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An Analysis of Characteristics of Magnetostatic Waves Propagating in Nonhomogeneous Fields Across the Ferrospinel Film Thickness
The amplitude-frequency characteristics (AFCs) of magnetostatic waves in the films of magnesium-manganese ferrospinels with nanostructured inhomogeneities are discussed. A common effect, observed in the film AFCs under different process conditions, is the ‘oscillations of propagation’ of magnetostatic waves as a function of the frequency. The oscillation pattern is thought to depend on the inhomogeneous exchange parameters and the surface anisotropy constants. The wave instability is characterized by the resonant interaction of the dipole magnetostatic waves with the surface spin waves. It is shown that the ferrospinel films with periodic nanostructured inhomogeneities of 30–40 nm could be treated as magnon crystals. An inclusion of the inhomogeneity into consideration allows one to provide reasoning for the formation of the rejection bands within the range 9–12 GHz, whose frequencies correspond to Bragg frequencies.
Iterative spectral method for solving electrostatic or magnetostatic problems in complex and evolving heterostructures
Electrostatic or magnetostatic problems involving complex heterogeneity are nontrivial for modeling and simulation. Most existing numerical methods focus on sharp interface models and the computational cost increases with increasing complexity of the geometry. Here we develop an iterative spectral method, the bound charge successive approximation algorithm, to solve electrostatic or magnetostatic heterogeneity problems in the context of diffuse-interface modeling. As tests and verifications, this algorithm is applied to calculation of the depolarization factor of an ellipsoid, and simulation of random dielectric mixtures and the dielectophoretic motion of multiple particles. The algorithm shows excellent efficiency and the computational cost mainly depends on the permittivity or permeability contrast in the whole system, regardless of the complexity of the geometry. Specifically, for evolving heterostructures the solution of bound charge in one time step can be used as input for the next, which could further significantly shorten the iteration (approximation) process, making it practical to simulate the long-range electrostatic or magnetostatic interaction in complex and evolving heterostructures.
On the magnetostatics of chains of magnetic nanoparticles.
A novel approach is presented for the computation of the magnetostatic energy of straight and bent chains of identical, uniformly magnetized particles of arbitrary shape. The formalism relies on the concept of the magnetometric tensor field, and allows for closed form expressions for the magnetostatic energy, demagnetization factor, Young's modulus, and bending modulus of chains in terms of the shape amplitude of the particles. Analytical solutions are presented for straight chains of spheres, cubes, and cylinders, and for bent chains of spheres. Numerical results include chains of octahedra, tetrahedra, cuboctahedra, and bi-cones. The axial demagnetization factor for the bi-cone shape is derived in analytical form. An approximate energy expression, using the full shape-dependent interaction formalism for short separation distances, and the standard dipolar interaction expression for larger distances, is introduced.
Effects of Magnetic Nanoparticles and External Magnetostatic Field on the Bulk Heterojunction Polymer Solar Cells
The price of energy to separate tightly bound electron-hole pair (or charge-transfer state) and extract freely movable charges from low-mobility materials represents fundamental losses for many low-cost photovoltaic devices. In bulk heterojunction (BHJ) polymer solar cells (PSCs), approximately 50% of the total efficiency lost among all energy loss pathways is due to the photogenerated charge carrier recombination within PSCs and low charge carrier mobility of disordered organic materials. To address these issues, we introduce magnetic nanoparticles (MNPs) and orientate these MNPS within BHJ composite by an external magnetostatic field. Over 50% enhanced efficiency was observed from BHJ PSCs incorporated with MNPs and an external magnetostatic field alignment when compared to the control BHJ PSCs. The optimization of BHJ thin film morphology, suppression of charge carrier recombination, and enhancement in charge carrier collection result in a greatly increased short-circuit current density and fill factor, as a result, enhanced power conversion efficiency.
Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields
We derive via the interaction “representation” the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field—the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement – the uniform electron gas – the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.
Magnetostatic effects on switching in small magnetic tunnel junctions
Perpendicular CoFeB/MgO/CoFeB magnetic tunnel junctions with diameters under 100 nm are investigated by conductive atomic force microscopy. Minor loops of the tunnel magnetoresistance as a function of applied magnetic field reveal the hysteresis of the soft layer and an offset due to the magnetostatic field of the hard layer. Within the hysteretic region, telegraph noise is observed in the tunnel current. Simulations show that in this range, the net magnetic field in the soft layer is spatially inhomogeneous, and that antiparallel to parallel switching tends to start near the edge, while parallel to antiparallel reversal favors nucleation in the interior of the soft layer. As the diameter of the tunnel junction is decreased, the average magnitude of the magnetostatic field increases, but the spatial inhomogeneity across the soft layer is reduced.
Diffusive cosmic-ray acceleration at relativistic shock waves with magnetostatic turbulence
The analytical theory of diffusive cosmic-ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds V{sub s}=β{sub 1}c, including, in particular, relativistic speeds. This is achieved by applying the diffusion approximation to the relevant Fokker–Planck particle transport equation formulated in the mixed comoving coordinate system. In this coordinate system, the particle's momentum coordinates p and μ=p{sub ∥}/p are taken in the rest frame of the streaming plasma, whereas the time and space coordinates are taken in the observer's system. For magnetostatic slab turbulence, the diffusion–convection transport equation for the isotropic (in the rest frame of the streaming plasma) part of the particle's phase space density is derived. For a step-wise shock velocity profile, the steady-state diffusion–convection transport equation is solved. For a symmetric pitch-angle scattering Fokker–Planck coefficient, D{sub μμ}(−μ)=D{sub μμ}(μ), the steady-state solution is independent of the microphysical scattering details. For nonrelativistic mono-momentum particle injection at the shock, the differential number density of accelerated particles is a Lorentzian-type distribution function, which at large momenta approaches a power-law distribution function N(p⩾p{sub c})∝p{sup −ξ} with the spectral index ξ(β{sub 1})=1+[3/(Γ{sub 1}√(r{sup 2}−β{sub 1}{sup 2})−1)(1+3β{sub 1}{sup 2})]. For nonrelativistic (β{sub 1}≪1) shock speeds, this spectral index agrees with the known result ξ(β{sub 1}≪1)≃(r+2)/(r−1), whereas for ultrarelativistic (Γ{sub 1}≫1) shock speeds the spectral index value is close to unity.
Critical role of isopotential surfaces for magnetostatic ponderomotive forces
By producing localized wave regions at the ends of an open-field-line magnetic confinement system, ponderomotive walls can be used to differentially confine different species in the plasma. Furthermore, if the plasma is rotating, this wall can be magnetostatic in the laboratory frame, resulting in simpler engineering and better power flow. However, recent work on such magnetostatic walls has shown qualitatively different potentials than those found in the earlier, nonrotating theory. Here, using a simple slab model of a ponderomotive wall, we resolve this discrepancy. We show that the form of the ponderomotive potential in the comoving plasma frame depends on the assumption made about the electrostatic potential in the laboratory frame. If the laboratory-frame potential is unperturbed by the magnetic oscillation, one finds a parallel-polarized wave in the comoving frame, while if each field line remains equipotential throughout the perturbation region, one finds a perpendicularly polarized wave. As a result, this in turn dramatically changes the averaged ponderomotive force experienced by a charged particle along the field line, not only its scaling, but also its direction.
Coupled Electronic–Nuclear Magnetostatic Oscillations in Magnetic Materials
Magnetization dynamics in spheroidal ferromagnetic samples is studied theoretically. It is shown that, in a magnetostatic approximation, electronic-nuclear magnetostatic modes with a discrete spectrum of eigen oscillations exist in such samples. The structure and the field dependence of the frequencies of these oscillations are substantially dependent on the parameter of the spheroid shape that is the ratio of it’s axes and also on the external magnetic field value. In a certain region of values of these parameters, the dependence of the eigenfrequencies of the system on them becomes nontrivial. The external field strength and the sample shape determine not only the eigenfrequencies in the system, but also the number of the eigenmodes. In addition, for each of the eigenmodes, there exists a “forbidden” region of magnetic fields and shape parameters in which this mode cannot be observed.
Diffusive cosmic ray acceleration at relativistic shock waves with magnetostatic turbulence. II. Influence of a finite downstream medium
The diffusive acceleration of relativistic cosmic rays at parallel shock waves with magnetostatic turbulence and a finite size of the downstream medium is investigated. For ultrarelativistic shock speeds with Lorentz factor Γ{sub 1}≫1, both the differential momentum spectrum at the shock and the volume-integrated momentum spectrum are power-law distribution functions with different spectral indices as compared to the case of an infinitely extended downstream medium. However, the spectral differences are only modest as compared to the case of nonrelativistic shocks. The behavior of the momentum spectrum of shock-accelerated particles depends sensitively on the relativistic shock wave Peclet number G(p)=τ{sub D}(p)/τ{sub C}, i.e., the ratio between the diffusion and convection timescales of cosmic rays to propagate from the shock position to the downstream boundary z {sub 0}. For large values of G(p)≫1 the free-escape boundary has no influence on the effectiveness of particle acceleration, still providing a flat momentum power-law spectrum of the accelerated particles. In the opposite case of small Peclet numbers G(p)≪1 at all momenta, the momentum spectrum at the shock steepens to the greater spectral index ξ{sub 0}=3−s+(3.18/Γ{sub 1}), whereas the volume-integrated momentum spectrum flattens by the same factor 2−s for its power-law spectral index, where s denotes the spectral index of the downstream power spectrum of magnetostatic turbulence. This effectiveness of relativistic shocks in generating flat power-law momentum spectra irrespective of the Peclet number G(p) differs completely from the behavior of nonrelativistic shocks.
Some properties of toroidal isodynamic magnetostatic equilibria
We establish some general properties of a 3D isodynamic magnetostatic equilibrium admitting a family of nested toroidal flux surfaces. In particular, we use the virial theorem to prove a simple relation between the total pressure (magnetic + thermal) and the magnetic pressure on each flux surface, and we derive some useful consequences of the latter. We also show the constancy on each rational surface of two integrals along magnetic lines. As a simple application of our results, we show the nonexistence of an equilibrium with vanishing toroidal current, and of an equilibrium with closed lines.
Analytical examples of reversal current, zero core current, and surface current, toroidal magnetostatic equilibria with nested flux surfaces
We present exact analytical examples of three types of axisymmetric toroidal magnetostatic equilibria with nested flux surfaces: (1) current reversal equilibria, for which the net toroidal current switches from a negative to a positive value when moving away from the magnetic axis; these equilibria have a non-monotonic pressure profile, in accordance with Hammett et al.'s theorem stating that the pressure on the current reversal surface has to exceed the volume-averaged pressure within that surface; (2) zero core current equilibria, in which the toroidal current density vanishes inside some flux surface; and (3) surface current equilibria, constituted of an arbitrary number of nested layers inside which the plasma pressure is constant and the magnetic field force-free, with two adjacent layers being separated by a current sheet. All these configurations are obtained by shaping in an adequate way the arbitrary function which intervenes in the class of generalized isodynamic equilibria first constructed by Palumbo and recovered later on by Bishop and Taylor. A derivation of these equilibria by a method slightly different from Palumbo's is given in an Appendix.
Electron random walk and collisional crossover in a gas in presence of electromagnetic waves and magnetostatic fields
This paper deals with random walk of electrons and collisional crossover in a gas evolving toward a plasma, in presence of electromagnetic (EM) waves and magnetostatic (B) fields, a fundamental subject of importance in areas requiring generation and confinement of wave assisted plasmas. In presence of EM waves and B fields, the number of collisions N suffered by an electron with neutral gas atoms while diffusing out of the volume during the walk is significantly modified when compared to the conventional field free square law diffusion; N=1.5({Lambda}/{lambda}){sup 2}, where {Lambda} is the characteristic diffusion length and {lambda} is the mean free path. There is a distinct crossover and a time scale associated with the transition from the elastic to inelastic collisions dominated regime, which can accurately predict the breakdown time ({tau}{sub c}) and the threshold electric field (E{sub BD}) for plasma initiation. The essential features of cyclotron resonance manifested as a sharp drop in {tau}{sub c}, lowering of E{sub BD} and enhanced electron energy gain is well reproduced in the constrained random walk.
An extended magnetostatic Born-Infeld model with a concave lower order term
This paper concerns an extended Born-Infeld model with a concave lower order term for the magnetostatic case. Three types of boundary value problems are considered: the boundary condition prescribing the tangential component of A, the natural boundary condition, and the boundary condition prescribing the tangential component of curl A. In each case we obtain existence and regularity of solutions for small boundary data.
Confinement of magnetostatic forward volume waves in two-dimensional magnonic crystals with line defects
The mode patterns of magnetostatic forward volume waves (MSFVWs) propagating in two-dimensional magnonic crystals with line defects via periodic variation in thickness of square lattice in a yttrium iron garnet thin film are reported. The theoretical approach based on Walker's equation was employed to analyze the confinement of MSFVWs in the line defects. A good agreement between the theoretical predictions and the experimental results was obtained.
Unidirectional propagation of magnetostatic surface spin waves at a magnetic film surface
An analytical expression for the amplitudes of magnetostatic surface spin waves (MSSWs) propagating in opposite directions at a magnetic film surface is presented. This shows that for a given magnetic field H, it is forbidden for an independent MSSW to propagate along the direction of −H{sup →}×n{sup →}, where n{sup →} is the surface normal. This unidirectional propagation property is confirmed by experiments with both permalloy and yttrium iron garnet films of different film thicknesses, and has implications in the design of spin-wave devices such as isolators and spin-wave diodes.
Localized excitation of magnetostatic surface spin waves in yttrium iron garnet by shorted coaxial probe detected via spin pumping and rectification effect
We demonstrate the localized excitation and dc electrical detection of magnetostatic surface spin waves (MSSWs) in yttrium iron garnet (YIG) by a shorted coaxial probe. Thin films of NiFe and Pt are patterned at different regions onto a common bulk YIG substrate. A shorted coaxial probe is used to excite spin precession locally near various patterned regions. The dc voltages across the corresponding regions are recorded. For excitation of the Pt regions, the dc voltage spectra are dominated by the spin pumping of MSSWs from YIG, where various modes can be clearly distinguished. For the NiFe region, it is also found that spin pumping from MSSWs generated in YIG dominated the spectra, indicating that the spin pumped currents are dissipated into charge currents via the inverse Spin Hall effect (ISHE) in NiFe. For all regions, dc signals from YIG MSSWs are observed to be much stronger than the ferromagnetic resonance (FMR) uniform mode, likely due to the nature of the microwave excitation. The results indicate the potential of this probe for microwave imaging via dc detection of spin dynamics in continuous and patterned films.