Phenomenological Damping Research Articles

Coherent magnetization rotation induced by optical modulation in ferromagnetic/antiferromagnetic exchange-coupled bilayers

We have demonstrated recently that ultrafast (\ensuremath{\sim}100 ps) coherent magnetization rotation can be induced by optical modulation of the exchange coupling in an exchange coupled bilayer (NiFe/NiO) with short laser pulses [Phys. Rev. Lett. 82, 3705 (1999)]. In this paper, we acquire further support of the coherent magnetization model by studying the details of magnetization switching dynamics, including the dependence on the amplitude of exchange bias field. The exchange bias field is subject to large transient modulation by femtosecond pulsed laser excitation, providing the impulsive force for subsequent magnetization dynamics. Good agreement is obtained with a simple model of coherent magnetization processes based on the Landau-Lifshitz-Gilbert equations of motion. We have also measured a strong dependence of the phenomenological damping constant (\ensuremath{\alpha}) on the exchange bias in the coupled ferromagnetic/antiferromagnetic spin system.

Spin-current interaction with a monodomain magnetic body: A model study

I examined the consequence of a spin-current-induced angular momentum deposition in a monodomain Stoner-Wohlfarth magnetic body. The magnetic dynamics of the particle are modeled using the Landau-Lifshitz-Gilbert equation with a phenomenological damping coefficient $\ensuremath{\alpha}.$ Two magnetic potential landscapes are studied in detail: One uniaxial, the other uniaxial in combination with an easy-plane potential term that could be used to model a thin-film geometry with demagnetization. Quantitative predictions are obtained for comparison with experiments.

Dynamic relaxation in thin films

The dynamic magnetization process in thin film platelets is studied by numerical micromagnetics. Simulations are conducted without the addition of the phenomenological damping term in the Landau–Lifshitz equation. Excess Zeeman energy is transferred to magnetostatic-exchange coupled spin waves. This allows the average magnetization to relax towards the equilibrium configuration. The strength of the applied field and the size of the platelet both affect how much energy can be transferred to the spin wave modes. For large enough platelets and fields that are not too large, nearly complete reversal can be obtained without a mechanism to dissipate magnetic energy.

Intrinsic mechanism of nonlinear damping in magnetization reversal

The process of magnetization reversal in a fine ferromagnetic grain with a strong uniaxial anisotropy has been simulated for the case of an instantaneously applied reversal magnetic field. The “quasi” single-domain grain was considered as a system of 64 or 1000 subcubes coupled by exchange and dipole–dipole interactions. The system of Landau–Lifshitz equations was numerically solved without any phenomenological damping terms. The dynamic process is characterized by a rapid magnetization reversal accompanied by a decrease in the average magnetization. The system exhibits a nonlinear excitation of nonuniform magnetic oscillations (spin waves) driven by the uniform mode. We found limitations on magnetization reversal for small grain size and large applied field magnitude. The damping parameter has been obtained for small magnetization oscillations.

Raman analysis of LO phonon–plasmon coupled modes at ZnS:N/(n+,p+)–GaAs interfaces

The activation of p-type doping due to nitrogen incorporation in ZnS layers deposited by MOCVD over both n+- and p-GaAs substrates is investigated by Raman spectroscopy. The study is realized on the substrate side by taking advantage of the high-sensitivity of the substrate-related LO phonon–plasmon (LO-P) lineshape to the carrier density in narrow gap materials. The aim in view is to give evidence for large hole transfer from the layer to the near-interfacial substrate in case of even moderate p-type doping of ZnS. The Raman response from the space charge region of the substrate remains unchanged when ZnS is deposited by using precursor diethyl-Zn (DEZn). On the contrary deep changes are observed when precursor dimethyl-Zn (DMZn) is used. These are directly related to a high doping efficiency of nitrogen in the layer. It appears indeed that the interfacial hole transfer from the DMZn-based p-ZnS layers to the n+- and p-substrates generate LO-P modes, respectively inside and outside the optical phonon band. These contrasted behaviors are qualitatively discussed on the basis of the dispersive and phenomenological damping approaches.

Phenomenological damping in optical response tensors

Although perturbation theory applied to the optical response of a molecule or material system is only strictly valid far from resonances, it is often applied to ``near-resonance'' conditions by means of complex energies incorporating damping. Inconsistent signs of the damping in optical response tensors have appeared in the recent literature, as have errors in the treatment of the perturbation by a static field. The ``equal-sign'' convention used in a recent publication yields an unphysical material response, and Koroteev's intimation that linear electro-optical circular dichroism may exist in an optically active liquid under resonance conditions is also flawed. We show that the isotropic part of the Pockels tensor vanishes.

Numerical studies of two-dimensional Faraday oscillations of inviscid fluids

The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed interface, is studied under normal- and low-gravity conditions. The motion is simulated over an extended period of time, or up to the point where the interface intersects itself or the curvature becomes very large, using two numerical methods: a boundary-integral method that is applicable when the density of one fluid is negligible compared to that of the other, and a vortex-sheet method that is applicable to the more general case of arbitrary densities. The numerical procedure for the boundary-integral formulation uses a global isoparametric parametrization based on cubic splines, whereas the numerical method for the vortex-sheet formulation uses a local boundary-element parametrization based on circular arcs. Viscous dissipation is simulated by means of a phenomenological damping coefficient added to the Bernoulli equation or to the evolution equation for the strength of the vortex sheet. A comparative study reveals that the boundary-integral method is generally more accurate for simulating the motion over an extended period of time, but the vortex-sheet formulation is significantly more efficient. In the limit of small deformations, the numerical results are in excellent agreement with those predicted by the linear model expressed by Mathieu's equation, and are consistent with the predictions of the Floquet stability analysis. Nonlinear effects for non-infinitesimal amplitudes are manifested in several ways: deviation from the predictions of Mathieu's equation, especially at the extremes of the interfacial oscillation; growth of harmonic waves with wavenumbers in the unstable regimes of the Mathieu stability diagram; formation of complex interfacial structures including paired travelling waves; entrainment and mixing by ejection of droplets from one fluid into the other; and the temporal period tripling observed recently by Jiang et al. (1998). Case studies show that the surface tension, density ratio, and magnitude of forcing play a significant role in determining the dynamics of the developing interfacial patterns.

Electron correlations in an electron bilayer at finite temperature: Landau damping of the acoustic plasmon

We report angle-resolved Raman scattering observations of the temperature-dependent Landau damping of the acoustic plasmon in an electron bilayer system realized in a GaAs double-quantum-well structure. Corresponding calculations of the charge-density excitation spectrum of the electron bilayer using forms of the random-phase approximation (RPA), and the static local field formalism of Singwi, Tosi, Land and Sjölander (STLS) extended to incorporate non-zero electron temperature Te and phenomenological damping, are also presented. The STLS calculations include details of the temperature dependence of the intra- and inter-layer local field factors and pair correlation functions. Good agreement between experiment and the various theories is obtained for the acoustic plasmon energy and damping for Te TF/2, where TF is the Fermi temperature. However, contrary to current expectations, all of the calculations show significant departures from our experimental data for Te TF/2. From this, we go on to demonstrate unambiguously that real local field factors fail to provide a physically accurate description of exchange correlation behaviour in low-dimensional electron gases. Our results suggest instead that one must resort to a dynamical local field theory, characterized by a complex field factor to provide a more accurate description.

Magnetization reversal as a nonlinear multimode process

Dynamic magnetization reversal has been simulated in a single grain for an instantaneously applied reversal magnetic field. The grain was considered as a system of n(=2,4,8) subgrains with uniaxial anisotropy coupled by exchange interaction. The gyromagnetic equations of motion were solved without phenomenological damping terms. The evolution of the magnetization was found to exhibit nonlinear spin wave excitation on a short timescale. The average magnetization significantly decreases and demonstrates irregular oscillations at a well defined mean value. The final stage of reversal is the spin-lattice damping on a longer time scale. The magnetic moment is, thereby, reassembled in a new equilibrium direction.

Determination of the magnetic damping constant in NiFe films

A two-dimensional, dynamic, micromagnetic model of a thin strip of permalloy is described and used to model the magnetization dynamics of the strip as it is subjected to a transverse step field. The numerical results are compared to experimental data. The experimental precession frequency is matched by varying Hk, the longitudinal, uniaxial, magnetocrystalline anisotropy field. The damping is matched by varying α, the phenomenological damping parameter in the LLG equation. A good fit to the data was obtained with a single damping constant of α=0.013.

Nonlinear dynamics and the problem of slip at material interfaces

The problem of dry friction between two metallic interfaces is discussed from the perspective of large scale molecular dynamics (MD) simulations. For flat interfaces between identical metals, two-dimensional MD simulations using embedded-atom-method potentials for copper have shown a variety of phenomena associated with a velocity weakening of the tangential force at high relative velocities (approaching significant fractions of the transverse sound speed). These include dislocation generation, dislocation motion both parallel and normal to the sliding interface, large plastic deformation, nucleation of microstructure, diffusive coarsening of microstructure, and material mixing. The early time behavior of a flat sliding interface is dominated by dislocation motion parallel to the interface. For this early stage, lower-dimensional models are useful in interpreting some of the simulation data. A two-chain forced Frenkel-Kontorova model reproduces some of the behavior of the larger scale simulations when the phenomenological damping is taken to be consistent with the MD simulations. This model exhibits four velocity regimes of steady state flow which will be discussed. Some of the implications for the nucleation of microstructure will be addressed.

High frequency initial permeability of NiFe and FeAlN

The initial permeability of NiFe single layer films and single and multi-layer FeAlN films up to 500 MHz are presented. The permeability of thin (<1500 /spl Aring/) NiFe and FeAlN films were fit with calculations based on the Landau-Lifshitz/Gilbert model for phenomenological damping, using damping factors of /spl sim/0.016 and /spl sim/0.026, respectively. Transverse bias permeability measurements identified larger ripple fields in FeAlN samples compared to those in thin NiFe samples. The permeability of /spl sim/2 /spl mu/m thick NiFe and FeAlN films were well described by eddy current theory. The permeability roll off frequency of 2 /spl mu/m thick patterned FeAlN films Increased from 20 to 200 MHz when laminated into 32 layers separated by 25 /spl Aring/ thick SiN interlayers.

Phenomenological damping of nonlinear-optical response tensors

The damping factors that occur in nonlinear-optical response tensors are commonly assigned signs that depend upon the temporal ordering of the associated photon interactions. However, time-reversal symmetry is satisfied only if all these signs are identical. For example, only then is there a formal equivalence between the amplitudes for second-harmonic generation and parametric down-conversion and only then is electro-optic rotation forbidden in fluids. This correction reflects deficiencies in certain commonly employed semiclassical approaches to nonlinear optics.

Theory of giant magneto-impedance effect in amorphous wires with different types of magnetic anisotropy

The effect of various types of magnetic anisotropy on the giant magneto-impedance spectra of amorphous wires with low magnetostriction is studied theoretically. For the first of the model considered the easy anisotropy axis is supposed to be parallel to the wire axis, whereas for the second model it has circumferential direction. In case of a wire with axial type of magnetic anisotropy the transverse magnetic permeability is obtained as a function of external magnetic field amplitude H 0 and other magnetic parameters of the wire. A strong dependence of this quantity on H 0 is shown to explain the giant magneto-impedance (GMI) effect in this type of amorphous wire. Besides, the amplitude of the GMI effect depends substantially on the value of a phenomenological damping parameter. In case of a wire with circumferential anisotropy the classical expression [Landau and Lifshitz, Electrodynamics of Continuous Media, 2nd ed, Pergamon, New York, 1984] for the wire impedance is not valid in the range of external magnetic field 0⩽ H 0⩽ H a, where H a is the anisotropy field. In this range of external magnetic field the wire impedance becomes a tensor. It has both longitudinal and transverse components that can be measured experimentally [Antonov et al., IEEE Trans. Magn. 33 (1997) 3367]. In case of a wire with circumferential anisotropy the peak of the longitudinal component of wire impedance as the function of H 0 corresponds to the anisotropy field, whereas in case of axial anisotropy it is found at zero magnetic field. The results obtained show that the good magnetic softness of amorphous wire is one of the most important conditions to observe the GMI effect; neither any domain structure nor circumferential anisotropy are strictly necessary.

Coherent optical processes of 1s ortho-excitons in Cu 2O by two-photon excitations

Emission spectra of natural single crystals of Cu 2O are examined under a two-photon excitation of 1s ortho-excitons of yellow series in degenerate regime at 2K. It is found that a second harmonic generation (SHG) via an electric quadrupole transition followed by a two-photon electric dipole transition and a hyper-Raman scattering process accompanied with 1LO ( Γ 12 −)-phonon are enhanced resonantly by the 1s ortho-exciton level. The integrated intensities of the SHG light is analyzed as a function of the excitation photon energy giving a phenomenological damping constant of the 1s ortho-exciton.

Comparison of Zakharov simulation and open boundary Vlasov simulation of strong Langmuir turbulence

Both Zakharov equations and Vlasov equations are solved numerically to study the strong Langmuir turbulence developed in a plasma driven by an external pump field oscillating at the plasma frequency. A steady state turbulence in Vlasov simulations is reached by using open boundary conditions under which hot particles generated by strong caviton fields are replaced by initial cold Maxwellian particles when they cross the boundaries of simulation domain. A similar steady turbulent state in Zakharov simulations is easily achieved by implementing a phenomenological damping model and using periodic boundary conditions. Simulation results of these two different models are compared and investigated.

Intersubband optical response of semiconductor quantum wells dressed by strong infrared fields.

A strong infrared field tuned in resonance with dipole-allowed intersubband transitions in quantum-well conduction bands can act to coherently mix or dress the resonant states. The effects of dressing two excited conduction subbands on the linear response of a weak probe field nearly resonant with one of the excited subbands and the partially occupied ground subband is theoretically treated to arbitrary order in the coupling-field strength. Three critical coupling-field strengths are identified that demark: (i) the minimum coupling required to observe changes in the linear response, (ii) the onset of a resolvable doublet in the response, and (iii) the strong-coupling limit in which the line doubling is fully developed. Analytic expressions for these three critical fields are obtained in terms of the Rabi frequency and the phenomenological damping parameters associated with states in the three subbands.

Electric Conduction Due to Charged Solitons in Polyacetylene*

In order to estimate the mobility of a charged soliton in polyacetylene, the dynamics of a soliton in an electric field is numerically investigated in the presence of a phenomenological damping of the lattice motion. Except for the damping term in the equation of motion for the lattice displacements, the dynamics is assumed to be determined by Su, Schrieffer and Heeger's model. It is shown that a Drude-type treatment of the soliton motion is applicable. The mobility is found to be µ=88.9 cm 2 /Volt·sec, and the conductivity is estimated to be σ=7.54×10 3 Ω -1 cm -1 on the assumption that the concentration of the solitons is one per 100 carbon atoms. The present result is compatible with experimental data in the non-magnetic regime.

Velocity damping of moving soliton in polyacetylene

We present studies of velocity relaxation of moving soliton in polyacetylene by using numerical simulations within Su-Schrieffer-Heeger's (SSH) model. The system is assumed to include the phenomenological damping in the lattice dynamics. The soliton is accelerated by an external electric field to get an initial velocity. After the field was cut off, the soliton velocity declines exponentially. It is shown that the soliton can be viewed as a particle obeying the Drude theory.

Real Time Approach to Relaxation and Dephasing Processes in Semiconductors

AbstractStarting from the kinetic equations for the nonequilibrium Green's functions, a practical method is proposed which allows to solve the set of equations for the two‐time propagators numerically. In contrast to the usual semiconductor Bloch equations with phenomenological damping relaxation and dephasing processes are treated microscopically for the case of coupling to a bath of LO‐phonons. Beside a standard approximation for the treatment of LO‐phonon scattering, no further approximations are performed. For the low‐density limit we compare exact results with approximate treatments, as the Marcovian and non‐Marcovian approximations resulting from a density matrix approach. First results concerning nonlinear optical properties are presented.