Vibrational Anisotropy Research Articles

Interpretation of the Cu K-edge EXAFS spectra of Cu3N using ab initio molecular dynamics

Cubic copper nitride (Cu3N) has anti-perovskite structure, and its properties are strongly affected by anisotropic thermal vibrations of copper atoms. Ab initio molecular dynamics (AIMD) simulations were performed in the temperature range from 300 K to 700 K in order to probe the details of Cu3N lattice dynamics. The Cu K-edge extended X-ray absorption fine structure (EXAFS) spectrum of bulk Cu3N was used to validate AIMD simulations at 300 K. The AIMD results suggest strong anharmonicity of the Cu–N and Cu–Cu bonds, the rigidity of NCu6 octahedra and strong correlation in atomic motion within –N–Cu–N– atom chains as well as support anisotropy of copper thermal vibrations.

Highly In-Plane Anisotropic 2D GeAs2 for Polarization-Sensitive Photodetection.

Due to the intriguing anisotropic optical and electrical properties, low-symmetry 2D materials are attracting a lot of interest both for fundamental studies and fabricating novel electronic and optoelectronic devices. Identifying new promising low-symmetry 2D materials will be rewarding toward the evolution of nanoelectronics and nano-optoelectronics. In this work, germanium diarsenide (GeAs2 ), a group IV-V semiconductor with novel low-symmetry puckered structure, is introduced as a favorable highly anisotropic 2D material into the rapidly growing 2D family. The structural, vibrational, electrical, and optical in-plane anisotropy of GeAs2 is systematically investigated both theoretically and experimentally, combined with thickness-dependent studies. Polarization-sensitive photodetectors based on few-layer GeAs2 exhibit highly anisotropic photodetection behavior with lineally dichroic ratio up to ≈2. This work on GeAs2 will excite interests in the less exploited regime of group IV-V compounds.

Vacuum ultraviolet photodissociation dynamics of N2O via the C1Π state: The N(2Dj=5/2, 3/2) + NO(X2Π) product channels.

We study the vacuum ultraviolet photodissociation dynamics of N2O via the C1Π state by using the time-sliced velocity map ion imaging technique. Images of N(2Dj=5/2, 3/2) products from the N atom elimination channels were acquired at a set of photolysis wavelengths from 142.55 to 148.19 nm. Vibrational states of the NO(X2Π) co-fragments were partially resolved in experimental images. From these images, the product total kinetic energy release distributions (TKERs), branching ratios of the vibrational states of NO(X2Π) co-fragments, and the vibrational state specific angular anisotropy parameters (β) have been determined. Notable features were found in the experimental results: the TKERs show that the NO(X2Π) co-fragments are highly vibrationally excited. For the highly vibrationally excited state of NO(X2Π), a bimodal rotational structure is found at all the studied photolysis wavelengths. Furthermore, the vibrational state specific β values of both spin-orbit channels (j = 3/2, 5/2) clearly show a monotonic decrease as the vibrational quantum number of NO(X2Π) increases. These observations suggest that multiple dissociation pathways play a role in the formation of the N(2Dj=5/2, 3/2) + NO(X2Π) products: one corresponds to a fast dissociation pathway through the linear state (the C1Π state) following the initial excitation to a slightly bent geometry in the vicinity of the linear C1Π configuration, leading to the low rotationally excited components with relatively large β values; the other corresponds to a relatively slow dissociation pathway through the bent C(31A') or C(31A″) state, leading to moderately rotationally excited NO(X2Π) products with smaller β values.

Influence of interfaces on the phonon density of states of nanoscale metallic multilayers: Phonon confinement and localization

Isotope-selective $^{57}\mathrm{Fe}$ nuclear resonant inelastic x-ray scattering (NRIXS) measurements and atomic-layer resolved density functional theory (DFT) calculations were used to investigate the effect of interfaces on the vibrational (phonon) density of states (VDOS) of (001)-oriented nanoscale Fe/Ag and Fe/Cr multilayers. The multilayers in the experiment contained isotopically enriched $^{57}\mathrm{Fe}$ monolayers as probe layers located either at the Fe/Ag or Fe/Cr interfaces or in the center of the Fe films. This allows probing of the vibrational dynamics of Fe sites either at the buried interfaces or in the center of the Fe films. For Fe/Ag multilayers, distinct differences were observed experimentally between the Fe-partial VDOS at the interface and in the center. At the Fe/Ag interface, the high-energy longitudinal-acoustic (LA) phonon peak of Fe near $\ensuremath{\sim}35$ meV is suppressed and slightly shifted to lower energy, and the low-energy part of the VDOS below $\ensuremath{\sim}20$ meV is drastically enhanced, as compared to the Fe-specific VDOS in the center Fe layers or in bulk Fe. Similar phenomena are found to a less degree in the Fe/Cr multilayers. The measured Fe-partial VDOS was used to determine the Fe site-selective vibrational thermodynamic properties of the multilayers. Our theoretical findings for the layer-dependent VDOS of the multilayers are in qualitative agreement with the experimental results obtained by NRIXS. For Fe/Ag multilayers, which are characterized by a large atomic mass ratio, the experimental and theoretical results demonstrate phonon confinement in the Fe layers and phonon localization at the Fe/Ag interfaces due to the energy mismatch between Ag and Fe LA phonons. These phenomena are reduced or suppressed in the Fe/Cr multilayers with their about equal atomic masses. Moreover, direction-projected Fe VDOS along the (nearly in-plane) incident x-ray beam was computed in order to address the intrinsic vibrational anisotropy of the Fe/Ag multilayer. We have also performed spin-resolved electronic band structure (DFT) calculations, predicting an enhanced magnetic moment $({\ensuremath{\mu}}_{\mathrm{Fe}}=2.8\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}})$ of the interfacial Fe atoms and a high electron spin polarization (79%) at the Fermi energy for the Fe/Ag interface, as compared to the case of Fe center layers. This is a result of charge transfer from Fe to Ag at the interface. On the contrary, Cr tends to donate electrons to Fe, thus reducing the interfacial Fe moment $({\ensuremath{\mu}}_{\mathrm{Fe}}=1.9\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}})$. This implies strong chemical bonding at the Fe/Ag and Fe/Cr interfaces, affecting the interfacial VDOS.

How Does a Heme Carbene Differ from Diatomic Ligated (NO, CO, and CN-) Analogues in the Axial Bond?

Compared to well studied diatomic ligands (NO, CN-, CO), the axial bonds of carbene hemes is much less known although its significance in biological chemistry. The unusually large quadrupole splitting (Δ EQ = +2.2 mm·s-1) and asymmetric parameter (η = 0.9) of the five-coordinate heme carbene [Fe(TTP)(CCl2)], which is the largest among all known low spin ferrohemes, has driven investigations by means of Mössbauer effect Nuclear Resonance Vibrational Spectroscopy (NRVS). Three distinct measurements on one single crystal (two in-plane and one out-of-plane) have demonstrated comprehensive vibrational structures including stretch (429) and bending modes (472 cm-1) of the axial Fe-CCl2, and revealed iron vibrational anisotropy in three orthogonal directions for the first time. Frontier orbital analysis especially comparisons with diatomic analogues (NO, CN-, CO) suggest that CCl2, similar to NO, has led to strong but anisotropic π bonding in a ligand-based "4C"-coordinate which induced the vibrational anisotropies and very large Mössbauer parameters. This is contrasted to CN- and CO complexes which possess a porphyrin-based "4N"-coordinate electronic and vibrational structures due to inherent on-axis linear ligation.

Bond compressibility and bond Grüneisen parameters of CdTe

Extended x-ray absorption fine structure (EXAFS) at the Cd K edge and diffraction patterns have been measured on CdTe as a function of pressure from 100 kPa (1 bar) to 5 GPa using a cell with nano-polycrystalline diamond anvils and an x-ray focussing scanning spectrometer. Three phases—zincblende (ZB), mixed cinnabar-ZB and rocksalt (RS)—are well distinguished in different pressure intervals. The bond compressibility measured by EXAFS in the ZB phase is slightly smaller than the one measured by diffraction and decreases significantly faster when the pressure increases; the difference is attributed to the effect of relative vibrations perpendicular to the Cd–Te bond. The parallel mean square relative displacement (MSRD) decreases, the perpendicular MSRD increases when the pressure increases, leading to an increasing anisotropy of relative atomic vibrations. A constant-temperature bond Grüneisen parameter (GP) has been evaluated for the ZB phase and compared with the constant-pressure bond GP measured in a previous experiment; an attempt is made to connect the bond GPs measured by EXAFS and the more familiar thermodynamic GP and mode GPs; the comparisons suggest the inadequacy of the quasi-harmonic approximation to deal with the local vibrational properties sampled by EXAFS.

2D GeP: An Unexploited Low-Symmetry Semiconductor with Strong In-Plane Anisotropy.

Germanium phosphide (GeP), a new member of the Group IV-Group V compounds, is introduced into the fast growing 2D family with experimental and theoretical demonstration of strong anisotropic physical properties. The indirect band gap of GeP can be drastically tuned from 1.68 eV for monolayer to 0.51 eV for bulk, with highly anisotropic dispersions of band structures. Thin GeP shows strong anisotropy of phonon vibrations. Moreover, photodetectors based on GeP flakes show highly anisotropic behavior with anisotropic factors of 1.52 and 1.83 for conductance and photoresponsivity, respectively. This work lays the foundation and ignites future research interests in Group IV-Group V compound 2D materials.

Photodissociation Dynamics of Nitrous Oxide near 145 nm: The O(1S0) and O(3P J=2,1,0) Product Channels.

We report the study of photodissociation dynamics of nitrous oxide in the vacuum ultraviolet region, using the time-sliced velocity map ion imaging technique. Ion images of the O(1S0) and O(3P J=2,1,0) products were measured at nine photolysis wavelengths from 142.55 to 148.79 nm. The product channels O(1S0) + N2(X1Σg+) and O(3P J=2,1,0) + N2(A3Σu+) have been observed. For these dissociation channels, the total kinetic energy releases of the dissociated products were acquired. With vibrational structures of the N2 coproducts partially resolved in the experimental images, the branching ratios of different vibrational states of the N2 coproducts were determined, and the vibrational state specific anisotropy parameters (β values) were derived. Analysis shows that the O(1S0) + N2(X1Σg+) channel is primarily formed via nonadiabatic couplings between the C (1Π) state and the higher-lying D (1Σ+) state of the N2O. A moderate rotational excitation and high vibrational excitation of N2(X1Σg+) products have been observed through this pathway. On the other hand, for the O(3P J=2,1,0) + N2(A3Σu+) channels, where a slightly higher rotational excitation of N2 coproducts have been observed, the possible pathway would be via nonadiabatic couplings from the C (1Π) state to the lower-lying A(1Σ-)state.

First-principles momentum distributions and vibrationally corrected permittivities of hexagonal and cubic ice

Three-dimensionally resolved proton momentum distributions and end-to-end distributions have been calculated for hexagonal and cubic water ice. First-principles quantum nuclear wave functions have been used to investigate the impact of vibrational anisotropy, anharmonicity, proton and stacking disorder, temperature, and pressure on these distributions. Moreover, the effects of vibrations on the electronic density in hexagonal ice are shown to lead to a 5% vibrational correction with respect to the static-lattice optical permittivity, and proton disorder is found to be crucial in explaining its experimentally observed temperature dependence.

Ultrafast Transmission Modulation and Recovery via Vibrational Strong Coupling

Strong coupling between vibrational modes and cavity optical modes leads to the formation of vibration-cavity polaritons, separated by the vacuum Rabi splitting. The splitting depends on the square root of the concentration of absorbers confined in the cavity, which has important implications on the response of the coupled system after ultrafast infrared excitation. In this work, we report on solutions of W(CO)6 in hexane with a concentration chosen to access a regime that borders on weak coupling. Under these conditions, large fractions of the W(CO)6 oscillators can be excited, and the anharmonicity of the molecules leads to a commensurate reduction in the Rabi splitting. We report excitation fractions > 0.4, depending on excitation pulse intensity, and show drastic increases in transmission that can be modulated on the picosecond time scale. In comparison to previous experiments, the transient spectra that we observe are much simpler because excited-state transitions lie outside of the transmission spectrum of the cavity, thereby contributing only weakly to the spectra. We find that the Rabi splitting recovers with the characteristic vibrational relaxation lifetime and anisotropy decay of uncoupled W(CO)6, implying that polaritons are not directly involved in the relaxation we observe after the first few ps. The results help corroborate the model that we proposed to describe the results at higher concentrations and show that the ground-state bleach of cavity-coupled molecules has a broad, multisigned spectral response.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer.

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Isotropic Zero Thermal Expansion and Local Vibrational Dynamics in (Sc,Fe)F3.

Scandium fluoride (ScF3) exhibits a pronounced negative thermal expansion (NTE), which can be suppressed and ultimately transformed into an isotropic zero thermal expansion (ZTE) by partially substituting Sc with Fe in (Sc0.8Fe0.2)F3 (Fe20). The latter displays a rather small coefficient of thermal expansion of -0.17 × 10-6/K from 300 to 700 K. Synchrotron X-ray and neutron pair distribution functions confirm that the Sc/Fe-F bond has positive thermal expansion (PTE). Local vibrational dynamics based on extended X-ray absorption fine structure indicates a decreased anisotropy of relative vibration in the Sc/Fe-F bond. Combined analysis proposes a delicate balance between the counteracting effects of the chemical bond PTE and NTE from transverse vibration. The present study extends the scope of isotropic ZTE compounds and, more significantly, provides a complete local vibrational dynamics to shed light on the ZTE mechanism in chemically tailored NTE compounds.

Pressure-Induced Phase Transition in Weyl Semimetallic WTe2.

Tungsten ditelluride (WTe2 ) is a semimetal with orthorhombic Td phase that possesses some unique properties such as Weyl semimetal states, pressure-induced superconductivity, and giant magnetoresistance. Here, the high-pressure properties of WTe2 single crystals are investigated by Raman microspectroscopy and ab initio calculations. WTe2 shows strong plane-parallel/plane-vertical vibrational anisotropy, stemming from its intrinsic Raman tensor. Under pressure, the Raman peaks at ≈120 cm-1 exhibit redshift, indicating structural instability of the orthorhombic Td phase. WTe2 undergoes a phase transition to a monoclinic T' phase at 8 GPa, where the Weyl states vanish in the new T' phase due to the presence of inversion symmetry. Such Td to T' phase transition provides a feasible method to achieve Weyl state switching in a single material without doping. The new T' phase also coincides with the appearance of superconductivity reported in the literature.

Comparative studies of the cage systems ThFe2Al10 and UFe2Al10

We have grown single crystals of ThFe2Al10 and used them for the refinement of its crystal structure. From the specific heat data, we determined the phonon components, that is, the Debye and Einstein modes, for Th- and U-based isostructural aluminides. To approximate the Sommerfeld coefficients, we had to include the T3lnT term characteristic of spin-fluctuations originating from the Fe-sublattice. The roughly estimated spin-fluctuation temperature is about 11 K. ThFe2Al10 is a weakly temperature-dependent Pauli-paramagnet. However, at lower temperatures the ferromagnetic correlations are observed, which signals that the system drives to quantum criticality. The distinct minimum in electrical resistivity observed at about 20 K suggests a realization of a nonmagnetic two-channel Kondo-effect in ThFe2Al10, as discussed for ThAsSe [Phys. Rev. Lett. 94, 236603 (2005)], for example. The [ρ(T) – ρmin] versus T curves of ThFe2Al10, determined along the a- and c-axes, were used to subtract the phonon contributions from the corresponding ρ(T)a,c of UFe2Al10. The resulting magnetic part of the average ρm(T)av curve was then analysed in terms of the influence of the crystal field effect on the transport properties. However, to obtain agreement with the experiment, we had to take into account another effect, namely the Kondo-like one. This kind of probe has been applied for the first time in the case of uranium compounds. Based on the magnetoresistivity, we have revealed the anisotropic low-frequency vibrations of the Th atom (located in its [Al16Fe4] cage) interacting with the conduction band, the phenomenon revealed previously in the metallic UB12 [Phil. Mag. B 95, 2343 (2015)]. Furthermore, fully relativistic band structure calculations performed for ThFe2Al10 revealed its metallic-like character with a similarly large contribution of the Fe 3d electrons at the Fermi level as predicted previously for its 5f-electron analogue UFe2Al10. In addition, there are substantial differences between their Fermi surfaces.

Controlled Terahertz Birefringence in Stretched Poly(lactic acid) Films Investigated by Terahertz Time-Domain Spectroscopy and Wide-Angle X-ray Scattering.

We report a correlation between the dielectric property and structure of stretched poly(lactic acid) (PLA) films, revealed by polarization-sensitive terahertz time-domain spectroscopy and two-dimensional (2D) wide-angle X-ray scattering (WAXS). The experiments evidence that the dielectric function of the PLA film becomes more anisotropic with increasing draw ratio (DR). This behavior is explained by a classical Lorentz oscillator model assuming polarization-dependent absorption. The birefringence can be systematically altered from 0 to 0.13 by controlling DR. The combination of terahertz spectroscopy and 2D WAXS measurement reveals a clear correlation between the birefringence in the terahertz frequency domain and the degree of orientation of the PLA molecular chains. These findings imply that the birefringence is a result of the orientation of the PLA chains with anisotropic macromolecular vibration modes. Because of a good controllability of the birefringence, polymer-based materials will provide an attractive materials system for phase retarders in the terahertz frequency range.

Atomic-Resolution Transmission Electron Microscopic Movies for Study of Organic Molecules, Assemblies, and Reactions: The First 10 Years of Development

A molecule is a quantum mechanical entity. "Watching motions and reactions of a molecule with our eyes" has therefore been a dream of chemists for a century. This dream has come true with the aid of the movies of atomic-resolution transmission electron microscopic (AR-TEM) molecular images through real-time observation of dynamic motions of single organic molecules (denoted hereafter as single-molecule atomic-resolution real-time (SMART) TEM imaging). Since 2007, we have reported movies of a variety of single organic molecules, organometallic molecules, and their assemblies, which are rotating, stretching, and reacting. Like movies in the theater, the atomic-resolution molecular movies provide us information on the 3-D structures of the molecules and also their time evolution. The success of the SMART-TEM imaging crucially depends on the development of "chemical fishhooks" with which fish (organic molecules) in solution can be captured on a single-walled carbon nanotube (CNT, serving as a "fishing rod"). The captured molecules are connected to a slowly vibrating CNT, and their motions are displayed on a monitor in real time. A "fishing line" connecting the fish and the rod may be a σ-bond, a van der Waals force, or other weak connections. Here, the molecule/CNT system behaves as a coupled oscillator, where the low-frequency anisotropic vibration of the CNT is transmitted to the molecules via the weak chemical connections that act as an energy filter. Interpretation of the observed motions of the molecules at atomic resolution needs us to consider the quantum mechanical nature of electrons as well as bond rotation, letting us deviate from the conventional statistical world of chemistry. What new horizons can we explore? We have so far carried out conformational studies of individual molecules, assigning anti or gauche conformations to each C-C bond in conformers that we saw. We can also determine the structures of van der Waals assemblies of organic molecules, thereby providing mechanistic insights into crystal formation-phenomena of general significance in science, engineering, and our daily life. Whereas many of the single organic molecules in a vacuum seen by SMART-TEM are sufficiently long-lived for detailed studies, molecules with low ionization potentials (<6 eV) were found to undergo chemical reactions, for example, [60]fullerene and organometallic compounds possibly via a hole catalysis mechanism, where a radical cation of CNT generated under electron irradiation catalyzes the transformation via an electron transfer mechanism. Common organic molecules whose ionization potentials are much higher (>8 eV) than that of CNT (5 eV) remain stable for a time long enough for observation at 60-120 kV acceleration voltage, as they are not oxidized by the CNT radical cation. Alternatively, the reaction may have taken place via an excited state of a molecule produced by energy transfer from CNT possessing excess energy provided by the electron beam. SMART-TEM imaging is a simple approach to the study of the structures and reactions of molecules and their assemblies and will serve as a gateway to the research and education of the science connecting the quantum mechanical world and the real world.

Vibrational properties and stability of FePt nanoalloys

The structural and dynamical properties of FePt nanoparticles were studied within the density functional theory. The effect of size and chemical composition on dynamical stability of nanoparticles was investigated for the cuboctahedral and icosahedral symmetries. In cuboctahedra, the structural distortion is observed, which for systems with odd number of Pt layers leads to lowering of the tetragonal symmetry. Significant differences between the vibrational properties of FePt particles and bulk crystal is observed, but similarly to the FePt crystal, cuboctahedral particles exhibit a strong anisotropy of atomic vibrations. The icosahedral particles with perfect shell geometry are unstable due to enlarged distances between Fe atoms. They can be stabilized by removing a central atom or replacing it by a smaller one. The heat capacity and entropy of nanoparticles show typical enhancement due to low-energy vibrations at the surface layers.

Borates—Crystal Structures of Prospective Nonlinear Optical Materials: High Anisotropy of the Thermal Expansion Caused by Anharmonic Atomic Vibrations

In the present study the thermal structure evolution is reviewed for known nonlinear optical borates such as β-BaB2O4, LiB3O5, CsLiB6O10, Li2B4O7, K2Al2B2O7, and α-BiB3O6, based on single-crystal and powder X-ray diffraction data collected over wide temperature ranges. Temperature-dependent measurements of further borates are presented for the first time: α-BaB2O4 (295–673 K), β-BaB2O4 (98–693 K), LiB3O5 (98–650 K) and K2Al2B2O7 (98–348 K). In addition to the established criteria for nonlinear optical (NLO) properties of crystals, here the role of the anisotropy and anharmonicity of the thermal vibrations of atoms is analysed as well as changes in their coordination spheres and the anisotropy of the thermal expansion of the crystal structure. Non-centrosymmetric borates, especially those that have NLO properties, often show distinct anisotropies for each cation in comparison to centrosymmetric borates. All considered NLO borates contain BO3 triangles, which are the principal cause of the strong anisotropy of the thermal expansion.

Thermal disorder and correlation effects in anti-perovskite-type copper nitride

Reverse Monte Carlo simulations coupled with evolutionary algorithm were employed for the analysis of the temperature dependent (10–300 K) Cu K-edge extended X-ray absorption fine structure (EXAFS) spectra of polycrystalline copper nitride (Cu3N) with the goal to extract information on the thermal disorder and interatomic correlations in anti-perovskite-type crystal lattice. The obtained results are discussed in comparison with metallic copper and perovskite-type rhenium trioxide. The analysis of EXAFS spectra suggests that the anisotropy of copper atom vibrations is significantly enhanced upon increasing temperature, leading to pronounced tilting motion of NCu6 octahedra. Strong correlation in the motion of atoms was found along –N–Cu–N– atomic chains but it reduces rapidly with an increase of interatomic distance. Finally, anticorrelated motion of neighboring Cu atoms occurs along Cu–Cu bonds and is consistent with breathing-type motion of NCu6 octahedra.

Lattice dynamics and thermal transport in multiferroicCuCrO2

Inelastic neutron and x-ray scattering measurements of phonons and spin waves were performed in the delafossite compound ${\mathrm{CuCrO}}_{2}$ over a wide range of temperature, and complemented with first-principles lattice dynamics simulations. The phonon dispersions and density of states are well reproduced by our density functional calculations, and reveal a strong anisotropy of Cu vibrations, which exhibit low-frequency modes of large amplitude parallel to the basal plane of the layered delafossite structure. The low frequency in-plane modes also show a systematic temperature dependence of neutron and x-ray scattering intensities. In addition, we find that spin fluctuations persist above 300 K, far above the N\'eel temperature for long-range antiferromagnetic order, ${T}_{N}\ensuremath{\simeq}24\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Our modeling of the thermal conductivity, based on our phonon measurements and simulations, reveals a significant anisotropy and indicates that spin fluctuations above ${T}_{N}$ constitute an important source of phonon scattering, considerably suppressing the thermal conductivity compared to that of the isostructural but nonmagnetic compound ${\mathrm{CuAlO}}_{2}$.