We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of SiO 2 . The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal (α-quartz). This, however, holds when comparing a lower-density glass to a higherdensity crystal. For glassy and crystalline polymorphs with matched densities, the DOS of the glass appears as the smoothed counterpart of the DOS of the corresponding crystal; it reveals the same number of the excess states relative to the Debye model, the same number of all states in the low-energy region, and it provides the same specific heat. This shows that glasses have higher specific heat than crystals not due to disorder, but because the typical glass has lower density than the typical crystal. DOI: 10.1103/PhysRevLett.112.025502 PACS numbers: 63.20.-e, 07.85.-m, 76.80.+y The low-temperature thermodynamic properties of glasses are accepted to be anomalously different from those of crystals due to the inherent disorder of the glass structure. At temperatures of ∼10 K, the specific heat of glasses shows an excess relativetothatofthecorrespondingcrystals.Theexcessspecific heat is related to a distinct feature in the spectrum of the atomic vibrations: At frequencies of ∼1 THz, glasses exhibit an excess of states above the Debye level of the acoustic waves, the socalled "boson peak." The excess of specific heat and the boson peak are universally observed for all glasses and by all relevant experimental techniques. However, the results still do not converge to a unified answer to how disorder causes these anomalies.Themajorityofthemodelsexplainthebosonpeakbyappealing tovarious glass-specific features. Theseincludelow-energy optical modes [1], onset of mechanical instability related to saddle points in the energy landscape [2] or to jamming [3][4][5], local vibrationalmodes of clusters [6] or locally favoured structures [7], librations [8] or other coherent motions [9] of molecular fragments, crossover of local and acoustic modes [10], quasilocal vibrations of atoms in an anharmonic potential [11], broadening of vibrational states in the Ioffe-Regel crossover regime [12], spatial variation of the elastic moduli [13], breakdown of the continuum approximation [14,15], and topologically diverse defects [16], to cite the most important ones.Alternatively, the boson peak is identified as the counterpart of the acoustic van Hove singularities of crystals, i.e., explained by the piling up of the vibrational states of the acousticlike branches near the boundary of the pseudoBrillouin zone [17][18][19][20].Diverging in explanations of the boson peak, all models agree that the excess states and the excess specific heat of

The vibrational dynamics of a permanently densified silica glass is compared to the one of an -quartz polycrystal, the silica polymorph of the same density and local structure. The combined use of inelastic x-ray scattering experiments and ab initio numerical calculations provides compelling evidence of a transition, in the glass, from the isotropic elastic response at long wavelengths to a microscopic regime as the wavelength decreases below a characteristic length of a few nanometers, corresponding to about 20 interatomic distances. In the microscopic regime the glass vibrations closely resemble those of the polycrystal, with excitations related to the acoustic and optic modes of the crystal. A coherent description of the experimental results is obtained assuming that the elastic modulus of the glass presents spatial heterogeneities of an average size a $ =2. DOI: 10.1103/PhysRevLett.110.185503 PACS numbers: 63.50.Lm, 62.30.+d, 62.65.+k, 64.70.ph Amorphous solids lack the long-range translational periodicity of crystalline materials. Nevertheless, their structure presents a residual order on the short and medium ranges [1]. At short distances the structure can be characterized in terms of interatomic distances and bond-angles distribution. The medium-range order extends typically over a length D $ 2=ÁQ 0 of a few ($ 5) interatomic distances, as indicated by the width ÁQ 0 of the first sharp diffraction peak in the static structure factor, SðQÞ. The length scale of the nanometer is believed to be the relevant one to understand the phenomenology of the glass transition. In fact, close to the dynamical arrest, the atomic motion of a supercooled liquid is characterized by nanometer-sized regions where the molecules move cooperatively [2][3][4][5][6][7]. Recent numerical simulation studies [8][9][10] have also given some evidence of the presence of static correlation lengths of a size comparable to the dynamical correlations, by investigating either subtle structural order parameters [8] or point to set correlations [9,10]. However these quantities are not easily accessible experimentally, because they are not revealed by standard two-points correlation functions, such as the SðQÞ. Thereby a detailed description of the medium-range order in glasses is still missing.Only recently, the development of new experimental probes has given some evidence of the presence of atomic regions of nanometric size in a few amorphous materials. Local symmetries in a colloidal suspension have been detected by means of a cross correlation analysis using coherent x rays [11]. Subnanoscale-ordered regions originating from atomic polyhedra have also been detected in a metallic glass employing an electron nanoprobe supported by an ab initio molecular dynamics simulation [12]. On a similar glass a wide spatial distribution of the elastic modulus, on the length scale of the nanometer, has been detected by means of atomic force acoustic microscopy [13]. Here we employ an alternative way to gather information on the structure of the canon...

We present a model of the lattice dynamics of the rare-earth titanate pyrochlores R 2 Ti 2 O 7 (R = Tb, Dy, Ho), which are important materials in the study of frustrated magnetism. The phonon modes are obtained by density functional calculations, and these predictions are verified by comparison with scattering experiments. Single crystal inelastic neutron scattering is used to measure acoustic phonons along high symmetry directions for R = Tb, Ho; single crystal inelastic x-ray scattering is used to measure numerous optical modes throughout the Brillouin zone for R = Ho; and powder inelastic neutron scattering is used to estimate the phonon density of states for R = Tb, Dy, Ho. Good agreement between the calculations and all measurements is obtained, allowing confident assignment of the energies and symmetries of the phonons in these materials under ambient conditions. Knowledge of the phonon spectrum is important for understanding spin-lattice interactions, and can be expected to be transferred readily to other members of the series to guide the search for unconventional magnetic excitations.

Inelastic X-ray scattering with meV energy resolution (IXS) is an ideal tool to measure collective excitations in solids and liquids. In non-resonant scattering condition, the cross-section is strongly dominated by lattice vibrations (phonons). However, it is possible to probe additional degrees of freedom such as magnetic fluctuations that are strongly coupled to the phonons. The IXS spectrum of the coupled system contains not only the phonon dispersion but also the so far undetected magnetic correlation function. Here we report the observation of strong magnon–phonon coupling in LiCrO2 that enables the measurement of magnetic correlations throughout the Brillouin zone via IXS. We find electromagnon excitations and electric dipole active two-magnon excitations in the magnetically ordered phase and heavily damped electromagnons in the paramagnetic phase of LiCrO2. We predict that several (frustrated) magnets with dominant direct exchange and non-collinear magnetism show surprisingly large IXS cross-section for magnons and multi-magnon processes.