Phonons In Crystals Research Articles

Observation of phonons in multiferroicBiFeO3 single crystals by Raman scattering

We have grown BiFeO3 bulk single crystals by a flux method and characterized the phononspectra in detail by Raman scattering in the temperature range 4–1100 K.All the 13 Raman-active phonon modes predicted by group theory,4A1+9E, were observed at low temperature and successfully assigned by a polarized Ramanmeasurement. Moreover, drastic spectral changes in the Raman spectra were observed attemperatures 600–700 K and 1000–1100 K. These features are discussed from the viewpointof phonon coupling with the magnetic ordering and the structural phase transition,respectively.

Effects of time reversal symmetry on phonons in sapphire substrate for ZnO and GaN

Vibrational states in a crystal are classified according to the irreducible representations (irreps) of the corresponding factor group G0k/T. The wave vector k runs over the entire Brillouin zone (BZ). For trigonal BZs, the factor groups are determined by the symmetry points Γ, F, L, T, and the symmetry lines Λ, Σ, Y. When the irreps are complex, the time reversal symmetry has to be taken into account. Using the Frobenuis–Schur criterion adapted to space groups with real and complex irreps, we have investigated high symmetry points and lines of the phonons in trigonal crystals: Cr2O3,Fe2O3,Ti2O3,V 2O3,FeCO3,CaCO3,CdCO3,MgCO3,MnCO3,NaCO3 and ZnCO3, with the common space group D3d6(R3c). We have found several phonons which are influenced by the time reversal symmetry. Therefore, an extra degeneracy of phonons arises. The theoretical results are also compared with available experimental data.

Time-resolved dynamics of coherent acoustic phonons in CdMnTe diluted-magnetic single crystals

The authors report on observation of pronounced coherent acoustic phonon (CAP) oscillations in diluted-magnetic Cd1−xMnxTe (x=0.09) single crystals by means of femtosecond, optical single-color, and two-color pump-probe spectroscopy. The observed properties of CAP oscillations are consistent with the propagating-strain-pulse model, with electronic stress as the main CAP generation mechanism. The experimental dispersion relation between the CAP oscillation frequency and the probe-beam wave vector allowed them to extract the Cd0.91Mn0.09Te refractive index dependence on wavelength, while the dependence of oscillation amplitudes on the photon energy near the Cd0.91Mn0.09Te band gap edge indicated that the material energy gap is 1.63eV. Two-color pump-probe studies showed that the speed of sound in our material is 3590m∕s and that the absorption depth of probe light, rather than the decay time of CAPs, is the dominant source of the experimentally observed oscillation dephasing time. The intrinsic lifetime of CAPs in CdMnTe crystals has been found to be at least in the nanosecond range.

Condensed matter theory by computer simulation: from materials to chemical biology features

solids to complex multi-component materials and even biological matter, are governed by well understood laws of physics: on the relevant scales of length and time; the appropriate description would be just the Schrodinger equation for the quantum-many-body problem of the nuclei and electrons interacting with Coulomb forces. Statistical mechanics would then provide the framework to extend this quantum theory of condensed matter towards a statistical description in terms of averages taken at nonzero temperature. However, this program cannot be carried out straightforwardly: even dealing only with the associated electrons is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the manybody problem can be effectively reduced to a problem of independent particles or quasi-particles. Such problems are, for instance, ideal gases, paramagnets, or the multidimensional harmonic oscillator describing phonons in harmonic crystals. While all these problems are useful and educative (we hence teach them all to students to illustrate the spirit of the general theoretical framework) they do not encompass most of the problems of interest in condensed matter physics: the interactions among the considered degrees of freedom introduce nontrivial correlations between them. Systematic perturbation-theory type methods usually do not lead very far, and uncontrolled closed form approximations often fail utterly. A well-known example is the study of the liquid gas transition in fluids: simple theories such as the van der Waals equation and its extensions (e.g. the perturbed chain statistical associating fluid theory [PC-SAFT] intended to model the equation of state of polymer melts [1]) give rise to spurious loops in the isotherms, fail to describe the critical behavior correctly, and may even predict completely unphysical phase equilibria that do not correspond to any physical behavior of the system but are mere artefacts of the inappropriate approximations [1]. The theory of condensed matter systems contains a never-ending list of such failures! Hence, until about 50 years ago, condensed matter theory suffered from the basic problem that only a formal framework for the theoretical description in terms of quantum theory and statistical mechanics did exist, while a reliable set of tools that would allow accurate explicit predictions to be made for the static and dynamic properties of these systems from first principles was simply missing! This unsatisfactory situation has changed fundamentally through the invention of computer simulation, which provides a much more promising approach to these problems. Computer simulation is a novel methodic route allowing the Condensed matter theory by computer simulation: from materials to chemical biology [DOI: 10.1051/EPN:2007009]

Far-infrared photon absorption by phonons in ZnTe crystals

One-phonon and two-phonon contributions to polarization are determined for ZnTe crystals in the frequency range of 1–4THz using the existing experimental data on far-infrared absorption and neutron scattering. The two-phonon contribution in the 1.7THz band is higher than the first-order absorption related to the ion dipole (TO mode) resonance (comparable in the 3–4THz band). LA→TO phonon difference transitions are concluded to dominate in the 1.7THz band, whereas TA→TO, TA→LO and mixed-mode A→O difference transitions are of primary importance in the 3–4THz band. The contributions of the 2TA-overtone and other two-phonon-sum processes are comparatively weak. Matrix element squares for partial inter-phonon-band transitions are compared, and the photon–two-phonon coupling coefficients are estimated.

The velocity of acoustic phonons in crystals with edge dislocations and point impurities

The velocity of longitudinal long-wave phonons in crystals with a small number of randomly distributed static edge dislocations was shown to be the same as in ideal crystals. The correction to the velocity of phonons is determined by their interaction with the field of lattice deformations caused by the presence of dislocations. The field of deformations of dislocation displacements is long-range. In addition, these deformations experience sign reversal when the sign of the coordinate perpendicular to the dislocation line and Burgers vector changes. It follows that a crystal contracts or expands in this direction because of the interaction of phonons with dislocations as the defect deformation sign alters. Such an anisotropic volume (and density) change over the whole crystal should however be balanced somehow. For this reason, the density of samples with edge dislocations should remain constant, and the correction δc to the velocity of phonons should be zero. The procedure for averaging that gives δc = 0 is based on the independence of this macro value from the orientation of phonon momemtum incident on randomly distributed dislocations, the unaveraged correction being a diverging value because of the long-range character of the field of defect deformations. For comparison, the correction to the velocity of phonons in crystals with point impurities was calculated. Lattice deformation caused by such defects is isotropic. For this reason, the mean density of crystals with point impurities and the velocity of phonons in them are different from those in ideal crystals. All calculations were performed using the Dyson equation derived on the basis of the Keldysh diagram technique.

IR-active vibrational modes of CdTe and CdSe colloidal quantum dots and CdTe/CdSe core/shell nanoparticles and coupling effects

The frequencies of the vibrational modes of CdTe and CdSe quantum dots and CdTe/CdSe core/shell nanoparticles prepared by the colloid chemistry method are determined using IR transmission and IR reflection spectroscopy. The experimental IR transmission spectrum of CdTe and CdSe nanocrystals exhibits a broad minimum located between the frequencies of the transverse optical (TO) and longitudinal optical (LO) phonons of bulk CdTe and CdSe crystals. The frequencies of the modes for ensembles of CdTe and CdSe quantum dots are considerably shifted toward lower frequencies as compared to those calculated for single quantum dots. This is explained by the dipole-dipole interaction between quantum dots. The frequencies of modes for the structures with core/shell nanoparticles differ little from the calculated frequencies. This suggests a weakening of the interaction in these structures due to the enhancement of dielectric screening.

Dissipative phenomena and acoustic phonons in isothermal crystals: A density-functional theory study

We derive the nonlinear transport equations for isothermal crystalline solids using a density-functional theory based free energy and the Poisson bracket formalism. The model is comprised of three characteristic time scales: A fast one of sound waves and two slow ones of diffusive phenomena. It also combines long-range elastic features with a density field $\ensuremath{\rho}$ having an atomistic resolution. At the level of linearized hydrodynamics, our results are identical to transport equations obtained from the Mori projection operator treatment when the coupling of mass density and phonons becomes weak. At the linear level, we also show that Fick's law breaks down without dislocations in accordance with Cahn's theory of stress effects on diffusion in solids. In contrast, with no bilinear couplings between the density and the displacement fields, it is possible to use a nonlinear local theory to describe diffusion and elastic effects using just a single scalar field $\ensuremath{\rho}$, which is numerically efficient. We show how a variety of phenomenological phase field crystal models---which have recently demonstrated their power in materials science applications---can be derived, and how their parameters can be related to more microscopic ones.

Anomalous temperature behavior of hypersonic acoustic phonons in a lysozyme crystal

The behavior of acoustic phonons in tetragonal lysozyme crystals is studied using Brillouin scattering over a temperature range from 298 to 330 K. Around 307 K, anomalies in the temperature dependence of the velocity and integral intensity of a quasi-transverse phonon and in the velocity of a quasi-longitudinal phonon are detected. The experimental results are discussed in terms of the current concepts of the dynamics of proteins. The observed anomalies in the behavior of hypersonic acoustic phonons are indicative of a structural phase transition occurring in a lysozyme crystal at 307 K.

Generation, detection and spectroscopic studies of high-frequency nonequilibrium phonons in crystals

In this article we will review studies conducted in the past two decades on the dynamic properties of high-frequency (THz) phonons generated monochromatically with high power far infrared (FIR) laser pulses using defect-induced phonon absorption and detected using a vibronic sideband spectrometer fashioned after that devised by Kaplyanskii, the honoree of this special issue. The temporal and spectral evolution of the phonon signature provides information on the mechanisms that dominate the relaxation of high-frequency phonons in real crystals.

Acoustic properties of the disordered relaxor ferroelectric PbSc1/2Ta1/2O3

The behavior of acoustic phonons in crystals of a relaxor ferroelectric, namely, the lead scandium tantalate PbSc1/2Ta1/2O3 (PST), is studied in the vicinity of the diffuse phase transition. The behavior of longitudinal and transverse acoustic phonons in a PST single crystal is examined using Brillouin scattering. The phonon subsystem is found to behave anomalously in the vicinity of T = 297 K, which can probably be assigned to the existence of a phase transition. Analysis of the results obtained yields the values of the elastic moduli C11, C12, and C44 for the cubic phase of the crystal over a wide temperature range.

Investigation of II –VI alloy lattice dynamics by IR spectroscopic ellipsometry

Optical properties related to lattice vibrations of bulk Zn1-xBexSe, Zn1-x-yBexMnySe and Cd1-xBexSe alloys are reported. Optical phonons of the mixed crystals grown by the Bridgman method have been investigated by infrared spectroscopic ellipsometry in the wave-number range 300-8000 cm-1. The complex dielectric functions can be reproduced using a model with two or three classical damped oscillators corresponding to the BeSe-like transverse-optical phonon-modes and a Drude contribution from the free carriers. The frequencies of longitudinal-optical phonons have been found from the imaginary parts of the dielectric loss functions. The influence of the alloy composition on the zone-centre optical phonon frequencies is discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Elementary vibrations in rare-gas crystals: Frequencies of phonons in compressed argon, krypton, and xenon crystals

The lattice dynamics of rare-gas crystals is investigated in the framework of the ab initio approach with the inclusion of the nonadiabatic effects over a wide range of pressures. The frequencies of phonons in argon, krypton, and xenon crystals are calculated at pressures p ≠ 0. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the difference between the phonon frequencies calculated within several models is most pronounced at the boundary of the Brillouin zone. Under strong compressions, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction, with the relative contribution decreasing in the series Ar, Kr, and Xe. The calculated phonon frequencies are in good agreement with the experimental data available in the literature for argon crystals at a pressure p = 3.1 GPa.

Anomalous phonon shifts in the paramagnetic phase of multiferroicRMn2O5(R=Bi, Eu, Dy): Possible manifestations of unconventional magnetic correlations

A Raman spectroscopic study of the high-frequency optical phonons in single crystals of the multiferroic system $R{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$ ($R=\mathrm{Bi}$, Eu, Dy) was performed. All studied materials show anomalous phonon shifts, below a new characteristic temperature for these materials, ${T}^{*}\ensuremath{\sim}60--65\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The sign and magnitude of such shifts appear to be correlated with the ionic radius of $R$, envolving from softenings for $R=\mathrm{Bi}$ to hardenings for $R=\mathrm{Dy}$ and showing an intermediary behavior for $R=\mathrm{Eu}$. Additional phonon anomalies were identified below $\ensuremath{\sim}{T}_{N}\ensuremath{\sim}40--43\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, reflecting the onset of long-range ferroelectric and/or magnetic order of the Mn sublattice. Complementary dc-magnetic susceptibility $[\ensuremath{\chi}(T)]$ measurements for $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$ up to $800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ yield a Curie-Weiss temperature ${\ensuremath{\theta}}_{CW}=\ensuremath{-}253(3)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, revealing a fairly large frustration ratio $(\ensuremath{\mid}{\ensuremath{\theta}}_{CW}\ensuremath{\mid}∕{T}_{N}=6.3)$. Deviations of $\ensuremath{\chi}(T)$ from a Curie-Weiss paramagnetic behavior due to magnetic correlations were observed below temperatures of the order of $\ensuremath{\mid}{\ensuremath{\theta}}_{CW}\ensuremath{\mid}$, with the inverse susceptibility showing inflection points at $\ensuremath{\sim}160\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $\ensuremath{\sim}{T}^{*}$. Supported by $\ensuremath{\chi}(T)$ data, the anomalous Raman phonon shifts below ${T}^{*}$ are interpreted in terms of the spin-phonon coupling, in a scenario of strong magnetic correlations. Overall, these results support significant magnetic frustration, introduce a new characteristic temperature $({T}^{*})$, and suggest a surprisingly rich behavior for the magnetic correlations in the paramagnetic phase of this system.

Laser-induced quantum adsorption of neutral atoms in dielectric surfaces

We propose an optical technique to load neutral atoms in quantum adsorption states of a dielectric surface. Considering a realistic atom–surface potential well, we show that free cold lithium atoms approaching a LiF surface may be transferred to a surface bound state of the first excited atomic state. We also discuss schemes to populate adsorption energy levels of the atomic electronic ground state, and we find that spontaneous mechanisms transfer more than 90% of the excited adsorbed atoms into vibrational levels of the fundamental adsorption potential. The lifetime of the resulting two-dimensional waveguide is calculated, considering the adatoms’ interaction with the crystal phonons.

Acoustic velocity of phonons in complex plasma crystal lattices

Low-frequency longitudinal (compressional) and transverse (shear) modes of phonons in Debye–Yukawa complex plasma crystals are studied. The general dispersion relations obtained for two-dimensional modes [Wang, Bhattacharjee, and Hu, Phys. Rev. Lett. 86, 2596 (2001)] are applied to the long-wavelength phonon regime with the wavenumber k → 0, and the shielding parameter κ → 0 to calculate the acoustic velocity of phonons in complex plasma crystals. Our analytic work confirms earlier numerical results.

Anharmonic phonon energies in rare-gas solids derived by path-integral simulations

Vibrational properties of rare-gas solids are studied as a function of temperature and pressure by path-integral Monte Carlo simulations with a Lennard-Jones potential model. The calculation of the static susceptibility tensor, that represents the linear response of the equilibrium system to vanishingly small forces on the atomic nuclei, leads to a nonperturbative approximation of the crystal phonons. The intrinsic anharmonicity of vibrational modes is quantified by comparison to harmonic phonon energies calculated at the equilibrium volume of the solid. Results obtained for longitudinal and transverse phonon energies at the boundary of the Brillouin zone, as well as elastic constants estimated from the propagation velocity of selected phonons, are compared to available experimental data for solid Ne and Ar. The studied temperatures cover a range from $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to the triple point of the rare-gas solids, while the largest studied pressures amount to about $40\phantom{\rule{0.3em}{0ex}}\mathrm{kbar}$, that corresponds roughly to the validity limit of the employed potential model.

Lennard-Jones approach to optical zero-phonon spectra of impurities in glasses

Frequency dependent properties of zero-phonon lines are considered on the basis of persistent hole burning in the inhomogeneous optical bands of dye-doped polymer glasses. The energy spread of optical transitions was expressed as a difference of Lennard-Jones (L-J) potentials of the ground state and the excited state. Pressure shift coefficients of spectral holes depend on the difference of the first derivatives of L-J potentials. From the second derivatives the quadratic electron–phonon coupling constants were calculated and compared to temperature induced shift and broadening of spectral holes. A softening of local phonons in glasses or defect crystals containing empty space can be associated with the vanishing of force constants at intermolecular distances exceeding the equilibrium value by a mere 11%.

Silicon crystal growth from the melt: Analysis from atomic and macro scales

AbstractThe effect of impurity concentration on thermal conductivity of natural and isotope silicon by using equilibrium molecular dynamics simulation is investigated. It was found that the concentrations of the impurities such as boron, phosphor and arsene play an important role in the propagation of phonons in silicon crystals. It was also clarified that a mass difference of impurities and host crystals results in degradation of thermal conductivity of silicon. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Interface and confined optical phonons in wurtzite nanocrystals

We derive within the dielectric-continuum model an integral equation that defines interface and confined polar optical-phonon modes in nanocrystals with a wurtzite crystal structure. It is demonstrated theoretically that, while the frequency of confined polar optical phonons in zinc-blende nanocrystals is equal to that of the bulk crystal phonons, the confined polar optical phonons in wurtzite nanocrystals have a discrete spectrum of frequencies different from those of the bulk crystal. The calculated frequencies of confined polar optical phonons in wurtzite ZnO nanocrystals are found to be in an excellent agreement with the experimental resonant Raman-scattering spectra of spherical ZnO quantum dots.