Nonzero Wave Vector Research Articles

Mass conservation and anticorrelation effects in the colloidal aggregation of dense solutions.

Recent experimental data show that the scattered intensity distribution from dense solutions undergoing diffusion limited aggregation exhibits a peak at a nonzero wave vector. This article presents a simple phenomenological model based on the conjecture that the form factor for a realistic cluster should satisfy local mass conservation and hence exhibit a pronounced depression at zero wave vector. The model introduces two characteristic lengths, the cluster radius ${\mathit{R}}_{1}$ and the radius ${\mathit{R}}_{2}$ of the depletion region feeding the growing cluster, mass being conserved over the latter length. The intensity distributions observed during the initial stages of the aggregation process are interpreted on the basis of the form factor alone, while the description of the distributions in the later stages, in which scaling occurs, requires in addition the introduction of a structure factor which takes into account steric interactions among the clusters. The model shows remarkably good agreement with the experimental data, and also explains why earlier measurements on dilute solutions failed to exhibit the peak at a nonzero wave vector.

Elastic Interaction Between Modulated Steps on a Vicinal Surface

We study in this paper trie elastic interaction between modulated steps, in both homoepitaxy and heteroepitaxy. The influence of this interaction on the step fluctuation spec- trum is discussed. There are two important consequences that emanate from our analysis, 1) in the homoepitaxy case the elastic interaction favors a modulated step profile. However, the gain in the elastic interaction does not generally overcome the fine tension effect and ii) more importantly, for the heteroepitaXial case the elastic contribution to the energy modulation is of the same order as that of the fine tension part. Elasticity results in an effective fine tension (but singular), which may be either positive or negative depending on the phase shift between two adjacent steps. This analysis shows that the elastic contribution for non-zero wavevectors should be incorporated in any statistical theory of fluctuating steps, if one wants ta account properly for experimental observations. We point eut similarities between this problem, and others arising in quite different systems. We suggest that, m general, tensorial (dipolar and multipolar) interactions between fines, surfaces, etc. of electrostatic, magnetic, hydrodynamic, etc. nature, should lead ta the same generic behaviour.

Quantum Monte Carlo calculations for solids using special k points methods.

We describe a quantum Monte Carlo method for calculating the electronic properties of solids using wave functions with nonzero wave vectors. Our method uses the idea of "special k points" derived from band structure theory, and leads to greatly improved accuracy for insulating systems. We illustrate our method with calculations on germanium in the diamond structure.

Excitation modes of neutral jellium slabs.

The excitation modes of electrons in symmetric, neutral jellium slabs are studied within the time-dependent local density and related approximations, in the regime when there are several bound states below the Fermi level. Unlike most previous calculations, the present ones do not require all single-particle wave functions to vanish at some small distance from the slab. This modification of the boundary conditions significantly affects the excitation spectra, generally reducing the number of peaks that appear. In particular, from our calculations modeling excitation by longitudinal near fields with nonzero surface-parallel wave vector, we do not find resolvable peaks above the bulk plasmon frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ which could be interpreted as standing plasma waves resonating across the neutral slab. This is in contrast to the case of a symmetric but non-neutral jellium slab (wide parabolic quantum well or embedded electron gas) where we do predict distinct (but weak) standing plasmon resonances above ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ at nonzero surface-parallel wave vector, even for a well with only a few occupied bound states. Although bulk plasmon resonances seem to be unobservable in the relatively narrow, symmetric, neutral jellium slabs studied here, we do find the following peaks consistently at low surface-parallel wave vector: an ``intraband'' mode near the two-dimensional-plasmon frequency and a ``multipole surface plasmon'' near 0.8${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$, the latter being amenable also to other interpretations for very thin slabs. Further peaks, including a cluster near ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$, are harder to interpret. They can be related to single-particle transitions in the case of thin slabs. However, in the intermediate-thickness regime it is difficult to assign a unique physical cause to each peak in a spectrum, and various ways to help sort out ambiguities are illustrated. These do not always resolve matters since for neutral jellium slabs one has a relatively wide transition region between quantum and classical size effects.

Excitonic model for second-order resonant Raman scattering.

A theoretical model for second-order resonant Raman scattering is presented. The effect of Coulomb interaction between electrons and holes is fully taken into account in the framework of the effective-mass approximation. By introducing discrete and continuous excitonic intermediate states in the Raman process, an explicit expression for the Raman scattering efficiency is given for long-range Fr\"ohlich electron-phonon interaction. The model developed can be used to evaluate Raman profiles around the resonant region. A closed-form expression for all matrix elements of the exciton-phonon interaction is obtained once the Coulomb problem for the relative electron-hole motion is separated in spherical coordinates. For the first time, to our knowledge, transitions between states from the excitonic ionization continuum for nonzero phonon wave vectors are exactly included in the calculations. The dependence of the Raman scattering efficiency on electron and hole masses is analyzed. The contribution of the different excitonic transitions to the scattering process is also studied. Finally, the model is compared to available experimental data for GaP, InP, GaAs, and GaSb. The overall agreement with the measured resonance profiles and their absolute scattering efficiencies confirms that excitonic effects are required for a satisfactory interpretation of these phenomena.

Direct observation of resonant tunneling dynamics in high magnetic fields.

Magnetotunneling of electrons in an asymmetric double quantum well is investigated by time-resolved luminescence spectroscopy. The tunneling time decreases strongly when the bottom of the lowest electronic subband of the narrow well is brought to intersect the lowest wide well subband at nonzero wave vector by a magnetic field perpendicular to the growth direction. This decrease is particularly pronounced when longitudinal optical phonon emission is possible. Transfer becomes then as fast as in electrically tuned resonances in zero magnetic field.

Compressive and tensile strain effects on hole tunneling in an InGaAs/AlInAs asymmetrical coupled quantum well

Hole tunneling dynamics are investigated in a strained asymmetrical coupled quantum well (ACQW). The tunneling probabilities between heavy-hole states are calculated at different internal strains on the basis of the time-dependent Schrödinger equation analysis with the Luttinger–Kohn and an additional strain Hamiltonians. In a certain range of strain, a higher oscillation frequency (but a smaller oscillation amplitude) of hole tunneling at resonance is obtained in a biaxial tensile strain ACQW at in-plane wave vector k∥=0. The biaxial compressive strain is observed to lower the oscillation frequency. With a nonzero wave vector (k∥≠0), the oscillation frequency is found to be dominated by mixing effects and less dependent on the internal strain. The oscillation frequency remains roughly constant; however, the biaxial compressive strain ACQWs would still have a larger oscillation amplitude than biaxial tensile strain ACQWs.

Valence-band mixing effects on hole oscillations in coupled quantum wells.

Valence-band mixing effects on the dynamics of the heavy- and light-hole oscillations in coupled quantum wells are described by a numerical implementation using the time-dependent Schr\"odinger equation with the Luttinger Hamiltonian. With a nonzero in-plane wave vector (${\mathit{k}}_{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\ne}0), mixing tunneling (between heavy- and light-hole states) and spatial tunneling (from one well to the other) occur at the same time. This time-dependent analysis clearly resolves these two tunneling mechanisms and shows several effects which have not been addressed by previous time-independent analysis.

Transverse polarisation instabilities in a Kerr medium

The amplitude and polarisation stabilities of beams counter-propagating in a Kerr medium are considered with the inclusion of transverse diffraction effects and non-zero medium response time. Lowest thresholds are found for non-zero transverse wavevectors.

Evidence for collective exchange modes in Co/Pd multilayers observed by Brillouin light scattering (abstract)

Recently, exchange-dominated collective spin-wave excitations have been predicted for multilayered structures consisting of alternating magnetic and nonmagnetic layers.1 These types of collective excitations exist for nonzero propagation wave vectors if the magnetic layers are exchange coupled across the spacer layers.1 The modes are the collective counterpart to the optic dipolar-exchange mode observed in magnetic double layers by Vohl, Barnás and Grünberg.2 For a multilayer with N periods of bilayer thickness Λ there exist N modes which, in the absence of exchange coupling, form the well-known band of dipolar collective spin-wave excitations. The modes are dominantly surface-mode-like at the upper band edge and mostly bulk-mode-like at the lower band edge. With the onset of exchange coupling the stack bulk modes are shifted to higher frequencies and become exchange-mode-like in character. In the full exchange coupling limit these modes become the so-called standing spin waves of the total multilayer stack, and their frequencies depend on the stack thickness NΛ. The stack surface mode in this limit becomes the surface Damon–Eshbach mode of a single film of thickness NΛ. Brillouin light-scattering experiments have been performed on magnetron-sputtered Co/Pd multilayers.3,4 The number of atomic layers (AL) is the same in each Co and Pd layer. The number of periods was chosen to be N=8 and 30, with Λ varying between 4 and 140 Å. In the case of N=30 a strong increase of spin-wave frequencies for all but the stack surface mode is observed for d<8 AL. Decreasing d0 increases the interlayer exchange coupling and the band of collective bulklike modes increases in frequency to become a band of exchange-dominated modes. Depending on the strength of the coupling (i.e., spacer layer thickness), this band can have frequencies higher than that of the stack surface mode. From the crossing regime the maximum exchange coupling length is estimated to be 10 Å. For samples with N=8, collective exchange modes were not observed. Model calculations show that for N=8 the expected frequency increase near the onset of interlayer exchange coupling is much steeper than in the N=30 case, which might prohibit their experimental observation. Also, the cross section is reduced by a factor of 4 due to the smaller total stack thickness.

Many-body formulation of the antiferromagnetism of chromium alloys

A tight-binding formulation of the many-body enhanced paramagnetic spin susceptibility derived within the local-density approximation is applied to the antiferromagnetism of Cr alloys. The effects of alloying on the band structures are modelled by a Slater-Koster version of the coherent-potential approximation and matrix elements are computed directly using an averaged linear-combination-of-atomic-orbitals treatment. Antiferromagnetic ordering of the ground state, manifested by a spin-density wave of non-zero wave vector, is predicted when the zero-temperature static susceptibility exhibits a singularity for that wave vector. The spin-density-wave wave vectors computed using this method for dilute Cr1-xVx and Cr1-xMnx alloys are in good agreement with neutron scattering measurements of the wave vectors as functions of impurity concentration. For larger concentrations of impurities, predictions of magnetic order can be made for alternate cubic structures of other 3d transition metals, whose novel structural phases might be stabilized by alloying. In the case of Cr1-xMnx, a transition to ferromagnetism is predicted for x=0.5. Stabilization of Cr1-xMnx>0.5 in the simple BCC crystal structure could permit an experimental test of an earlier prediction of ferromagnetism in delta -Mn.

Submillimetre spectroscopy of acoustic phonons in crystals with modulated structures

Abstract I t is now well established that in periodically layered super lattices one can observe Raman activation of acoustic modes with non-zero wave vectors k in the direction perpendicular to layers, where n is integer and b is the period of the super lattice. These modes become effectively long-wavelength and therefore possibly Raman and infrared (IR) active due to the folding of the Brillouin zone (BZ). This was observed in semiconductor heterostructures, crystalline lamellar polymers and can be expected in modulated crystal phases as well although we are not aware of any work devoted systematically to this problem.

Stress as an order parameter for the glass transition.

The stress tensor has been considered as a possible order parameter for the liquid-glass transition, and its autocorrelation matrix (elements of which are the integrands in the Green-Kubo formulas for bulk and shear viscosity) have been measured in simulations. However, only the k=0 spatial Fourier component has apparently been previously measured. We have measured four Fourier components of all matrix elements of the stress-stress correlation function, and we find that some of those with nonzero wave vector are significantly more persistent (slower decaying) than the k=0 component.

Spin-wave calculations for multilayered structures.

Results are presented on the calculations of spin-wave frequencies in ferromagnetic layers, double layers, and multilayered structures for small, nonzero wave vectors such as can be investigated by, e.g., Brillouin light scattering. The underlying continuum-type magnetostatic theory includes both dipolar and exchange contributions and fully takes into account magnetic surface and interface anisotropies as well as interlayer exchange coupling. For single magnetic layers the detailed influence of surface anisotropies on both film surfaces is studied. For magnetic double layers the interlayer exchange coupling mechanism is investigated. In the case of multilayers consisting of alternating magnetic and nonmagnetic layers, the crossing regime between dipolar and exchange modes shows a strong dependence of the gap width on the amount of interface anisotropy. For small layer thicknesses the interlayer exchange coupling shifts the spin-wave frequencies of all but the highest-frequency dipolar modes into the exchange-mode regime. In the case of all-magnetic multilayered structures, a new type of collective spin-wave excitations arising from coupled exchange modes is predicted.

On the magnetic behaviour of heavy Fermion systems

Abstract Using a Stoner-like expression for the magnetic susceptibility of the Anderson lattice, which has been derived earlier within the perturbational approach, we discuss the occurence of magnetic phases at low temperatures. An explicit calculation using an ideal hybridized quasiparticle band structure reveals that Heavy Fermion systems are typically close to a magnetic instability and that modulated structures with nonzero wavevectors are favoured.

Computation of dipolar fourier transforms

We describe a novel approach to the computation of dipolar Fourier transforms, distinct from Ewald's method. As in the latter, each Fourier transform is the sum of two rapidly convergent series in the direct and the reciprocal lattices, respectively. The method works equally well for the uniform mode as for nonzero wave vectors.

Study of ion-implantation damage in GaAs:Be and InP:Be using Raman scattering

The Raman spectra of GaAs and InP implanted with Be ions with fluences ranging from 5×1012 to 1×1016 cm−2 were investigated. A marked difference in the behavior of the TO and LO modes with respect to broadening with fluence was observed and the results indicate that this is caused by frequency dependent anharmonic damping constants. The Raman spectra of high fluence samples are interpreted in terms of disorder-induced first-order Raman spectra due to phonons with nonzero wave vectors. The similarities between our ‘‘Reduced Raman Spectra’’ of the disordered form and the theoretical one-phonon density of states, are presented without introducing Gaussian broadening as suggested by earlier authors studying amorphous materials. The observations support the conclusion that the form essentially retains the short-range order of the crystalline phase; the phonon spectrum of the crystal is largely determined only by near-neighbor interactions; and the existence of a frequency-dependent coupling constant for the scattering intensity at least in the low frequency region.

Time correlation functions for a model of liquid carbon disulphide

A three centre Lennard-Jones model of CS2 predicts time dependent properties of the liquid, along the orthobaric curve, in good agreement with experiment. The molecules diffuse more easily parallel to their original orientation. The angular velocity autocorrelation function (acf) is an excellent approximation to the first memory function of the reorientational acf. Simple models of the orientational motion fail because the torque and angular velocity acf's relax on similar time scales. Collective correlations of the orientational and centre of mass density fluctuations are calculated with increased accuracy at a number of small non-zero wavevectors.

Light-scattering study of the non-zero wave vector incommensurate soft mode in K 2SeO 4

Observations are reported of inelastic light scattering from the non-zero wave vector soft phonon that drives the incommensurate structural phase transition in K 2SeO 4. They are shown to correlate with neutron scattering measurements of phonon frequency shifts on cooling to the incommensurate transition temperature. The observed light scattering is suggested to arise from intrinsic disorder.

Early stages of spinodal decomposition in superfluidHe3-He4mixtures

A generalization of the linearized analysis of Cahn, Hilliard, and Cook is applied to a simple model of phase separation dynamics in $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures at early times. An instability region is found in which the structure function for concentration fluctuations exhibits maximum growth at a nonzero wave vector. The coupling of concentration fluctuations to the superfluid second-sound mode produces an additional flickering component in the scattering. Equilibrium experimental data from both sides of the coexistence curve are used to estimate the size of these effects. The instability region is found to be quite asymmetrically placed inside the two-phase region.