of spectroscopic ellipsometry or polarization-modulation infrared reflection absorption spectroscopy providing equivalent information about surface. In the case of weakly absorbing bulk medium, the real parts of the excesses can be neglected, permitting calculation of their imaginary parts using the angular dependence of the absorbance. The calculation of these parameters allows to check consistency of the data obtained. Measurements of the angular dependence of the absorbance of p-polarized radiation reflected from the DPPC monolayer upon distilled water were performed. The data obtained turned to be in good agreement with the proposed theoretical analysis.

Analytical expression for the angular correlation function of two Lyman- α photons in the photodissociation of hydrogen molecules

An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.

Coarse-Grained Simulation of CaCO3 Aggregation and Crystallization Made Possible by Nonbonded Three-Body Interactions

Calcium-containing minerals are key model systems for investigating fundamental principles of nucleation and mineral formation both experimentally and by simulation. Due to the rare event character of nucleation, the different dimensions of pre- and postnucleation stages and the possible relevance of nonclassical nucleation pathways, such investigations require advanced sampling techniques and simulation models on a range of resolution levels. To this end, we have developed coarse-grained (CG) models for calcium carbonate. We present a strategy to devise CG parameters, including nonbonded angular-dependent terms such that the model correctly represents the calcite phase along with properties of the constituents in solution. We show how the CG interactions affect the crystallization pathways by stabilizing different intermediates, spanning a wide range of degrees of crystallinity and water content. This will allow us to investigate contributions to crystallization transitions and link them to experimentall...

NiFe local ordering in segregated Ni3Fe alloys: A simulation study using angular dependent potential

In this work, we analyze the compositional disordering in the Ni3Fe alloy (with surface layers exposed to vacuum) at elevated temperatures in simulations using a Modified Embedded Atom potential with the Angular Dependent terms (ADP). We find that the Fe enrichment primarily occurs in the sub-surface layers of the alloy samples with (1 0 0), (1 1 0), and (1 1 1) orientated surfaces exposed to vacuum at elevated temperatures. Nickel enrichment occurs primarily in the surface layers with the (1 0 0) and (1 1 0) orientations. In the case of (1 1 1) orientated surfaces exposed to vacuum, the surface layer composition (25% Fe, 75% Ni) is not significantly altered even at a relatively high temperature of 1100 K. Our findings are qualitatively in agreement with the experimental and density functional theory (DFT) studies in the literature on the segregation in Ni3Fe alloys. We find that, irrespective of the orientation of the surface layers, Fe segregation (in the bulk of the alloy) predominantly occurs so as to achieve a local ordering similar to that in the NiFe alloy. In particular, the Fe atoms form planar 5-Fe atom clusters in the (1 0 0) planes, which are sandwiched between pure Ni layers with the (1 0 0) orientations. Thus, the central Fe atom of the 5-Fe atom cluster in the (1 0 0) plane has a local environment (in terms of nearest neighbor atoms) similar to that of a Fe atom in the NiFe alloy. We also find that a significant proportion of disordered Ni atoms in the bulk are associated with the Fe segregation in the form of 5-Fe atom clusters (i.e., NiFe local ordering). Furthermore, in the disordered Ni3Fe alloy, the Ni atoms with pure Ni nearest neighbor environment (i.e., with no nearest neighbor Fe atoms) exist primarily in the bulk, while in the surface layers the percentage of such Ni atoms is relatively insignificant.

Improved Tight-Binding Charge Transfer Model and Calculations of Energetics of a Step on the Rutile TiO2(110) Surface

A second-moment, tight-binding charge equilibration (SMTB-Q) model for the atomic interactions in TiO2 is refined by comparison with results of density functional theory (DFT) calculations within the generalized gradient approximation and used to study the atomic structure of the ⟨11̅1⟩ step on the rutile (110) surface. The model is parametrized to reproduce the structure and energetics of a rutile crystal and its low index surfaces but also reproduces well anatase crystal and its surfaces. The application to a stepped surface represents an extrapolation to lower coordinated atoms, and two extensions of the model were made. First, a continuous dependence of the effective radius of the O atoms on atom coordination was introduced, and second, a covalent O–O interaction was added. The revised SMTB-Q model is then found to reproduce well the relative energy of local minima on the DFT energy surface. In particular, we demonstrate that the refined model is useful in global optimization studies by using it to search for reconstructions of the ⟨11̅1⟩ step on the rutile (110) surface. The low energy configurations generated with the model were used as input in subsequent DFT calculations. A low energy reconstruction involving a large corrugation along the step edge is found in this manner. When additional TiO2 units are introduced, a reconstruction previously found by Martinez et al. (U. Martinez et al. Phys. Rev. B 2011, 84, 205434) is also successfully reproduced. However, in the present model the atomic forces are not reproduced accurately as compared to DFT, which shows that additional terms such as angular-dependent terms may be needed to improve the accuracy.

Asymmetric Velocity Distributions from Halo Density Profiles in the Eddington Approach

We show how to obtain the energy distributionf(E)in our vicinity starting from WIMP density profiles in a self-consistent way by employing the Eddington approach and adding reasonable angular momentum dependent terms in the expression of the energy. We then show how we can obtain the velocity dispersions and the asymmetry parameterβin terms of the parameters describing the angular momentum dependence. From this expression, forf(E), we proceed to construct an axially symmetric WIMP a velocity distribution, which, for a gravitationally bound system, automatically has a velocity upper bound and is characterized by the same asymmetriyβ. This approach is tested and clarified by constructing analytic expressions in a simple model, with adequate structure. We then show how such velocity distributions can be used in determining the event rates, including modulation, in both the standard and the directional WIMP searches.

On Convertibility From Antenna to Sensor Brightness Temperature for ATMS

The Advanced Technology Microwave Sounder (ATMS) onboard the Suomi National Polar-orbiting Partnership (NPP) satellite is a total power radiometer and scans across the track within a range of ±52.77° from nadir. It has 22 channels and measures the microwave radiation at either quasi-vertical or quasi-horizontal polarization from the Earth's atmosphere. Without simultaneous measurements at both polarizations at the same frequency, the conversion from ATMS antenna temperature to sensor brightness temperature becomes nonunique if the antenna subsystem has a significant spillover from cross-polarization. In addition, the antenna temperature could be contributed from both the near- and far-field radiation through the sidelobes of the ATMS antenna subsystem. An analysis of the ATMS antenna gain measurements reveals that the efficiencies of both ATMS antenna sidelobes and cross-polarization are frequency dependent. From the ATMS pitchover maneuver data, it is found that the contributions of spacecraft radiation through the near-field sidelobes are significant and dominates the scan-angle-dependent features in the ATMS antenna temperatures. A theoretical model is developed for the conversion from antenna to sensor brightness temperatures, which incorporates the angular dependent terms derived from the pitchover maneuver data.

Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods

The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy.

Ultrasonic scattering by a fluid cylinder of elliptic cross section, including viscous effects

This paper analyzes acoustic scattering by a viscous compressible fluid cylinder of elliptic cross section submerged in an unbounded viscous nonheat-conducting compressible fluid medium. The classical method of eigenfunction expansion along with the appropriate wave field expansions and the pertinent boundary conditions are used to develop a solution in the form of infinite series involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with the appearance of additional angular-dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A multiprecision code was developed for computing the Mathieu functions of complex argument in terms of complex Fourier coefficients that are themselves calculated by numerically solving appropriate sets of eigen-systems. The numerical results point to the imperative influence of fluid viscosity in notable reduction of pressure amplitudes at intermediate and high frequencies. They also reveal the central role of the cross sectional ellipticity in conjunction with the angle of incidence in altering the pressure directivities. Limiting cases are considered, and fair agreements with well-known solutions are obtained.

ACOUSTIC RADIATION FORCE AND TORQUE ON A SOLID ELLIPTIC CYLINDER

Exact expressions for the acoustic radiation torque and force components experienced by elastic cylinders of elliptic cross-section immersed in ideal fluids and placed in a progressive or standing wave field is developed. The classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop analytical expressions in the form of infinite series involving Mathieu and modified Mathieu functions. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding with distinct wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. Numerical calculations of the radiation force and torque function amplitudes are performed in a wide range of frequencies and cross-sectional eccentricities for a stainless steel cylinder submerged in water. Particular attention is paid to assessment of the effects of cross-sectional ellipticity as well as incident field asymmetry on the acoustic radiation force/torque acting on the elliptical cylinder. Limiting case involving an elastic circular or elliptic cylinder in an ideal fluid is considered and fair agreements with well-known solutions are established.

Ultrasonic Scattering by a Spheroidal Suspension Including Dissipative Effects

This study treats the axisymmetric interaction of a plane compressional sound wave with a viscoelastic (viscous) prolate spheroidal particle (droplet) suspended in a boundless viscous fluid medium. The method of eigen‐function expansion along with the novel features of Havriliak‐Negami model for viscoelastic material behavior and the linearized equations of Navier‐Stokes for wave motion in a viscous non‐heat‐conducting compressible fluid are employed to develop a closed form series solution involving Spheroidal harmonics of complex argument. The complications arising due to the non‐orthogonality of angular Spheroidal functions corresponding to different wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Spheroidal functions in terms of Lengedre functions which are themselves expanded in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of unknown scattering and transmission coefficients. The presented solution demonstrates that the acoustic characteristics of particulate suspensions are strongly influenced by spheroidicity of particle cross‐section. Limiting case involving an elastic (ideal) spheroidal particle (droplet) in an ideal fluid is considered and fair agreement with available solution is established.

Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites

Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.

Ultrasonic Scattering by a Viscoelastic Fiber of Elliptic Cross‐Section Suspended in a Viscous Fluid Medium

This study treats the two‐dimensional interaction of a plane compressional sound wave with a viscoelastic fiber of elliptic cross‐section submerged in a boundless viscous nonheat‐conducting compressible fluid medium. The classical method of eigen‐function expansion along with the novel features of Havriliak‐Negami model for viscoelastic material behavior and the pertinent boundary conditions are used to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex argument. The complications that arise because of the nonorthogonality of angular Mathieu functions corresponding to different wave numbers, as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions, are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. The presented solution demonstrates that acoustic characteristics of fiber suspensions are strongly influenced by cross‐sectional ellipticity of the fibers in addition to the dynamic viscoelastic properties of the fiber material. It also shows that the common rigid circular fiber approximations used to model fiber suspensions can not capture the important resonance and damping effects associated with the highly viscoelastic noncircular fibers. The proposed model is valid for a wide range of cross‐sectional geometries (aspect ratios) and incident wave frequencies where most numerical methods fail. Limiting case involving an elastic elliptic cylinder in an ideal fluid is considered and fair agreement with a recent solution is established.

Effective operators and spectroscopic properties

In 1968, Wybourne1Brian Wybourne died unexpectedly on 26 November, 2003; this paper was presented during a Special Session devoted to the Judd–Ofelt theory to demonstrate Wybourne’s impact upon the spectroscopy of f-electron systems.1 [J. Chem. Phys. 48 (1968) 2596] asked two major questions while pointing out that a few years earlier, “Judd and Ofelt considered only second-order contributions to the oscillator strength:1.Are the higher-order contributions significant?2.What new angular-dependent terms enter when the higher-order contributions are considered?”In the present paper, the answers to these questions are discussed in the form of a report woven onto the background of Wybourne’s publication. The very last sentence of his paper might be taken as an obligation and also as a source of inspiration for all of us who have been trying to describe the properties of rare earth ions over the years. Indeed, he remarks: “At this state (1968) there would seem to be little point in extending calculations to higher orders until actual numerical estimates of the relative importance of the second- and third-order contributions are established.” In this context, the present analysis is performed up to the third-order terms, and the new effective operators are discussed. In addition, to fulfill the demand for “actual numerical estimates”, the results of ab initio calculations are presented to illustrate the hierarchy of important physical mechanisms that contribute to the f↔f transition amplitude.

High energy behavior ofγγ→ff¯processes in the standard model and minimal supersymmetric standard model

We compute the leading logarithms electroweak contributions to gamma gamma to f f(bar) processes in SM and MSSM. Several interesting properties are pointed out, such as the importance of the angular dependent terms, of the Yukawa terms, and especially of the $\tan^2\beta$ dependence in the SUSY contributions. These properties are complementary to those found in e+e- to f f(bar). These radiative correction effects should be largely observable at future high energy gamma gamma colliders. Polarized beams would bring interesting checks of the structure of the one loop corrections. We finally discuss the need for two-loop calculations and resummation.

Temperature and angular dependence of the anisotropic magnetoresistance in epitaxial Fe films

We perform detailed temperature dependent measurements of the magnetoresistance (MR) and its angular dependence of epitaxial Fe (110) films. The angular dependence of the MR at $H=10$ kOe is found to change strongly when going from $T=4.2$ K to $T=230$ K. We analyze the data on the basis of D\"oring's equation. Second- and fourth-order angular dependent terms are found to be of equal importance, indicating strong deviations of the MR from a simple ${\mathrm{cos}}^{2}\ensuremath{\varphi}$ dependence. One of the MR components is the ordinary or Lorentz magnetoresistance, which is strong at low temperatures and becomes smaller at higher temperatures, due to the reduction of the mean free path. By subtracting the ordinary magnetoresistance from the MR data we obtain the anisotropic magnetoresistance. We decompose the temperature dependent anisotropic magnetoresistance in the temperature dependent k constants of D\"oring's equation. These constants show a reduction between $T=20$ K and $T=100$ K, which reflects the observed decrease of the anisotropic magnetoresistance. We present arguments that the temperature dependence of the anisotropic magnetoresistance is most likely due to the change from defect-dominated scattering to phonon-dominated scattering, each of which has its own anisotropic magnetoresistance.

Effects of Angular Dependent Terms in the Interatomic Potential on Defect Properties in TiAl

AbstractInteratomic potentials of the Embedded Atom and Embedded Defect types were used to study the effect of the angular dependent term in the Embedded Defect potential on the properties of defects in TiAl. The defect properties were computed with interatomic potentials developed with and without angular dependent terms. It was found that the inclusion of the angular dependent terms tends to increase the energies of the APB’s and lower the energies of stacking faults. The effects of the angular term on the relaxation around vacancies and antisites in TiAl was also studied, as well as the core structure of several dislocations in this compound.

Calculation of the total collision cross section of H 2-Ar for a particular rotational j, m j-state of the H 2-molecule

The effect of angular dependent terms in the intermolecular potential of the system H 2-Ar is investigated in a close coupling and a distorted wave calculation. The contributions from attractive and repulsive terms are compared. The use of WKB-wave functions in the distorted wave approximation is discussed.

Influence of the dipole-quadrupole dispersion forces on the total collision cross section between atoms and polarized diatomic molecules

The effect of the angular dependent dipole-quadrupole dispersion forces is investigated for heavy collision partners. The parameters, giving the strength of the angular dependent potential terms, are estimated by use of the Drude model. The Landau and Lifshitz approximation leads then to explicit expressions for the state-dependent part of the total collision cross section, in first order of these asymmetry parameters.