Magnetic excitations in solids

This article presents a review of low to moderate frequency magnetic excitations, termed magnons or spin waves, in magnetically ordered materials. The emphasis is on intuitive behavior rather than analytical theory. Topics include spin waves, magnetostatic modes, dipole-exchange modes, surface anisotropy, dispersion properties, nonlinear effects, and relaxation. These phenomena are illustrated with experimental examples based on magnon light scattering results as well as conventional microwave techniques.     

Femtosecond spectroscopy of optical excitations in single-walled carbon nanotubes: evidence for exciton-exciton annihilation

Frequency-resolved femtosecond transient absorption spectra and kinetics measured by optical excitation of the second and first electronic transitions of the (8,3) single-walled carbon nanotube species reveal a unique mutual response between these transitions. Based on the analysis of the spectra, kinetics, and their distinct amplitude dependence on the pump intensity observed at these transitions, we conclude that these observations originate from both the excitonic origin of the spectrum and nonlinear exciton annihilation.     

Ga-NMR study of the low-energy excitations in

We report the results of ⁶⁹Ga- and ⁷¹Ga-NMR measurements on NdGa₂ at temperatures between 0.1 and and in applied magnetic fields between zero and 74 kOe. NdGa₂ orders antiferromagnetically below and undergoes several metamagnetic transitions in external magnetic fields. In zero applied magnetic field and below the temperature dependence of the spin-lattice relaxation rate T1 ^-1 ( T ) shows a large linear-in-T term, about two orders of magnitude higher than for the reference compound LaGa₂. This strong enhancement confirms the presence of low-energy excitations in the antiferromagnetic phase of NdGa₂ as was previously indicated by specific heat data. Above , T1 ^-1 ( T ) is dominated by an exponential term, which we associate with excitations between the lowest energy levels of the f-electron system. The separation of these energy levels is determined by exchange, crystal-field and Zeeman interactions. Received 3 September 1998 and Received in final form 3 November 1998     

Attenuation lengths of low-energy electrons in solids

A compilation is presented of measured attenuation lengths of low-energy electrons in solids in the energy range (40 to 2000 eV) normally employed in X-ray photoelectron and Auger-electron spectroscopy. The techniques used to obtain electron attenuation lengths are summarized, and it is pointed out that the accuracy of measurement needs both to be defined adequately and to be improved for more meaningful intercomparisons of data and theory. An approximate expression is derived to predict attenuation lengths using either dielectric data (derived from optical or electron-energy-loss data) or average excitation energies estimated from electron binding energies for given materials at electron energies greater than about 500 eV. Good agreement is found between the predictions of this formula and some measured attenuation lengths (e.g. for Al, C, Mo, W) but further work is required to validate the formula and to extend it to lower electron energies.     

Femtosecond mechanisms of electronic excitations in crystalline materials

The lattice dynamics of crystals is investigated in the course of high-power electronic excitation. It is revealed that, at W _e < W _eo , atoms and ions are displaced from their regular sites for 100–300 fs. Subsequent relaxation of the crystal lattice in response to a strong local electric field induced by the collisional displacement of ions occurs for 10–50 ns in an oscillatory manner with a period of 0.5–1.5 ps.     

Entanglement of low-energy excitations in conformal field theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Rényi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Rényi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.     

Reflection of low-energy hydrogen from solids

The Monte Carlo Simulation Program TRIM is used to calculate particle and energy reflection coefficients as well as energy and angular distributions of reflected H, D, and T. To account for binding effects at the target surface a planar potential is applied. This binding potential reduces the reflection below an energy of a few eV.     

Universality of anomalous excitations in amorphous solids

A general proof for the universal existence of anomalous, non-Debye harmonic excitations in disordered solids is proposed. Starting from an ideal amorphous solid with fixed mean positions of all atoms and harmonic interactions, it was demonstrated that any increase of disorder leads stringently to an increase of the spectral density for low (and also very high) frequencies. That means, the density of states shows additional contributions to the low-frequency part of the standard Debye density, even though the wavelength of corresponding phonon like excitations is of an order of magnitude on which the amorphous solid is still homogeneous and the sound waves are not strongly effected by the disorder.     

Hidden order and low-energy excitations in NpO2

We investigate the nature of the hidden order parameter in the ordered phase of NpO2, which had been identified with a staggered arrangement of Gamma5 magnetic multipoles. By analyzing the existing experimental data, we show that the most likely driving order parameter is not provided by octupoles, as usually assumed, but rather by the rank-5 triakontadipoles. Calculations of the coupled dynamics of spins, Gamma5 quadrupoles, and Gamma5 triakontadipoles in the ordered phase enable us to analyze the resulting structure of low-energy excitations. We show that the powder inelastic neutron scattering cross section should contain, in addition to the already-observed peak at 6.5 meV, a second weaker peak at about 14 meV.     

Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified. Received 14 August 2000     

On the computation of electronic excitations in solids

An approximation scheme is proposed for calculating electronic excitations in solids. It is described within a projection operator formalism of the Mori-Zwanzig type. The approximation consists in successively limiting the space of dynamical variables which are treated. The selection of the variables is done by making use of the local character of the correlation hole which is surrounding an electron. The method is distinct from a perturbation expansion and can be related to a variational ansatz via the Sauermann functional. The computation of the spectral density of the Green's function is reduced to the diagonalization of matrices. Their dimension depends on the required degree of accuracy of the calculations. The present method can be considered as an extension to excited states of a previously developed. Local Approach for ground state calculations.Dedicated to Prof. S. Methfessel on the occasion of his 60th birthday     

Collective low-energy excitations of two-level tunnelling defects in mixed crystals

The dynamics of strongly interacting two-level tunnelling defects in mixed crystals as KCl: Li is investigated in the framework of Mori's projection method. Applying a mode-coupling scheme on the memory functions and performing the average over the random defect configuration in a mean-field type approximation, the ensueing self-consistent equations can be solved analytically. At low concentration this solution coincides with the exact dynamics of the pair model, whereas for higher concentration the motional spectrum shows several novel features. In particular we find a strong relaxation peak and a characteristic two-peak structure for the density of states; there is an additional feature at energies far below the bare tunnelling amplitude which accounts well for several experiments indicating the existence of such low-energy states.     

Femtosecond stimulated Raman spectroscopy

Advances in the field of Femtosecond Stimulated Raman Spectroscopy (FSRS), a new time‐resolved structural technique that provides complete vibrational spectra on the ultrafast timescale, are reviewed. When coupled with a femtosecond optical trigger, the time evolution of a reacting species can be monitored with unprecedented <25 femtosecond temporal and 5 cm^‐1 spectral resolution. New technological and theoretical advances including the development of tunable FSRS and a background‐free FSRS format are discussed. The most recent experimental studies focus on ultrafast reaction dynamics in electronically excited states: isomerization in cyanobacterial phytochrome, ultrafast spin flipping in a solar cell sensitizer, and excited state proton transfer in green fluorescent protein. The use of FSRS to directly map multidimensional reactive potential energy surfaces and to probe the mechanism of reactive internal conversion is prospectively discussed.     

Vacancy-induced low-energy excitations in the one-dimensional ionic conductor β-eucryptite

We have measured the specific heat C of β-Li_xAl_xSi_2?xO₄ (β-eucryptite) for x = 1 and 0.93 between 0.1 and 2.5 K. Below 1 K, an anomaly is observed in C which exhibits a maximum at 0.6 K. This anomaly is enhanced by a factor of 10 in the substoichiometric sample. These results are interpreted in the Frenkel-Kontorova model of configurational excitations which arise in this material because of vacancies in the ion channels. Below 0.5 K a time dependence of the specific heat is observed which hints at rather slow dynamics of the configurational excitations.     

Frequency-comb-referenced molecular spectroscopy in the mid-infrared region

A simple method for absolute-frequency measurements of molecular transitions in the mid-IR region is reported. The method is based on a cw singly resonant optical parametric oscillator (SRO), which is tunable from 3.2 to 3.45?μm. The mid-IR frequency of the SRO is referenced to an optical frequency comb through its pump and signal beams. Sub-Doppler spectroscopy and absolute-frequency measurement of the P(7) transition of the ν3 band of CH4 are demonstrated.     

Infrared spectroscopy of solids

For materials like small gap semiconductors or intercalated layered compounds the general form of the complex dielectric function is: ϵ(ω) = ϵ_x + Δϵ_inter + Δϵ_intra + Δϵ_ph, where ϵ_∞is the high frequency dielectric constant due to all interband transitions except the uppermost valence band and the lowest conduction band, Δϵ_inter is the contribution to the dielectric constant due to this two bands in particular, Δϵ_intra is the contribution due to intraband free carrier transitions and Δϵ_ph is the contribution due to lattice vibrations. The contribution from transitions between valence and conduction bands to the imaginary part of the dielectric function Δϵ_inter(ω,T) for a narrow gap material can be readily calculated in the random phase approximation (RPA) formalism. The real part Δϵ_inter is obtained by performing the Kramers-Kronig inversion on the expression Δϵ_inter. Dielectric function of HgTe between 8 and 300 K is discussed. The interband contribution to the complex dielectric function in a layered intercalation compound is also examined. Pure graphite, first and second stage compounds are treated as an example. Reflectivity and magnetoreflectivity spectra simultaneously determining the plasma and the cyclotron frequencies, allow one to measure the free carrier density, hence the Fermi level, and the effective mass of the carriers. The variation of the effective mass as a function of the position of the Fermi level traces the energy bands dispersion relation. An example of such investigations is given for PbSe layered materials like Bi₂Se₃ are also studied by infrared reflectivity spectroscopy. Intercalation of such materials increases the free carrier population which consequently moves the Fermi level up in the conduction band. Analysis of reflectivity spectra allows an accurate determination of the free carrier concentration and gives a useful tool for the investigation of atom insertion in layered materials. Recent experiments on the intercalation of Li in a certain number of layered materials will be presented. In the frame of the classical theory of independent harmonic oscillators, the phonon contribution to the dielectric function is given by the sum of transverse modes for each oscillator with the corresponding damping parameters and oscillator strength. The complex dielectric function can then be written as a set of separate equations for the real and imaginary parts of the wave-number-dependent dielectric function. In the spectral region when phonon and plasmon frequencies may coincide a strong plasmon-phonon coupling will be experienced. In a simple model with one LO and one TO frequency, one expects two singularities at the two maxima of the function 1m −ϵ⁻¹; representing longitudinal modes. The frequencies generally labeled ω₊ and ω_- correspond to longitudinal oscillations with the lattice and electron plasma vibrating, respectively, in phase and 180° out of phase. In small gap materials the situation is more complex. Because of the particular band structure, the contribution Δϵ_inter(ω) must be included. In some cases it also becomes necessary to include additional oscillators with strong polar character corresponding to a particular defect or to additional vibrations. The implications of all these fundamental concepts in the investigation of high Tc materials is discussed and examples given.