Wave Vector Research Articles

One-dimension Periodic Potentials in Schrödinger Equation Solved by the Finite Difference Method

Abstract The one-dimensional Kronig-Penney potential in the Schrödinger equation, a standard periodic potential in quantum mechanics textbooks known for generating band structures, is solved by using the finite difference method with periodic boundary conditions. This method significantly improves the eigenvalue accuracy compared to existing approaches such as the filter method. The effects of the width and height of the Kronig-Penney potential on the eigenvalues and wave functions are then analyzed. As the potential height increases, the variation of eigenvalues with the wave vector slows down. Additionally, for higher-order band structures, the magnitude of the eigenvalue significantly decreases with increasing potential width. Finally, the Dirac comb potential, a periodic δ potential, is examined using the present framework. This potential corresponds to the Kronig-Penney potential’s width and height approaching zero and infinity, respectively. The numerical results obtained by the finite difference method for the Dirac comb potential are also perfectly consistent with the analytical solution.

Widening the frequency bandgap and reducing thermal conductivity in phononic crystals by tuning structural parameters using a novel computational simulation method

AbstractThis paper introduces and models a phononic structure based on single-crystal silicon, aiming to investigate the width of its frequency bandgap and the impact of key parameters on thermal conductivity. The modeled phononic crystal structure features a periodic arrangement of cylindrical holes in a silicon matrix. This research holds the potential to enhance thermal management performance of thermal metamaterials. Utilizing a 3D finite element method (FEM) model in COMSOL, we have computed phonon dispersion to estimate thermal conductivity. The study systematically has explored the influence of phononic crystal parameters—specifically, porosity, lattice constant, and thickness—along with their interactions on both thermal conductivity and frequency bandgap width.A comprehensive investigation of these parameters has been conducted for their optimization to achieve the maximum frequency bandgap width and minimum thermal conductivity using the response surface method model. Eigenfrequencies and wave vector parameters are extracted from the finite element model using a MATLAB script. Subsequently, thermal conductivity is calculated through the Callaway–Holland model, a simplification of the Boltzmann transport equation (BTE).Our results indicate that the frequency bandgap begins to form at approximately 43% porosity for a lattice constant and thickness of 100 nm each. Furthermore, adjusting the parameters led to a significant reduction in thermal conductivity, decreasing from 43.89 W m−1 K−1 to 0.39 W m−1 K−1. The novelty of our research lies in thermal conductivity control of phononic crystal metamaterials through their parameter variations, or a predictive method of thermal conductivity and its parameter sensitivity. This study advances the state of the art in phononic crystal metamaterial research, contributing to improved thermal management performance by enlarging frequency bandgaps.Overall, our findings deepen the understanding of how porosity, lattice constant, and thickness influence thermal conductivity and frequency bandgap width. They offer valuable insights into optimizing phononic crystal parameters, enhancing thermal management performance, and designing more efficient and effective phononic crystal structures.

Control of spin-wave polarity and velocity using a ferrimagnetic domain wall

We present a theoretical study of the scattering of spin waves by a domain wall (DW) in a ferrimagnetic (FiM) spin chain in which two sublattices carry spins of unequal magnitudes. We find that a narrow but atomically smooth FiM DW exhibits a different behavior in comparison with similarly smooth ferromagnetic and antiferromagnetic DWs due to the inequivalence of the two sublattices. Specifically, for sufficiently weak anisotropy, the smaller spin at the center of the DW is found to become precisely normal to the easy axis, selecting an arbitrary direction in the xy plane and thereby breaking the U(1) spin-rotational symmetry spontaneously. This particular form of a FiM DW does not occur in antiferromagnetic systems and is shown to lead to a strong dependence of spin-wave scattering pattern on the state of polarization of the spin wave, which can be either right-handed or left-handed, suggesting the utilization of such a narrow DW as a spin-wave filter. Moreover, we find that in the case of an atomically sharp DW, where all the spins point either up or down due to strong easy-axis anisotropy and therefore the polarization of the spin wave is conserved upon transmission, the wave vector of the spin-wave changes after passing through the DW leading to a change in the group velocity of the spin wave. This change of the wave vector indicates the acceleration or deceleration of the spin waves and thus a sharp FiM DW could serve as a spin-wave accelerator or decelerator in spintronics devices, offering a functionality absent in a ferromagnetic and an antiferromagnetic counterpart. Our results indicate that FiM spin textures can interact with spin waves distinctly from ferromagnetic and antiferromagnetic counterparts, suggesting that they may offer spin-wave functionalities that are absent in more conventional magnets. Published by the American Physical Society 2024

Fano resonances in gated phosphorene junctions

Fano resonances appear in plenty of physical phenomena due to the interference phenomena of a continuum spectrum and discrete states. In gated bilayer graphene junctions, the chiral matching at oblique incidence between the spectrum of electron states outside the electrostatic barrier and hole bound states inside it gives rise to an asymmetric line shape in the transmission as a function of the energy or Fano resonance. Here, we show that Fano resonances are also possible in gated phosphorene junctions along the zigzag direction. The special pseudospin texture of the charge carriers in the zigzag direction allows at oblique incidence the interference phenomena of the spectrum of electron states outside the electrostatic barrier with hole bound states inside it, giving rise to an asymmetric Fano line shape in the transmission. Due to the energy scale of the electrostatic barriers in phosphorene ultra thin barriers are required to observe the Fano resonance phenomenon. The preservation of the pseudospin texture with the closing of the phosphorene band gap opens the possibility to observe Fano resonances in smaller and wider electrostatic barriers. The asymmetric Fano line shape is susceptible to the transverse wave vector, the strength and width of the electrostatic barrier. Additionally, the conductance shows a characteristic mark in the position where the Fano resonances take place. The similarities and differences with respect to Fano resonances in bilayer graphene are also addressed.

Short-Period Skyrmion Crystals in Itinerant Body-Centered Tetragonal Magnets

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure.

EFFECT OF EXTERNAL HARMONIC VIBRATION ON THE FORMATION OF SOLITARY WAVES IN FALLING TWO-LAYER LIQUID FILMS

Abstract We study the influence of a low-frequency harmonic vibration on the formation of the two-dimensional rolling solitary waves in vertically co-flowing two-layer liquid films. The system consists of two adjacent layers of immiscible fluids with the first layer being sandwiched between a vertical solid plate and the second fluid layer. The solid plate oscillates harmonically in the horizontal direction inducing Faraday waves at the liquid–liquid and liquid–air interfaces. We use a reduced hydrodynamic model derived from the Navier–Stokes equations in the long-wave approximation. Linear stability of the base flow in a flat two-layer film is determined semi-analytically using Floquet theory. We consider sub-millimetre-thick films and focus on the competition between the long-wavelength gravity-driven and finite wavelength Faraday instabilities. In the linear regime, the range of unstable wave vectors associated with the gravity-driven instability broadens at low and shrinks at high vibration frequencies. In nonlinear regimes, we find multiple metastable states characterized by solitary-like travelling waves and short pulsating waves. In particular, we find the range of the vibration parameters at which the system is multistable. In this regime, depending on the initial conditions, the long-time dynamics is dominated either by the fully developed solitary-like waves or by the shorter pulsating Faraday waves.

Double-Q Checkerboard Bubble Crystal in Centrosymmetric Tetragonal Magnets

We report our numerical studies on the emergence of a double-Q checkerboard bubble crystal in centrosymmetric tetragonal magnets. The double-Q checkerboard bubble crystal is characterized by a fourfold-symmetric collinear spin configuration consisting of a superposition of two sinusoidal waves with the out-of-plane spin modulations along the [110] and [1¯10] directions. The numerical calculations based on the simulated annealing for an effective spin model with the momentum-resolved easy-axis exchange interactions reveal that the double-Q checkerboard bubble crystal is energetically degenerate with the single-Q collinear state when the ordering wave vector lies on the quarter of the reciprocal lattice vector along the ⟨110⟩ direction. We show that such a degeneracy is lifted by considering the biquadratic interaction. We also find that the double-Q checkerboard bubble crystal turns into another double-Q state characterized by the in-plane spin modulations by increasing an external magnetic field.

Vortex Motion on the Surface of Shallow and Deep Water

The attenuation of vortex motion on the surface of shallow and deep water is investigated. The vortex flow was formed by two mutually perpendicular waves excited by plungers at a frequency of 6 Hz (wavelength λ = 5.6 cm) on the surface of water measuring 70 × 70 cm and depth h. After reaching a stationary state in the vortex system, the wave pumping was switched off, and the attenuation of the surface flow was recorded. On the surface of shallow water, λ/2π ≈ h, when the characteristic size of the vortices L exceeds the depth of the liquid, L h, the time dependence of the energy of the vortex flow Е(t) is described by an exponential function at all pumping levels, and the dependence of the enstrophy Ф(t) = Ω2(t) has an exponential dependence only in the range of wave vectors 0–0.3 см–1. On the surface of deep water λ/2π h, L ≈ h dependence Е(t) and Ф(t) are far from exponential in all ranges of wave numbers. At high pumping levels, the dependencies Е(t) and Ф(t) are nonmonotonic, which can be attributed to the influence of volumetric flows.

Multi-functional programmable active acoustic meta-device: acoustic switch, lens, and barrier

Active acoustic metamaterials (AAMM) have garnered special attention because of their potential as multi-function devices. In this direction, the present article demonstrates a novel AAMM that can be programmed as a multi-functional Active Acoustic Meta-device (AAMD) that can switch functionalities between Acoustic Switch (AS), Acoustic Lens (AL), and Acoustic Barrier (AB). Functionality: AL corresponds to the wave vector space, and AS and AB correspond to the frequency space of the proposed AAMM. Additional functionality, such as acoustic logic gates in phase space, is also envisaged. The proposed design is found to change the dispersion diagram by acquiring different configurations while keeping the basic design parameters constant. These design parameters include constituent elements, lattice constants, and filling fractions. Further, for the said functionalities, the proposed AAMM does not rely on the deformation characteristics of the constituents. It rather capitalises on the possible relative displacements of the scatterers. As an AL, AAMM demonstrates zero angle refraction, i.e., collimation, and negative refraction of the transmitted beam at a given angle of incidence over a frequency range of 200 kHz (22.22% of the applied frequency sweep, a.f.s.). AB is shown to attenuate acoustic energy over a frequency range of 700 kHz (77.78% of a.f.s.) compared to its reference and foundation design, a statically designed Phononic Crystal (PnC). Furthermore, as AS, it operates over the entire range of applied frequency sweep (100 kHz to 1000 kHz), i.e., over the frequency range of 900 kHz (100% of a.f.s.).

Local stability of differential rotation in magnetized radiation zones and the solar tachocline

ABSTRACT We study local magnetohydrodynamical instabilities of differential rotation in magnetized, stably stratified regions of stars and planets using a Cartesian Boussinesq model. We consider arbitrary latitudes and general shears (with gravity direction misaligned from this by an angle $\phi$), to model radial ($\phi =0$), latitudinal ($\phi =\pm 90^\circ$), and mixed differential rotations, and study both non-diffusive [including magnetorotational instability (MRI) and Solberg–Høiland instability] and diffusive instabilities [including Goldreich–Schubert–Fricke (GSF) and MRI with diffusion]. These instabilities could drive turbulent transport and mixing in radiative regions, including the solar tachocline and the cores of red giant stars, but their dynamics are incompletely understood. We revisit linear axisymmetric instabilities with and without diffusion and analyse their properties in the presence of magnetic fields, including deriving stability criteria and computing growth rates, wave vectors, and energetics, both analytically and numerically. We present a more comprehensive analysis of axisymmetric local instabilities than prior work, exploring arbitrary differential rotations and diffusive processes. The presence of a magnetic field leads to stability criteria depending upon angular velocity rather than angular momentum gradients. We find MRI operates for much weaker differential rotations than the hydrodynamic GSF instability, and that it typically prefers much larger length-scales, while the GSF instability is impeded by realistic strength magnetic fields. We anticipate MRI to be more important for turbulent transport in the solar tachocline than the GSF instability when $\phi \gt 0$ in the Northern (and vice versa in the Southern) hemisphere, though the latter could operate just below the convection zone when MRI is absent for $\phi \lt 0$.

Chiral Damping of Magnons.

Chiral magnets have garnered significant interest due to the emergence of unique phenomena prohibited in inversion-symmetric magnets. While the equilibrium characteristics of chiral magnets have been extensively explored through the Dzyaloshinskii-Moriya interaction (DMI), nonequilibrium properties like magnetic damping have received comparatively less attention. We present the inaugural direct observation of chiral damping through Brillouin light scattering (BLS) spectroscopy. Employing BLS spectrum analysis, we independently deduce both the DMI and chiral damping, extracting them from the frequency shift and linewidth of the spectrum peak, respectively. The resulting linewidths exhibit clear odd symmetry with respect to the magnon wave vector, unambiguously confirming the presence of chiral damping. Our study introduces a novel methodology for quantifying chiral damping, with potential ramifications on diverse nonequilibrium phenomena within chiral magnets.

Collisional Mechanism of Expanding Wavenumbers Range of Weibel-Type Instability in Magnetoactive Plasma

For plasma with anisotropic velocity distribution of particles in the form of two counter-propagating bi-Maxwellian beams, including bi-Maxwellian plasma, in the presence of external magnetic field parallel to the beams, it is shown that in a wide range of parameters, particle collisions lead to the expansion of the wavenumbers range, generally towards the long-wavelength region, and weaken the conditions for the occurrence of the Weibel-type instability. In the specified expanded range, its growth rate, found by means of solving the dispersion equation for the wave vectors orthogonal to the external magnetic field, turns out to be less than or on the order of the frequency of particle collisions. Thus, in this range of parameters, the instability development and formation of large-scale magnetic turbulence in a plasma with weak particle collisions require the long-term injection of particles with anisotropic velocity distribution.

Multiphysical design for optimised ventilation and noise attenuation in ducts: an approach using metamaterials

Noise generation and propagation through mechanical ventilation and air conditioning (MVAC) ducts have been increasingly investigated since commercial solutions allow sensible noise attenuation while reducing the duct section. So, a commercial silencer forces the MVAC power to rise to overcome the flow resistance, increasing the noise source. For this reason, this study focuses on soundproofing ventilation ducts through acoustic metamaterials with no inner duct section decreasing. A crucial part of this study falls into the multiphysical interaction between acoustics and fluid dynamics, which is a phenomenon that may result in a challenging analytical model. In conditions of flowing motion, the wave vector has been modelled according to the Lighthill model: the component of the velocity rotor potential becomes significant, influencing the soundproofing performance due to the metamaterial placed at the edge of the inner surface of the duct. FEM analysis helped design a series of samples which then have been tested experimentally in static conditions. Once the numerical method is calibrated, further multiphysical numerical analysis are used to implement the sound insulation properties of the metamaterial-based filter through dynamic flow conditions. Guidelines for multiphysical setup for wave-based simulation are drawn, and preliminary experimental results are presented.

High-latitude Observations of Dissipation-range Turbulence by the Ulysses Spacecraft during the Solar Minimum of 1993–96: The Spectral Break and Anisotropy

We examine Ulysses magnetic field observations from 1993 to 1996 as the spacecraft made its first fast-latitude scan from the southern to the northern hemisphere. Most of the observations we use are representative of high-latitude solar minimum conditions. We examine magnetic field power spectra characteristics of interplanetary turbulence at high frequencies, where the spectrum breaks from an inertial range into the ion dissipation range. The onset and spectral index of the dissipation spectrum are consistent with low-latitude observations at 1 au. Both ranges have a ratio of power in perpendicular magnetic field components to parallel components near 3. The power spectrum ratio test developed by Bieber et al. for single-spacecraft analyses that determines the underlying anisotropy of the wave vectors yields only marginally more energy associated with field-aligned wave vectors than perpendicular wave vectors when comparing the inertial and dissipation-range spectra. The lack of significant change in the anisotropies between the inertial and dissipation ranges contrasts strongly with the turbulence found typically for 1 au near-ecliptic observations, where significant differences in both anisotropies are observed.

Unveiling the magnetic structure of BaFeO3-y: Shedding light on the elusive magnetic behavior

This work provides a comprehensive examination of the structural and magnetic properties of 6H-BaFeO2.96 over a wide temperature range (10 K < T < 300 K) using neutron and synchrotron X-ray diffraction. Additionally, the local oxidation state of iron is examined using electron energy loss spectroscopy. No structural changes that could indicate a charge-order transition are observed in spite of a reported possible charge disproportionation of Fe4+ into Fe(4+δ)+ and Fe(4-δ)+ phenomenon at low temperature. According to the magnetic characterization, BaFeO2.96 orders antiferromagnetically at TN=156 K. The application of external magnetic fields strongly influences the magnetic behavior; the transition temperature shifts to lower values with the applied magnetic field and the long-range magnetic order melts with an applied field of 14 T. The magnetocaloric effect clearly shows at TN a change from negative to positive magnetic entropy. The Rietveld refinement of the neutron powder diffraction data collected at 10 K, gives a magnetic ordering with propagation vector [0, 0, ½] and three magnetically distinct sites for the Fe atoms. This magnetic structure consists of ferromagnetic Fe-sheets perpendicular to the c-axis with the magnetic moments along the [110] direction coupled both ferromagnetic and antiferromagnetically along the c-axis. The magnetic moment values of the three Fe ions are very different evidencing a delicate equilibrium of competing magnetic interactions.

Dynamic properties of the magnetic skyrmion driven by electromagnetic waves with spin angular momentum and orbital angular momentum

Abstract We theoretically studied the dynamic properties of the skyrmion driven by electromagnetic (EM) waves with spin angular momentum (SAM) and orbital angular momentum (OAM) using micromagnetic simulations. First, the guiding centers of the skyrmion driven by EM waves with SAM, i.e., left-handed and right-handed circularly polarized EM waves, present circular trajectories, while present elliptical trajectories under linear EM waves driving due to the superposition of oppositely polarized wave components. Second, the trajectories of the skyrmion driven by EM waves with OAM demonstrate similar behavior to that driven by linearly polarized EM waves. Because the wave vector intensity varies with the phase for both linearly polarized EM waves and EM waves with OAM, the angular momentum is transferred to the skyrmion non-uniformly, while the angular momentum is transferred to the skyrmion uniformly for left-handed and right-handed circularly polarized EM driving. Third, the dynamic properties of the skyrmion driven by EM waves with both SAM and OAM are investigated. It is found that the dynamic trajectories exhibit more complex behavior due to the contributions or competition of SAM and OAM. We investigate the characteristics of intrinsic gyration modes and frequency-dependent trajectories. Our research may provide insight into the dynamic properties of skyrmion manipulated by EM waves with SAM or OAM and provide a method for controlling skyrmion in spintronic devices.

Ion Diffusive Transport Across the Separatrix Between the Low‐Latitude Mantle and the Plasma Sheet by Kinetic Alfvén Waves: MMS Observation

AbstractTo understand the entry of the cool low‐latitude mantle ions into the tail plasma sheet near the flanks under persistent interplanetary magnetic field By, we evaluate the role of the cross‐field diffusive transport by kinetic Alfvén waves (KAWs) by investigating two events observed by multiscale (MMS) spacecraft. Around the separatrix between the open and closed field‐line regions, a two‐component mixing of hot plasma sheet ions of a few keV with cool mantle ions of a few hundred eV was observed, indicating transport across the separatrix. The waves observed between 0.01 and 10 Hz around the separatrix had characteristics consistent with those of KAWs. The consistency allowed us to estimate the wave vectors as a function of frequency by fitting KAW dispersion to the observations. Using the observed wave powers, plasma moments, and the estimated wave vectors, we computed the cross‐field diffusion rates associated with KAWs. The diffusion rates were found to be comparable to or larger than the Bohm diffusion rates during the intervals when the two‐component mixing was observed, indicating that the KAW diffusive transport can play a role in the entry of low‐latitude mantle ions into the plasma sheet.

Phase Synchronism in the Generation of Harmonics in Gas Taking into Account Changes in the Wave Vector Detuning during the Propagation of an Intense Femtosecond Laser Pulse

Phase Synchronism in the Generation of Harmonics in Gas Taking into Account Changes in the Wave Vector Detuning during the Propagation of an Intense Femtosecond Laser Pulse

Local gaps in three-dimensional periodic media

The propagation of acoustic waves in a medium with a periodic array of small inclusions of arbitrary shape is considered. The inclusion size a is much smaller than the array period. We show that global gaps do not exist if a is small enough. We introduce and study the concept of local gaps, which depends on the choice of the wave vector k . We analytically determine the location of local gaps for the Dirichlet and transmission problems.

Scattering of a spinning dielectric sphere to polarized plane waves

The exact expression of the wave vector inside a spinning homogeneous dielectric sphere illuminated by polarized plane waves is derived utilizing the “instantaneous rest-frame” hypothesis and Minkowski’s theory. On this basis, the analytical expressions of the electromagnetic field in the rotation sphere system are attained. The asymmetry of the system is discussed, in which the cause is emphasized. The influence of the polarization states and rotation angular velocity on the scattering are analyzed, including the optical rotation effect and photonic hook (PH). The results of this manuscript have extensive application prospects in optical tweezers, particle manipulation, and antenna design.