Second-order Phonon Research Articles

First- and second-order resonant Raman scattering in graphite.

We report a determination of the Raman-scattering efficiency for first- and second-order phonon lines in graphite. These measurements are of interest for the analysis of the Raman spectra of amorphous carbon films, materials of increasing technological interest.

Calculation of NQR v's and T1 -1' s being proportional to T4 and T5 , respectively

Abstract The second-order Raman phonon process for a multilevel spin system is shown to give a quadru-polar spin-lattice relaxation rate T1 -1varying as T5 at very low temperatures. This relaxation rate for quadrupole spins is similar to the one discussed for a paramagnetic spin system having a multilevel ground state. The temperature dependence of T1 is discussed on the basis of some simplifying assumptions about the nature of the lattice vibrations in the Debye approximation. This type of relaxation process has been observed below 20 K in tetramethylammonium hydrogen bis-trichloroacetate for the 35Cl T1 -1 . Below 20 K the NQR frequency in the same crystal reveals a T4 temperature dependence due to the induced modulations of the vibrational and librational coordinates by the low-frequency acoustic phonons.

Erratum: Evidence of two-phonon vibronic progressions in layered3dmetal dihalides

Experimental evidence of two-phonon vibronic progressions due to second-order linear electron-phonon interactions is obtained in Ni${\mathrm{Cl}}_{2}$ and Ni${\mathrm{Br}}_{2}$ crystals, by comparing the phonon structure observed in $^{3}A_{2}(F)\ensuremath{\rightarrow}^{1}E(D)$ transition with Raman data. The vanishing of the spin-dependent first-order electron-phonon interaction is shown to be a necessary condition for observing prominent second-order phonon structures in isoconfigurational crystal-field transitions. According to this rule we predict and discuss the appearance of second-order progressions in other $d$-metal layered compounds.

Evidence of two-phonon vibronic progressions in layered3d-metal dihalides

Experimental evidence of two-phonon vibronic progressions due to second-order linear electron-phonon interactions is obtained in Ni${\mathrm{Cl}}_{2}$ and Ni${\mathrm{Br}}_{2}$ crystals, by comparing the phonon structure observed in $^{3}A_{2}(F)\ensuremath{\rightarrow}^{1}E(D)$ transition with Raman data. The vanishing of the spin-dependent first-order electron-phonon interaction is shown to be a necessary condition for observing prominent second-order phonon structures in isoconfigurational crystal-field transitions. According to this rule we predict and discuss the appearance of second-order progressions in other $d$-metal layered compounds.

Raman scattering from electronic excitations and phonons in paramagnetic and antiferromagnetic CoBr2

The Raman spectrum of CoBr2 has been measured over the energy range 0 to 1200 cm-1 at temperature above and below the Neel temperature. Spectral features due to first-order scattering from phonons and Co2+ electronic excitations are analysed and assigned to symmetry species. Unusual temperature-dependent electron-phonon coupling was discovered in the 250 cm-1 region of the spectrum and interpreted as arising from Fermi-type resonance between a two-phonon combination band a nearby electronic excitation. Weaker features associated with second-order phonon scattering have been identified together with magnon-phonon and magnon-exciton combination bands. Various models were used to describe the Co2+ electronic levels with the 4T1g(4F) manifold. A complete 3d7 calculation and an effective Hamiltonian model in second order produced the best results and gave equally good agreement with experiment. However, these models differed in their predictions of the ground manifold g-values and present experimental results favour the d7 model. Electronic energy levels in antiferromagnetically ordered CoBr2 are accurately predicted by a one-parameter molecular-field model based upon eigenvectors obtained from the full d7 analysis.

A quantum field theoretic formulation of Raman spectral line shapes

The Raman spectrum of a solid is formulated using quantum field theory. The photons are assumed to couple via localised electronic states, e.g. paramagnetic impurities. The laser is assumed to be of low power and to have a frequency well away from any electronic resonance. It is shown that the phonon-induced shift and width of each of the lines corresponding to an electronic transition, a first-order phonon line, and a vibronic transition is formally the same whether the transition is studied by absorption or by Raman spectroscopy. Width and shift contributions are given to second order in broadening interactions for the second-order phonon Raman spectrum. These results exhibit complications in some attempts to compare broadening parameters in different experiments. Some consequential adjustments to formulations of the spectrum of resonance fluorescence are suggested.

Electronic structure of metals. III. Properties of the lattice and of electron transport

For pt.II see ibid., vol.5, p.1849 (1975). The use of an energy-independent model pseudopotential, developed using a low-order pseudopotential perturbation theory (see part I) is extended to (i) first-principles calculation of second-order elastic constants and phonon spectra of the alkali metals employing a number of widely used exchange-correlation factors, F(q), of the electron gas and (ii) the derivation of a more reliable expression for a pseudopotential calculation of electrical resistivities of solid simple metals. Then, the authors consider a possible error from the omission of higher-order perturbation corrections and analyse the calculated results.

Second-order self-consistent phonon theories

In this paper we study the second order equations of self-consistent phonon theory, in the high temperature limit. The model we examine assumes (12−6) Mie-Lennard-Jones forces between nearest neighbors only. If we chose potential parameters appropriate for solid Ar, we find no self-consistent solutions of the equations. For potential parameters appropriate for solid Xe, solutions for the second order self-consistent equations exist up to about 80°K only. In this case we calculate the specific heat at constant volume and find very large corrections to the renormalized harmonic approximation and to the Improved Self-Consistent Phonon Theory. We conjecture that the linked cluster expansion of Choquard diverges and that his second order theory has no useful range of convergence. Alternative formulations of self-consistent phonon theory, such as Horner’s may avoid these problems.

Second-Order Raman Spectra and Phonon Dispersion in GaP

The second-order Raman spectrum of GaP has been investigated experimentally. The experiments were performed on oriented single crystals at both 300 and 77 °K. A critical point analysis of the data has been carried out with the aid of the polarization selection rules. The resulting frequencies are also consistent with a theoretical model which in turn is used to calculate the phonon dispersion throughout the Brillouin zone. The one- and two-phonon density of states and the specific heat have also been calculated and compared to our spectra and available specific heat data. The calculated quantities have also been compared to similar quantities obtained from neutron scattering experiments. This comparison provides information on the accuracy and reliability of phonon dispersion curves obtained from Raman scattering experiments.

Second-order Raman spectra and phonon spectrum of LiD

The second-order Raman spectra of LiD are studied at room and liquid nitrogen temperatures. These spectra are such that they can be compared with the temperature weighted two-phonon density of states to get information on phonons throughout the first Brillouin zone. This comparison is used to supplement the neutron scattering results to formulate a very good deformation dipole model for the lattice dynamics of LiD.

Infrared Absorption and Raman Scattering by Two-Magnon Processes in NiO

Strong two-magnon ($2M$) Raman scattering has been observed from NiO along with first- and second-order phonon scattering. The shape of the $2M$ scattering peak is well described by a simple-cubic Green's function for interacting spin waves with an intersublattice exchange ${J}_{2}$ = 148 ${\mathrm{cm}}^{\ensuremath{-}1}$. The temperature shift of the scattering peak is identical to that of the 2000-${\mathrm{cm}}^{\ensuremath{-}1}$ ir absorption peak described by Newman and Chrenko, but energy considerations require the absorption peak to be a phonon sideband of the $2M$ scattering peak, which is not seen in absorption.

A theoretical study of the lattice dynamics of neon and its isotopes

We present a computationally tractable version of Choquard's second-order self-consistent phonon theory and apply it by calculating selected thermodynamic properties of crystalline natural Ne and Ne22 using a Mie-Lennard-Jones nearest-neighbor central force. The model, which is shown to retain the leading correction to the first-order self-consistent theory, gives a quantitative account of the thermodynamics except near the melting point.