Anharmonic Phonon Interactions Research Articles

Ultrafast relaxation dynamics of hot optical phonons in graphene

Using ultrafast optical pump-probe spectroscopy, we study the relaxation dynamics of hot optical phonons in few-layer and multilayer graphene films grown by epitaxy on silicon carbide substrates and by chemical vapor deposition on nickel substrates. In the first few hundred femtoseconds after photoexcitation, the hot carriers lose most of their energy to the generation of hot optical phonons which then present the main bottleneck to subsequent cooling. Optical phonon cooling on short time scales is found to be independent of the graphene growth technique, the number of layers, and the type of the substrate. We find average phonon lifetimes in the 2.5–2.55 ps range. We model the relaxation dynamics of the coupled carrier-phonon system with rate equations and find a good agreement between the experimental data and the theory. The extracted optical phonon lifetimes agree very well with the theory based on anharmonic phonon interactions.

Physical and structural properties of some bismuth borate glasses

Glasses in the system ( x/2)Bi 2O 3–( x/2)Nb 2O 5–(1 − x)Na 2B 4O 7, 0 ≤ x ≤ 0.3, have been prepared by the melt quenching technique. Elastic properties and Debye temperature ( θ D) have been investigated using sound velocity measurements at 4 MHz. The ultrasonic parameters along with the IR spectroscopic studies have been employed to study the role of Bi 2O 3, and Nb 2O 5 on the structure of Na 2B 4O 7 glass. The density, the molar volume, the sound velocities, and the glass transition temperatures of these samples have been found to be compositional dependent. The results indicate that Bi 2O 3, and Nb 2O 5 act as a network modifier in the range 0 ≤ x ≤ 0.15, while beyond x = 0.15, Nb 2O 5 acts as a network former which affects the diborate units that mainly consist the strong borate network. These results are interpreted in terms of the transformation of NbO 6 into NbO 4, the increase in the number of non-bridging oxygen atoms, and the substitution of longer bond lengths of Bi–O, and Nb–O in place of shorter B–O bond. The observed compositional dependence of the elastic moduli is interpreted in terms of the effect of Bi 2O 3, and Nb 2O 5 on the Boron-coordination number of the glass structure and to the relatively large electron–phonon anharmonic interactions.

The influence of nanometric phase separation on the dielectric and magnetic properties of (1 − x)BaTiO3–xLaYbO3(0 ≤ x ≤ 0.60) ceramics

X-Ray diffraction analysis shows the co-solubility of La3+ and Yb3+ into BaTiO3 according to the formulae LaxBa1−xTi1−xYbxO3 (LBTYb) to be as high as x = 0.45. Raman spectroscopy analysis suggests the occurrence of continuous ion clustering with increasing x, which culminates with nanometric phase separation at x ≥ 0.35, as revealed by dark-field transmission electron microscopy. The room temperature relative permittivity, eRT, of LBTYb ceramics decreases from ∼1600 for x = 0 to ∼62 for x = 0.45. The Curie temperature, Tc, of LBTYb ceramics decreases at a average rate of ∼ 23 K/at% La/Yb for x ≤ 0.20. Relaxor-type behaviour is observed for 0.10 ≤ x ≤ 0.35. A nearly linear dielectric response is observed for 0.40 ≤ x ≤ 0.45, but below 25 K, er decreases sharply, whereas the magnetic susceptibility increases. The microwave dielectric properties of x = 0.40 ceramics are eRT ∼ 65 and tan δ ∼ 0.01 at ∼5 GHz. The high dielectric loss may be primarily associated with anharmonic phonon interactions resulting from the phase separation.

Back Cover: phys. stat. sol. (b) 245/6

AbstractThis issue's back cover illustration refers to the article by Pablo Etchegoin et al. (pp. 1125–1132) giving a detailed analysis of the Raman spectra of natural and isotopically substituted lead sulfide (PbS). PbS is an important semiconductor that has found technological applications for over a century. Raman scattering in isotopically substituted PbS reveals details of the phonon band structure and anharmonic interactions. For the quantitative interpretation of the spectra the authors performed ab‐initio calculations of phonon dispersion relations and the corresponding densities of two‐phonon states.

Temperature‐dependent Raman scattering studies of the geometrically frustrated pyrochlores Dy2Ti2O7, Gd2Ti2O7 and Er2Ti2O7

AbstractThe temperature‐dependent Raman studies of A2Ti2O7(A = Dy, Er, Gd) were performed on single crystals and polycrystalline samples in the 4.2–295 K temperature range. The Raman spectra showed softening of the majority of phonon modes upon cooling in the whole temperature range studied and large decrease of linewidths. These changes have been analyzed in terms of strong third‐order phonon–phonon anharmonic interactions. Moreover, the 312 and 330 cm−1 modes of Er2Ti2O7(Gd2Ti2O7) showed hardening upon cooling down to about 130 K (100 K) and then anomalous softening below this temperature. The observed anomalous behavior of the Raman modes indicates that some important changes occur in these materials at low temperatures. However, the origin of this behavior is still not clear. Copyright © 2008 John Wiley & Sons, Ltd.

Structural and acoustical studies of lead sodium borate glasses

Abstract Glasses in the system Na2−2xB4−4xPbxO7−6x, 0 ≤ x ≤ 0.8, have been prepared by the melt quenching technique. Elastic properties and Debye temperature have been investigated using sound velocity measurements at 4 MHz. The ultrasonic parameters along with the IR spectroscopic studies have been employed to study the role of PbO on the structure of Na2B4O7 glass. The density, the molar volume, and the ultrasonic parameters of these samples have been found to be compositional dependent. The results indicate that PbO acts as a network modifier in the range 0 ≤ x ≤ 0.4, while beyound x = 0.4, PbO acts as a network former which affects the diborate units that mainly consist the strong borate network. These results are interpreted in terms of the IR analysis that indicates the transformation of the structural units BO3 into BO4, the increase in the number of non-bridging oxygen atoms, and the substitution of longer Pb O bond length, in place of shorter B O bond. The observed compositional dependence of the elastic moduli is interpreted in terms of the effect of PbO on the boron-coordination number of the glass structure and to the relatively large electron–phonon anharmonic interactions. A good correlation was observed between the experimentally determined elastic moduli and those computed according to Makishima–Mackenzie model.

Temperature dependence of the thermal conductivity of different forms of diamond

We present a systematic theoretical investigation of the thermal conductivity of naturally abundant, isotopically enriched, fast neutron irradiated single crystals of diamond, and chemical vapor deposited diamond films of different types over a large temperature range. Existing experimental data have been analyzed using Callaway’s theoretical model [Phys. Rev. 113, 1046 (1959)] for thermal conductivity based on an isotropic continuum phonon dispersion relation and using normal and umklapp phonon-phonon relaxation times derived from the application of time-dependent perturbation theory within an anharmonic continuum model. In contrast to existing theoretical studies of the thermal conductivity of diamond, our approach considers Grüneisen’s constant as the only (semi)adjustable parameter for anharmonic phonon interactions. This work quantifies the enhancement of the thermal conductivity of diamond with isotopic purity. This work also accounts for the dip in the thermal conductivity curve for hot filament chemical vapor deposition of diamond films and neutron irradiated diamond at low temperatures and provides an estimate of the amount, type, and size of defects present in such samples. We find that the N-drift term in Callaway’s theory provides a significant contribution to the thermal conductivity of all the forms of diamond studied here.

Dielectric properties of KDP-type ferroelectric crystals in the presence of external electric field

Considering external electric field as well as third- and fourth-order phonon anharmonic interaction terms in the pseudospin-lattice coupled mode (PLCM) model Hamiltonian for KDP-type ferroelectrics, expressions for field-dependent shift, width, renormalized soft mode frequency, Curie temperature, dielectric constant and dielectric loss are evaluated. For the calculation, method of statistical double-time temperature-dependent Green’s function has been used. By fitting model values of physical quantities, temperature and electric field dependences of soft mode frequency, dielectric constant and loss have been calculated which compare well with experimental results of Baumgartner [8] and Choi and Lockwood [9]. Both dielectric constant and loss decrease with electric field.

Nonlinear optical diagnostic of semimagnetic semiconductors Pb 1− xYb xX (X = S, Se, Te)

Nonlinear optical measurements were performed to elucidate the influence of magnetic ions on the behavior of charge carriers in magnetic semiconductors—Pb 1− x Yb x X (X = S, Se, Te at x = 1–3%). It was shown that nonlinear optical methods could be used as sensitive tools for investigations of electron–phonon anharmonicity near low-temperature semiconductor–insulator phase transitions. There exists a difference between surface and bulk-like contributions to the nonlinear optical effects. It was shown that only low-temperature Two Photon Absorption (TPA) oscillator may be related to the number of the electron–phonon anharmonic modes responsible for the observed phase transformation. The explanation of the anomalous temperature dependences is given in accordance with dipole momentum's behaviors determined by low-temperature spin–spin interactions and by electron–phonon anharmonic interactions. We have discovered that low-temperature dependence of specific heat of Pb 1− x R x Te (R = Yb, Pr with x = 3% and 1.6%, respectively) exhibits a non-magnetic order caused by large electron–phonon contributions and structural disorder effects.

Topological theory of electron-phonon interactions in high-temperature superconductors

There are large isotope effects in the phonon kinks observed in angle-resolved photoemission spectroscopy of optimally doped cuprate high-temperature superconductors (HTSC), but they are quite different from those expected for a nearly free-electron metal (Fermi liquid) with strong electron-phonon interactions (Eliashberg model). These differences, together with many other anomalies in infrared spectra, seem to suggest that other particles (such as magnons) must be contributing to HTSC. Here we use topological methods to discuss the data, emphasizing nanoscale phase separation and the importance of a narrow band of quantum percolative states near the Fermi energy that is spatially pinned to a self-organized filamentary dopant array, resulting in a filamentary glass. Topological discrete, noncontinuum, nonperturbative methods have previously explained the form of HTSC phase diagrams without involving detailed microscopic assumptions, and they are especially useful in the presence of strong nanoscale glassy disorder. These methods also explain the ``miracle'' of an ideal nearly free-electron (gas or liquid) phonon kink in sharply defined nodal quasiparticle states in LSCO at the metal-insulator transition. Careful study of the data reveals anharmonic phonon interactions. Finally, the universality of the kink energy and Fermi velocities below the Debye cutoff in different cuprates is the result of the marginally elastic nature of these configurationally glassy materials, and specifically the isostatic character of the ${\mathrm{CuO}}_{2}$ planes.

IR-induced second-harmonic generation in PbSe microcrystallites

The IR-induced second-harmonic generation in PbSe microcrystallites with sizes of10–30 nm is observed for the first time. A phenomenological approach of the IR picosecondnonlinear optical response in PbSe is developed for the middle-IR spectral range(5–15 µm). A model reproducing the basic features of experimental data related to second-orderoptical nonlinearity caused by photoinduced electron–phonon anharmonic interactions isproposed. The model is based on the band structure calculations and photoinduced kineticswith account taken of electron–phonon anharmonic interactions.

IR optical limiting in europium and thulium doped oxide glasses

IR-induced two-photon absorption in PbO–Ga 2O 3–Bi 2O 3–CdO (PGBC) glasses doped by Eu 3+ and Tm 3+ rare earth (RE 3+) ions is reported. A pulsed CO laser ( λ=5.5 μm, power density up to 3.8 GW/cm 2 per pulse) was applied as a photoinducing IR-light beam. An optical parametrical generator cut from a proustite crystal was used as a source of the fundamental TPA beam within the 3–7.5 μm spectral range. Absolute values of the TPA coefficients were more than 13% higher compared to corresponding value for other similar glasses: As 2Te 3–CaCl 2–PbCl 2 [J. Appl. Phys. 85 (1999) 425; Phys. Rev. B 60 (1999) 942; Opt. Lasers Technol. 33 (3) (2001) 157; Mater. Lett. 54 (2002)] or Sb 2Se 3–BaCl 2–PbCl 2 [J. Mater. Sci. 35 (1) (2000) 215; Mater. Lett. 49 (2001) 272; J. Non-Cryst. Solids 297 (2002) 285]. The PGBC system possesses a shorter time response (about 12 ps), compared with other IR non-linear optical glasses. We have also established that all non-linear optical susceptibilities are crucially dependent on the type of RE 3+ ion. A maximal value of the TPA is achieved for the PGBC glasses doped by Tm 3+. The TPA values increase significantly below 45 K. We have carried out molecular dynamics and quantum chemical simulations in order to evaluate contribution of electron–phonon anharmonic interactions to the TPA.

Nonlinear IR absorption in europium- and thulium-doped oxide glasses

Infrared (IR)-induced two-photon absorption (TPA) in synthesized PbO–Ga2O3–Bi2O3–CdO (PGBC) glasses doped by Eu3+ and Tm3+ rare earth (RE3+) ions was investigated. Temperature-dependent measurements of TPA were carried out in the mid-IR spectral range. A CO pulsed laser (λ = 5.5 μm, energy power density up to 3.8 GW/cm2 per pulse with picosecond pulse duration) was applied as the source of photoinducing IR radiation. An optical parametrical generator cut from a proustite crystal was used as the source of the fundamental TPA beam within the 3–7.5 μm spectral range. Absolute values of the TPA coefficients were more than 13% higher than corresponding values obtained for other similar glasses (As2Te3–CaCl2–PbCl2 [1] or Sb2Se3–BaCl2–PbCl2 [2]). The PGBC system investigated possessed a shorter time response (about 12 ps) compared with other IR nonlinear optical glasses. It was also established that all nonlinear optical susceptibilities were dependent on the type of RE3+ ion. A maximum value of the TPA was achieved for the glasses doped by Tm3+. The TPA values increased significantly below 45 K. Ab initio molecular dynamics and quantum chemical simulations were performed in order to evaluate the possible role of electron–phonon anharmonic interactions in the observed phenomena. The influence of the external CO photoinduced pump beam through the photoinduced electrostricted anharmonic electron–phonon interactions was simulated. A decrease of picosecond delaying time response compared with other glasses was achieved. To obtain independent confirmation of the observed dependencies, measurements were carried out of χxxxx(E) during the external IR pumping. The measured and theoretically calculated dependencies of the third-order susceptibilities were also compared. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Microwave dielectric tangent losses in KDP and DKDP crystals

By adding cubic and quartic phonon anharmonic interactions in the pseudospin lattice coupled mode (PLCM) model for KDP-type crystals and using double-time temperature dependent Green's function method, expressions for soft mode frequency, dielectric constant and dielectric tangent loss are obtained. Using model parameters given by Ganguliet al [9] the dielectric losses are calculated for KDP and DKDP crystals. In the microwave frequency range an increase in frequency (1–35 GHz) is followed by an increase in dielectric tangent loss (1–35) at 98 K and (1–15) × 10−2 at 333 K for KDP and DKDP crystals respectively. The dielectric tangent loss decreases from 0.052 to 0.042 for KDP crystals with increase in temperature from 130 to 170 K and for DKDP crystals it decreases from 0.0166 to 0.0074 with an increase in temperature from 230–343 K in their paraelectric phases at 10 GHz. This shows Curie-Weiss behavior of the dielectric tangent loss

Synthesized rare-earth doped oxide glasses for nonlinear optics

Photostimulated nonlinear optical effects in synthesized PbO–Ga2O3–Bi2O3–CdO (PGBC) glasses doped by Yb3+, Er3+, and Dy3+ rare-earth (RE3+) ions were discovered. Temperature-dependent measurements of optical photoinduced second-harmonic generation (PISHG) and two-photon absorption were performed in the infrared (IR) range. CO pulse laser (λ=5.5 μm, energy power density up to 3.8 GW/cm2 per pulse) was applied as a source of IR-photoinducing and probing (fundamental) light. Absolute values of the PISHG were more than 22% higher than corresponding values obtained for other glasses: As2Te3–CaCl2–PbCl2 [1] or Sb2Se3–BaCl2–PbCl2 [2] type. The investigated PGBC system possesses a shorter time response (about 18 ps), compared with other IR nonlinear optical glasses. We have also established that all nonlinear optical susceptibilities are dependent on the type of RE3+ ion. A maximal value of the PISHG is achieved for the glasses doped by Yb3+. The PISHG values increase significantly below 25 K. We have carried out ab initio molecular dynamics and quantum chemical simulations in order to evaluate the possible contribution of electron–phonon anharmonic interactions in the observed phenomena. We have modeled the influence of the external CO photoinduced beam through the photoinduced anharmonic electron-phonon interactions. A decrease of the delaying time response is achieved. To obtain independent confirmation of the observed dependencies, we have carried out measurements of the ε2(E) during the external IR pumping. We have also compared the measured and theoretically calculated dependencies of the IR-induced effects.

IR-poled second-harmonic generation in glass

Infrared (IR)-induced second-harmonic generation in the chalcogenide glasses is observed. A phenomenological approach of IR picosecond non-linear optical (NLO) response in glass is developed for the middle IR spectral range (5– 15 μm ). The observed effect is explained within the framework of fifth-order NLO susceptibilities. A model that reproduces the basic characteristics of the experimental data, in which the optical non-linearities caused by photoinduced electron–phonon anharmonic interactions, is proposed. The role of the IR-induced phase matching conditions in the observed phenomenon is discussed.

Photoinduced electronic structure and nonlinear susceptibilities in Y–Ba–Cu–O ceramics

Photoinduced second harmonic generation in Y–Ba–Cu–O ceramics was investigated. An analysis of the observed effect was performed based on quantum chemical modeling taking account of electron–phonon anharmonic interactions. Using band energy structure, calculations we have revealed a correlation between photoinduced electron charge density redistribution within the Cu–O octahedra of the Y–Ba–Cu–O ceramic and appropriate second-order nonlinear optical susceptibilities. Other structural fragments play only a minor role in the observed photostructural changes. The possibility of using the photoinduced optical second harmonic generation for detection of superconducting phase transition is demonstrated.

STABILISATION OF PARAELECTRIC PHASE BY STRONG CUBIC AND QUARTIC PHONON ANHARMONICITIES IN KDP CRYSTAL

Considering cubic and quartic phonon anharmonic interactions into the pseudospinphonon coupled mode model of Kobayashi6 expressions for shift, width, soft mode frequency and hence Curie temperature, dielectric susceptibility, Curie-Weiss constant and dielectric (tangent) loss have been evaluated for ferroelectric KDP. The method of retarded double-time thermal Green’s function and the treatment of Dyson’s equation have been used in the development. It is shown that cubic and quartic phonon anharmonic interactions render real value to the soft mode frequency in the para-phase. Results are in agreement with the experimental results of others.

A study of high-temperature phonon anharmonicity in KBr films by the FT-IR emission technique

Polarised far-infrared spectral emission from KBr films is observed around the restrahlung band at an emission angle of 45 degrees . The spectra observed at elevated temperatures show an abnormal line shape around the longitudinal optical (LO) mode frequency. In order to discuss the effect of anharmonic phonon interaction on the spectra, these are analysed using a dielectric response function in which the empirical phonon self-energy function is considered. The results suggest that the shape of the damping function changes with temperature as well as with an increase of magnitude, which implies that the higher-order contribution to the self-energies becomes important at high temperatures as well as the lowest orders. The re-normalised quasi-harmonic LO mode frequency remains fairly constant close to the harmonic mode frequency for all temperatures. More than 10% of deviation from the Lyddane-Sachs-Teller relation is obtained at high temperatures.

Anisotropic heat conduction in diacetylenes.

We report measurements of the low-temperature thermal conductivity of diacetylene single crystals. Monomer samples show little anisotropy and display the temperature dependence of a crystalline dielectric. In polymerized samples, heat is conducted up to 60 times better parallel to the chains than perpendicular to them. Dislocations can account for this anisotropy at the lowest temperatures. Quasi one dimensionality of the polymer crystals induces anisotropy at higher temperatures and strongly suppresses anharmonic phonon interactions.