Phenomenological Damping Research Articles

Finite lifetime effects on the polarizability within time-dependent density-functional theory

We present an implementation for considering finite lifetime of the electronic excited states into linear-response theory within time-dependent density-functional theory. The lifetime of the excited states is introduced by a common phenomenological damping factor. The real and imaginary frequency-dependent polarizabilities can thus be calculated over a broad range of frequencies. This allows for the study of linear-response properties both in the resonance and nonresonance cases. The method is complementary to the standard approach of calculating the excitation energies from the poles of the polarizability. The real and imaginary polarizabilities can then be calculated in any specific energy range of interest, in contrast to the excitation energies which are usually solved only for the lowest electronic states. We have verified the method by investigating the photoabsorption properties of small alkali clusters. For these systems, we have calculated the real and imaginary polarizabilities in the energy range of 1-4 eV and compared these with excitation energy calculations. The results showed good agreement with both previous theoretical and experimental results.

QUANTUM DIFFUSION ON A DYNAMICALLY DISORDERED AND HARMONICALLY DRIVEN LATTICE WITH STATIC BIAS: DECOHERENCE

We revisit the problem of quantum diffusion of a particle moving on a lattice with dynamical disorder. Decoherence, essential for the diffusive motion, is introduced via a set of Lindblad operators, known to guarantee per se the positivity, Hermiticity and the trace-class nature of the reduced density matrix, are derived and solved analytically for several transport quantities of interest. For the special Hermitian choice of the Lindblad operators projected onto the lattice sites, we recover several known results, obtained by others, e.g. through the stochastic Liouville equation using phenomenological damping terms for the off-diagonal density-matrix elements. An interesting result that we obtained is for the case of a 1D lattice with static potential bias and a time-harmonic modulation (ac drive) of its transition-matrix element, where the diffusion coefficient shows an oscillatory behavior as function of the drive amplitude and frequency — clearly, a Wannier–Stark ladder signature. The question of dissipation is also briefly discussed.

Micromagnetic Dissipation, Dispersion, and Mode Conversion in Thin Permalloy Platelets

Micron-sized ferromagnetic Permalloy disks exhibiting an in-plane ferromagnetic vortex structure are excited by a fast rise time perpendicular magnetic field pulse and their modal structure is analyzed. We find azimuthal and axial modes. By a Fourier filtering technique we can separate and analyze the time dependence of individual modes. Analysis of the experimental data demonstrates that the azimuthal modes damp more quickly than the axial modes. We interpret these results as mode conversion from low-frequency azimuthal modes to the fundamental mode which is higher in frequency, i.e., mode-mode coupling in a system with a single Landau-Lifshitz-Gilbert phenomenological damping constant alpha.

Dynamical Susceptibility of Proton in a Two-Morse Potential

Dynamical susceptibility for a proton tunneling system is investigated by using the linear response theory and the mean field approximation. The double-minimum self-potential is constructed by a two-Morse potential, whose parameters are fixed to represent O–H stretching mode. Quantum mechanical calculations give a dynamic susceptibility showing a pronounced soft mode. The phase transitions for KDP and DKDP are described qualitatively, if an effective interaction between protons and a phenomenological damping factor are introduced. The temperature dependence of the dynamical susceptibility is discussed.

Charge Dependence of Surface Plasma Resonance on 2 nm Octanethiol-Protected Au Nanoparticles: Evidence of a Free-Electron System

Charge dependence of surface plasma resonance (SPR) was investigated on 2 nm octanethiol-protected Au nanoparticles. Remarkably, if assuming that each Au-thiol bond localizes one free electron, the observed variations in peak position of the SPR bands as a function of charge can be precisely calculated by simple Mie theory without any adjustable parameters but by using the number of the remaining free electrons in the particle and the experimentally determined dielectric constant for the protecting layer of octanethiol. Additionally, the variations in line-width of the SPR bands can also be quantitatively described by the phenomenological damping law ΔΓ = AvF/R with A = 1.2, a value that suggests a strong chemical-interface damping effect that is consistent with a strong metal−thiol bonding. In the calculations, Perdew's classic spherical jellium model is used to account for the electron spill-out effect. Altogether, these results not only strongly support recent findings by Dickson and co-workers (Phys. Rev. Lett. 2004, 93, 077402) who have shown that the nascent electronic properties of subnanometer Au nanoclusters are of free-electron characteristics but also provide much needed evidence of a continuation of a free-electron system into a particle size range where the collective plasmonic behavior has just emerged.

Bloch equations and completely positive maps

The phenomenological dissipation of the Bloch equations is re-examined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and coloured stochastic noise.

Influence of damping on the vanishing of the linear electro-optic effect in chiral isotropic media

Using first principles, it is demonstrated that radiative damping alone cannot lead to a nonvanishing electro-optic effect in a chiral isotropic medium. This conclusion is in contrast with that obtained by a calculation in which damping effects are included using the standard phenomenological model. We show that these predictions differ because the phenomenological damping equations are valid only in regions where the frequencies of the applied electromagnetic fields are nearly resonant with the atomic transitions. We also show that collisional damping can lead to a nonvanishing electrooptic effect, but with a strength sufficiently weak that it is unlikely to be observable under realistic laboratory conditions.

Fluctuation–dissipation considerations for phenomenological damping models for ferromagnetic thin films

Dissipation properties of ferromagnetic thin films are traditionally characterized by phenomenological damping models related to ferromagnetic resonance (FMR) linewidths. They may also be analyzed in terms of thermal magnetization fluctuations, the connection being made through the fluctuation–dissipation theorem. This article describes how fluctuation–dissipation relations provide a means for discriminating between alternative phenomenological magnetic damping models in ways that are not obvious using traditional uniform-magnetization descriptions appropriate to FMR experiments. In particular, it is shown that recently proposed alternatives to the well-known Gilbert damping model lead to physically untenable predictions/contradictions when analyzed in this light, unlike the traditional Gilbert model itself.

Thermal magnetization noise, damping fundamentals, and mode analysis: application to a thin film GMR sensor

Magnetization dynamic equations with thermal fluctuations are derived fundamentally for small amplitude oscillations. A tensor form of phenomenological damping occurs whose components reflect a general elliptical magnetization motion. This analysis implies that thermal energy and associated damping must be applied to independent normal modes of the system. As an example, this formalism is applied to a thin film magnetoresistance sensor to rind the eigenmodes for general nonuniform magnetization variations. Examples are given of both the various modes and the noise power spectra.

Thermal-dynamic reversal of fine magnetic grains with arbitrary anisotropy axes orientation

A method is developed to analyze thermally agitated magnetization reversal in a single-domain ferromagnetic grain with a uniaxial anisotropy axis oriented at an arbitrary angle to a magnetic field. Random forces and phenomenological damping consistent with thermodynamics are introduced into the dynamic equations of the normal modes. This general approach reduces to the Landau–Lifshitz–Gilbert formalism only when the magnetic energy is isotropic about the equilibrium position. A stochastic averaging method based upon a small damping parameter is used to transform the inherent two-dimensional problem into a one-dimensional form. The mean first exit time is calculated and the results for dynamic coercivity at different angles to the magnetic field are obtained. The method is ultilized to calculate the switching field versus pulse time for planar random media with noninteracting grains. The results fit well with direct Langevin simulation over short times and with Néel–Arrhenius models at long times. A general field and temperature dependent form of the attempt frequency, f0, is derived.

Plasmon damping in molecular beam epitaxial-grown InAs(100)

High-resolution electron-energy-loss spectroscopy (HREELS) has been used as a noninvasive probe to investigate the plasmon excitations and accumulation layers and determine the nominal electron mobility in the near-surface region of undoped molecular beam epitaxial-grown InAs(100). HREEL spectra were recorded at 300 and 600 K, over a wide range of incident electron energies, to observe the effects of temperature on the electron mobility, carrier concentration, surface state density, accumulation layer profile, and plasmon damping mechanisms. These data have been analyzed using semiclassical dielectric theory with a three-layer model, using a simple Drude dielectric function. A separate wave-vector-dependent Landau damping term was included to allow momentum scattering to be described independently by the usual phenomenological damping term. The probing electron energy and temperature dependence of this momentum damping is used to gauge the relative contributions of surface scattering, ionized impurity scattering, and phonon scattering. By extracting the surface scattering component of the plasmon damping, bulk mobility values have been estimated and are much higher than those determined from the high probing electron energy plasmon damping parameters. The bulk electron mobilities and bulk carrier concentrations are 28 800 cm2 V−1 s−1 and 2×1016 cm−3 at 300 K, respectively, and 12 900 cm2 V−1 s−1 and 2×1017 cm−3 at 600 K.

High frequency performance of laminated soft magnetic films (NiFe, FeAlN, and amorphous CoFeBSi) in external fields

Thin film multilayers of different compositions (NiFe, FeAlN, and amorphous CoFeSiB) were prepared by sputter deposition. The ultrahigh frequency performance was studied using rf fields perpendicular to the in-plane easy axis. By applying external bias fields either along or perpendicular to the easy axis (perpendicular to the rf field excitation), the cutoff frequency of the different alloys can be shifted significantly to higher frequencies (>1 GHz) according to theory. On the other hand, it is possible from these measurements to identify different phenomenological damping of the material systems due to structural effects. Although FeAlN exhibits the highest saturation magnetization compared to NiFe and CoFeBSi, it shows a higher damping which is explained by nonideal structure.

Tensor form of magnetization damping

A tensor form of phenomenological damping is derived for small magnetization motions. This form reflects basic physical relaxation processes for a general uniformly magnetized particle or film. Scalar Landau–Lifshitz damping is found to occur only for two special cases of system symmetry.

High-frequency behavior and damping of Fe-Co-N-based high-saturation soft magnetic films

Magnetization dynamics measurements at subnanosecond time scale have been performed on Fe-Co-N high-saturation soft magnetic films with Permalloy nanolayer seeds and having a saturation magnetization of 1.9 MA/m (1900 emu/cm/sup 3/). The damping parameter /spl alpha/ varies from 0.011 to 0.018, depending on applied bias field. The peak frequencies of the imaginary permeability spectra and the zero-crossing frequencies of the real permeability spectra cannot be fitted with a fixed value of anisotropy field, indicating that the Kittel equation is only qualitatively valid for these films. A phenomenological damping criterion is established based on a small-signal solution of the Landau-Lifshitz-Gilbert equation: critical damping occurs in a soft magnetic film when the damping parameter is /spl alpha/=2//spl radic/(/spl chi//sub 0/), where /spl chi//sub 0/ is the initial permeability. The experimentally observed damping parameters are smaller than the critical value for the range of bias fields employed. The Fe-Co-N-based films have a ferromagnetic resonance frequency of 2 GHz at zero-bias field, showing great promise for applications in write heads and integrated inductors in a frequency range >1 GHz.

Modeling of thermal magnetization fluctuations in thin-film magnetic devices

It has been recently shown that broad-band, thermally induced magnetization fluctuations in submicron magnetoresistive (MR) read sensors (used in all present and foreseeable magnetic hard-disk-drives), will serve as a fundamental limit to their achievable signal-to-noise ratio, independent of how large the intrinsic sensitivity parametrics, e.g., ΔR/R, may be. This type of magnetization noise may also be of consequence and/or interest for a broader class of future nanoscale magnetic devices. The foundation for understanding and quantitatively modeling this phenomenon on a practical device-physics level is the fluctuation-dissipation theorem (FDT). This paper develops a theoretical methodology for application of the FDT to the problem of micromagnetic modeling of thermal magnetization fluctuations in small, magnetically soft thin-film magnetic devices, using a generalized Gilbert formulation of magnetization dynamics with phenomenological damping.

Electric Conduction Due to an Acoustic Bipolaron in One-Dimensional Electron-Lattice System

In order to estimate the mobility of an acoustic bipolaron in a typical non-degenerated polymer such as polydiacetylene (PDA), which can be regarded as a one-dimensional electron-lattice system, the dynamical behavior of an acoustic bipolaron in an external electric field is numerically investigated in the presence of a phenomenological damping of the lattice motion. In these simulations, we use the Su, Schrieffer and Heeger (SSH) Hamiltonian extended to include on-site and nearest-neighbor Coulomb repulsion terms, and the damping is introduced by adding a phenomenological friction term in the lattice equation of motion. The repulsive interactions are treated within the unrestricted time-dependent Hartree–Fock approximation. It is confirmed that the mobility of a bipolaron increases with the increase of the repulsion strength and that the relevant quantity determining the mobility of a bipolaron is its width as far as the phenomenological friction is kept fixed. The mobility of a bipolaron is compared wit...

Self-consistency based control scheme for magnetization dynamics

A numerical framework is presented for the solution of the Landau–Lifshitz–Gilbert equation of magnetization motion using a semi-implicit Crank–Nicholson integration scheme. Along with the details of both space and time domain discretizations, we report on the development of a physically based self-consistency criterion that allows for a quantitative measurement of error in dynamic micromagnetic simulations. In essence, this criterion relies in recalculating from actual magnetization motion the imposed phenomenological damping constant. Test calculations were performed with special attention paid to the determination of suitable integration time steps.

Reply to “Comment on ‘Phenomenological damping in optical response tensors’ ”

We show that damping factors must not be incorporated in the perturbation of the ground state by a static electric field. If they are included, as in the theory of Stedman et al. [preceding Comment, Phys. Rev. A 63, 047801 (2001)], then there would be an electric dipole in the y direction induced in a hydrogen atom in the ${M}_{S}=+\frac{1}{2}$ state by a static electric field in the x direction. Such a dipole is excluded by symmetry.

Comment on “Phenomenological damping in optical response tensors”

Damping factors arise from static as well as dynamic perturbations. These must appear with constant sign in the perturbation theory denominators for compatibility with quantum mechanics, conformity with time-reversal symmetry, and agreement with experiment.

Spin-wave dynamic magnetization reversal in a quasi-single-domain magnetic grain

Magnetization reversal in a fine ferromagnetic grain is simulated for the case of an instantaneously applied reversal magnetic field. The Hamiltonian of the system contains the exchange interaction, uniaxial anisotropy, Zeeman energy, and dipole-dipole interactions. A cubic grain is discretized into 64 cubic subgrains and the coupled gyromagnetic equations of motion are solved without phenomenological damping. A scheme to solve these equations is developed that utilizes only two variables per sub-cube magnetization and strictly conserves the absolute magnitude. The initial stage of reversal is uniform rotation followed by a nonlinear excitation of nonuniform magnetic oscillations driven by this uniform mode. An excess of the initial Zeeman energy is transformed into nonlinear spin waves, allowing the average magnetization to substantially reverse. The process of magnetization reversal in fine quasi-single-domain grain exhibits general features of Hamiltonian wave systems with nonlinear diffusion. This nonlinear diffusion is forbidden for either a strong reversal field and/or a small grain size.