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The observation of unexpected polarisation textures such as vortices, skyrmions and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180{\deg} domain walls of PbTiO3 have recently been reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquitous nature of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarisation in the 180{\deg} domain walls in PbTiO3/SrTiO3 superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centres of the 180{\deg} domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves further attention.

We experimentally determine the lattice dynamics of black phosphorus layered crystals through a combination of x-ray diffuse scattering and inelastic x-ray scattering, and we rationalize our experimental findings using $\textit{ab initio}$ calculations. From the phonon dispersions at terahertz frequencies, we derive the full single-crystal elastic tensor and relate it to the macroscopic elastic response of black phosphorus, described by the elastic moduli. The elastic stiffness coefficients obtained here provide an important benchmark for models of black phosphorus and related materials, such as phosphorene and black phosphorus nanotubes, recently emerged quantum materials, disclosing a huge potential for nanophotonics, optoelectronics, and quantum sensing., Comment: 6 pages, 4 figures

Since their theoretical prediction by Peierls in the 30s, charge density waves (CDW) have been one of the most commonly encountered electronic phases in low dimensional metallic systems. The instability mechanism originally proposed combines Fermi surface nesting and electron-phonon coupling but is, strictly speaking, only valid in one dimension. In higher dimensions, its relevance is questionable as sharp maxima in the static electronic susceptibility \chi(q) are smeared out, and are, in many cases, unable to account for the periodicity of the observed charge modulations. Here, we investigate the quasi twodimensional LaAgSb2, which exhibits two CDW transitions, by a combination of diffuse xray scattering, inelastic x-ray scattering and ab initio calculations. We demonstrate that the CDW formation is driven by phonons softening. The corresponding Kohn anomalies are visualized in 3D through the momentum distribution of the x-ray diffuse scattering intensity. We show that they can be quantitatively accounted for by considering the electronic susceptibility calculated from a Dirac-like band, weighted by anisotropic electron-phonon coupling. This remarkable agreement sheds new light on the importance of Fermi surface nesting in CDW formation., Comment: 20 pages, 9 figures, submitted to Phys. Rev. Rep

We report an investigation of the combined structural and electronic properties of the bronze Na$_{1.5}$(PO$_{2}$)$_{4}$(WO$_{3}$)$_{20}$. Its low dimensional structure and possible large reconstruction of the Fermi surface due to charge density wave instability makes this bulk material a natural superlattice with a reduced number of carriers and Fermi energy. Signatures of multilayered 2D electron weak localization are consequently reported, with an enhanced influence of quantum oscillations. A crossover between these two antagonistic entities previously observed only in genuine low dimensional materials and devices, is shown to occur in a bulk crystal due to its hidden 2D nature.

Model materials are precious test cases for elementary theories and provide building blocks for the understanding of more complex cases. Here, we describe the lattice dynamics of the structural phase transition in francisite Cu3Bi(SeO3)2O2Cl at 115 K and show that it provides a rare archetype of a transition driven by a soft antipolar phonon mode. In the high-symmetry phase at hightemperatures, the soft mode is found at (0,0,0.5) at the Brillouin zone boundary and is measured by inelastic X-ray scattering and thermal diffuse scattering. In the low-symmetry phase, this softmode is folded back onto the center of the Brillouin zone as a result of the doubling of the unit cell, and appears as a fully symmetric mode that can be tracked by Raman spectroscopy. On both sides of the transition, the mode energy squared follows a linear behaviour over a large temperature range. First-principles calculations reveal that, surprisingly, the flat phonon band calculated for the high-symmetry phase seems incompatible with the displacive character found experimentally. We discuss this unusual behavior in the context of an ideal Kittel model of an antiferroelectric transition., Comment: 6 pages, 5 Figures, supplemental material included

The high pressure lattice dynamics of rhombohedral antimony have been studied by a combination of diffuse scattering and inelastic x-ray scattering. The evolution of the phonon behavior as function of pressure was analyzed by means of two theoretical approaches: density functional perturbation theory and symmetry-based phenomenological phase transition analysis. This paper focuses on the first structural phase transition, SbI-SbIV, and the role of vibrations in leading the transition. The phonon dispersion exhibits complex behaviour as one approaches the structural transition, with the branches, corresponding to the two transitions happening at high pressure in the Va elements (A7-to-BCC and A7-to-PC) both showing softening., Comment: 8 pages and 8 figures

We report a persistent low-energy phonon broadening around $q_{B} \sim 0.28$ r.l.u. along the Cu-O bond direction in the high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). We show that such broadening exists both inside and outside the conventional charge density wave (CDW) phase, via temperature dependent measurements in both underdoped and heavily overdoped samples. Combining inelastic hard x-ray scattering, diffuse scattering, angle-resolved photoemission spectroscopy, and resonant soft x-ray scattering at the Cu $L_3$-edge, we exclude the presence of a CDW in the heavily overdoped Bi-2212 similar to that observed in the underdoped systems. Finally, we discuss the origin of such anisotropic low-energy phonon broadening, and its potential precursory role to the CDW phase in the underdoped region., Comment: 11 pages, 9 figures

Among Transition Metal Dichalcogenides (TMD), NbS$_2$ is often considered as the archetypal compound that does not have a Charge Density Wave (CDW) in any of its polytypes. By comparison, close iso-electronic compounds such as NbSe$_2$, TaS$_2$ and TaSe$_2$ all have CDW in at least one polytype. Here, we report traces of CDW in the 2H polytype of NbS$_2$, using diffuse x-ray scattering measurements at 77\,K and room temperature. We observe 12 extremely weak satellite peaks located at $\pm$13$^\mathrm{o}$ 54' from $\vec{a}^*$ and $\vec{b}^*$ around each Bragg peaks in the $(h,k,0)$ plane. These satellite peaks are commensurate with the lattice via $3\vec{q}-\vec{q}\,'=\vec{a}^*$, where $\vec{q}\,'$ is the 120$^{\circ}$ rotation of $\vec{q}$, and define two chiral $\sqrt{13}\,a\times\sqrt{13}\,a$ superlattices in real space. These commensurate wavevectors and tilt angle are identical to those of the CDW observed in the 1T polytype of TaS$_2$ and TaSe$_2$. To understand this similarity and the faintness of the peaks, we discuss possible sources of local 1T polytype environment in bulk 2H-NbS$_2$ crystals.

We present a method for the precise determination of the full elasticity tensor from a single crystal diffraction experiment using monochromatic X-rays. For the two benchmark systems calcite and magnesium oxide we show that the measurement of thermal diffuse scattering in the proximity of Bragg reflections provides accurate values of the complete set of elastic constants. This approach allows for a reliable and model free determination of the elastic properties and can be performed together with crystal structure investigation in the same experiment.

We have determined the lattice dynamics of MgSiO$_3$ perovskite (bridgmanite) by a combination of single-crystal inelastic x-ray scattering and ab initio calculations. We observe a remarkable agreement between experiment and theory, and provide accurate results for phonon dispersion relations, phonon density of states and the full elasticity tensor. The present work constitutes an important milestone to extend this kind of combined studies to extreme conditions of pressure and temperature, directly relevant for the physics and the chemistry of Earth's lower mantle.

The lattice dynamics of TiO$_2$ in the rutile crystal structure was studied by a combination of thermal diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. We experimentally confirm the existence of an anomalous soft transverse acoustic mode with energy minimum at q = (1/2 1/2 1/4). The phonon energy landscape of this particular branch is reported and compared to the calculation. The harmonic calculation underestimates the phonon energies but despite this the shape of both the energy landscape and the scattering intensities are well reproduced. We find a significant temperature dependence in energy of this transverse acoustic mode over an extended region in reciprocal space which is in line with a substantially anharmonic mode potential-energy surface. The reported low energy branch is quite different from the ferroelectric mode that softens at the Brillouin zone center and may help explain anomalous convergence behavior in calculating TiO$_2$ surface properties.

The lattice dynamics of the silica polymorph {\alpha}-cristobalite has been investigated by a combination of diffuse and inelastic x-ray scattering and ab initio lattice dynamics calculations. Phonon dispersion relations and vibrational density of states are reported and the phonon eigenvectors analysed by a detailed comparison of scattering intensities. The experimentally validated calculation is used to identify the vibration contributing most to the first peak in the density of vibrational states. The comparison of its displacement pattern to the silica polymorphs {\alpha}-quartz and coesite and to vitreous silica reveals a distinct similarity and allows for decisive conclusions on the vibrations causing the so-called Boson peak in silica glass.

Single crystals of ice Ih, extracted from the subglacial Lake Vostok accretion ice layer (3621 m depth) were investigated by means of diffuse x-ray scattering and inelastic x-ray scattering. The diffuse scattering was identified as mainly inelastic and rationalized in the frame of ab initio calculations for the ordered ice XI approximant. Together with Monte-Carlo modelling our data allowed reconsidering previously available neutron diffuse scattering data of heavy ice as the sum of thermal diffuse scattering and static disorder contribution.

The lattice dynamics of the metallic tin {\beta} and {\gamma} polymorphs has been studied by a combination of diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. The non-symmorphic space group of the {\beta}-tin structure results in unusual asymmetry of thermal diffuse scattering. Strong resemblance of the diffuse scattering intensity distribution in {\beta} and {\gamma}-tin were observed, reflecting the structural relationship between the two phases and revealing the qualitative similarity of the underlying electronic potential. The strong influence of the electron subsystem on inter-ionic interactions creates anomalies in the phonon dispersion relations. All observed features are described in great detail by density functional perturbation theory for both {\beta}- and {\gamma}-tin at arbitrary momentum transfers. The combined approach delivers thus a complete picture of the lattice dynamics in harmonic description.

The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in harmonic description and thus eventually provides detailed information on the elastic properties, the stability and metastability of crystalline systems. The experimentally validated calculation was used for the investigation of eigenvectors, mode character and their influence on the density of vibrational states. High symmetry sections of the reciprocal space distribution of diffuse scattering and inelastic x-ray scattering spectra as well as the density of vibrational states and the dispersion relation are reported and compared to the calculation. A critical point at the zone boundary is found to contribute strongly to the main peak of the low energy part in the density of vibrational states. Comparison with the most abundant SiO2 polymorph - alpha-quartz - reveals similarities and distinct differences in the low-energy vibrational properties.

The temperature dependence of the phonon spectrum in the superconducting transition metal dichalcogenide 2H-NbS$_2$ is measured by diffuse and inelastic x-ray scattering. A deep, wide and strongly temperature dependent softening, of the two lowest energy longitudinal phonons bands, appears along the $\mathrm{\Gamma M}$ symmetry line in reciprocal space. In sharp contrast to the iso-electronic compounds 2H-NbSe$_2$, the soft phonons energies are finite, even at very low temperature, and no charge density wave instability occurs, in disagreement with harmonic ab-initio calculations. We show that 2H-NbS$_2$ is at the verge of the charge density wave transition and its occurrence is only suppressed by the large anharmonic effects. Moreover, the anharmonicity and the electron phonon coupling both show a strong in-plane anisotropy., Comment: 6 pages, 5 figures, accepted for publication in Physical Review B