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At least 433 records · Page 24

High Power Radiofrequency Operation of the Radiofrequency Quadrupoles in the Spallation Neutron Source

The Spallation Neutron Source (SNS) recently took delivery of a third Radiofrequency Quadrupole (RFQ03) that will ultimately be installed on the front-end (FE) of the SNS Linac. The first RFQ (RFQ01) operated in the SNS FE for more than a decade before being replaced with the second RFQ (RFQ02). RFQ01 was relocated to the Beam Test Facility (BTF) where it operated for five more years. The RFQ02 was initially installed in the BTF for high power testing and used with H- beam for BTF operation. It replaced RFQ01 in the SNS FE in 2017 and has been operating for beam production since then. There are some differences between the three RFQs. RFQ01 has a square cross-section with pi-mode stabilizing loops (PISLs) with the structure being fabricated using two layers of materials, GlidCop outside and OFHC inside. RFQ02 and RFQ03 has an octagonal cross-section with end-wall stabilizer rods and was fabricated using OFHC only. RFQ01 suffered some field flatness distortion incidents that resulted in degradation in beam transmission efficiency and required RF tuning. RFQ02 has performed well but had a melted RF seal in the high energy end wall, that was ultimately mitigated by a redesign of the end flange seals. The SNS decided to order RFQ03 that has a design that followed that of RFQ02 closely, but end-wall contacts were modified to prevent RF seal failure. This report presents the testing, installation, high power RF operation, and design improvements of the RFQ03.

Ren, Haitao↗

Gallery of soft modes: Theory and experiment at a ferromagnetic quantum phase transition

We examine the low-energy excitations in the vicinity of the quantum critical point in LiHoF4, a physical realization of the Transverse Field Ising Model, focusing on the long-range fluctuations which soften to zero energy at the ferromagnetic quantum phase transition. Microwave spectroscopy in tunable loop-gap resonator structures identifies and characterizes the electronuclear soft mode and higher-energy electronuclear states as a function of frequency and magnetic fields applied transverse and parallel to the Ising axis. These are understood in the context of a theoretical model of a soft electronuclear mode that interacts with soft photons as well as soft phonons. We identify competing infrared divergences at the quantum critical point, coming from the photons and the electronuclear soft mode. It is an incomplete cancellation of these divergences that leads to the muted but distinct signatures observed in the experiments. The application of a longitudinal magnetic field gaps the soft mode. As a result, measurements well away from the quantum critical point reveal a set of "Walker'' modes associated with ferromagnetic domain dynamics.

Dipolar interaction↗

Understanding Reproducibility of Sputter‐Deposited Metastable Ferroelectric Wurtzite Al 0.6 Sc 0.4 N Films Using In Situ Optical Emission Spectrometry

High‐Sc Al 1– x Sc x N thin films are of tremendous interest because of their attractive piezoelectric and ferroelectric properties, but overall film quality and reproducibility are widely reported to suffer as x increases. In this study, structural and electrical properties of metastable Al 0.6 Sc 0.4 N films are connected with plasma changes during film growth, identified via glow discharge optical emission spectroscopy (GD‐OES), and linked to the target mode changes. This in situ GD‐OES technique uses changes in the N 2 (I) intensity, correlated with DC bias hysteresis behavior of a Al 0.6 Sc 0.4 target in metallic and poisoned modes, to identify films that subsequently exhibit unacceptable structural and electrical performance. Two representative samples deposited under identical conditions but possessing distinct properties related to phases present in the films are focused on. Films sputtered under a poisoned target mode produce pure wurtzite ferroelectric Al 0.6 Sc 0.4 N with a reversible 80 μC cm −1 polarization and 3.1 MV cm −1 coercive field. When identical chamber settings are used but the process starts in metallic mode, a mixed wurtzite/rocksalt film is deposited which exhibits nanometer‐scale changes to the film microstructure and a nonferroelectric response. These results illustrate the utility of optical emission spectroscopy for tracking target mode fluctuations when fabricating metastable materials such as high‐Sc Al 1– x Sc x N films.

36 MATERIALS SCIENCE↗

Visualizing Electric and Magnetic Field Coupling in Au-Nanorod Trimer Structures via Stimulated Electron Energy Gain and Cathodoluminescence Spectroscopy: Implications for Meta-Atom Imaging

In this work, trimer meta-atoms composed of three gold rods in an equilateral triangular geometry were fabricated, and their near-field plasmonic responses were characterized via electron energy loss (EEL), cathodoluminescence (CL), and stimulated electron energy loss/gain (sEEL/sEEG) spectroscopy. The trimer structure hybridizes into a low-energy mode with all three rods coupling in-phase, which produces a circulating current and thus a magnetic field. The next highest-energy mode consists of two rods coupling out-of-phase and produces a net electric dipole. We investigate the near fields of hybridized magnetic and electric modes via EEL and CL and correlate their spectral characteristics and intensity maps. Then, by changing the length of the trimer rods, we tune the magnetic and electric modes to our laser energy and characterize the excited state via sEEL/sEEG spectroscopy. Exploration of the tilt dependence, relative to the optical source, of the two modes reveals that the electric mode sEEG intensity increases more than the expected sin 2 (θ) dependence of the optical electric field coupling (see the Supporting Information for a detailed description). After correcting for the tail of the close-proximity electric mode, we demonstrate sEEG via coupling of the magnetic component of the optical field to the magnetic meta-atoms, which has the expected cos 2 (θ) tilt dependence. This realization opens the possibility to explore the nanoscale excited-state near-field imaging of other magnetic meta-atom structures.

36 MATERIALS SCIENCE↗

Insights on the Influence of the Central-Cut Width of the Box Assembly with Removable Component on Its Dynamical Responses

This investigation focuses on the dynamical effects caused by varying the central-cut width within the Box Assembly with Removable Component (BARC) system. The central-cut widths included in this study are a 0.5″ cut, a 0.25″ cut, a thin 0.1″ cut, and a structure that did not have a cut at all. Finite element analysis was conducted to determine the mode shapes and natural frequencies of each of the BARC structures. Structural dynamics experiments were run to examine the effects of the central-cut width on the dynamical responses and nonlinear characteristics of the BARC system. Free vibration testing with an impact hammer was carried out to excite the system and extract the dominant frequencies and directions of the significant responses. A pseudorandom vibration test that allows for the qualitative determination of any nonlinear behavior within the system was performed. This type of behavior can include nonlinear softening, nonlinear hardening, and the most common, nonlinear damping due to the presence of several bolted-joint connections and the possible activation of geometric and inertia nonlinearities. To quantitatively investigate the impacts of the central-cut width on the dynamics of the system, swept sinusoidal testing was conducted. It is determined that almost all systems with central cuts demonstrate the presence of nonlinear softening, but at times, nonlinear hardening trends are seen, particularly in the 0.1″ cut and no-cut systems when testing harmonically. Each of the central-cut systems displays nonlinear damping, with the amount of damping generally increasing as the central cut decreases in size. The effect of the central cut of the BARC system on the mode-switching ability of the system is negligible; however, mode switching takes place when comparing the central-cut configurations to the no-cut one. These results show the significance of accurately measuring the central-cut width and how geometric uncertainty may change the dynamical responses and nonlinear properties of the system.

Padilla, Christopher (ORCID:000900033446732X)↗

Enhancing searches for resonances with machine learning and moment decomposition

A key challenge in searches for resonant new physics is that classifiers trained to enhance potential signals must not induce localized structures. Such structures could result in a false signal when the background is estimated from data using sideband methods. A variety of techniques have been developed to construct classifiers which are independent from the resonant feature (often a mass). Such strategies are sufficient to avoid localized structures, but are not necessary. We develop a new set of tools using a novel moment loss function (Moment Decomposition or MoDe) which relax the assumption of independence without creating structures in the background. Here, by allowing classifiers to be more flexible, we enhance the sensitivity to new physics without compromising the fidelity of the background estimation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Self-Assembly of Metallo-Supramolecules with Dissymmetrical Ligands and Characterization by Scanning Tunneling Microscopy

Asymmetrical and dissymmetrical structures are widespread and play a critical role in nature and life systems. In the field of metallo-supramolecular assemblies, it is still in its infancy for constructing artificial architectures using dissymmetrical building blocks. Herein, we report the self-assembly of supramolecular systems based on two dissymmetrical double-layered ligands. With the aid of ultra-high-vacuum, low-temperature scanning tunneling microscopy (UHV-LT-STM), we were able to investigate four isomeric structures corresponding to four types of binding modes of ligand LA with two major conformations complexes A. The distribution of isomers measured by STM and total binding energy of each isomer obtained by density functional theory (DFT) calculations suggested that the most abundant isomer could be the most stable one with highest total binding energy. Lastly, through shortening the linker between inner and outer layers and the length of arms, the arrangement of dissymmetrical ligand LB could be controlled within one binding mode corresponding to the single conformation for complexes B.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamics of continuous spin photons

Special relativity allows massless particles to have states of different integer (or half-integer) helicities that mix under boosts, much like the spin states of a massive particle. Such massless particles are known as “continuous spin” particles (CSPs), a term coined by Wigner, and they are notable for their infinite tower of spin polarizations. The mixing under boosts is controlled by a spin scale 𝜌 with units of momentum. Normally, we assume 𝜌 = 0. The interactions of CSPs are known to satisfy certain simple properties, one of which is that the 𝜌 → 0 limit generically recovers familiar interactions of massless scalars, photons, or gravitons, with all other polarizations decoupling in this limit. Thus, one can ask if the photon of the Standard Model is a CSP at small but nonzero 𝜌. One concern about this possibility—originally raised by Wigner—is that the infinite tower of polarizations could pose problems for thermodynamics. To address this question, we study the thermal evolution of a CSP photon gas coupled to isothermal matter, across CSP helicity modes and phase space. We find that the structure of the interactions dictated by Lorentz symmetry implies well-behaved thermodynamics. When the CSP photon’s interactions with charged matter are turned on, the primary ℎ =±1 helicity modes thermalize quickly, while the other modes require increasingly long time scales to thermalize, set by powers of 𝑇/𝜌. In familiar thermal systems, the CSP photon behaves like the QED photon with small 𝜌- and time-dependent corrections to its effective relativistic degrees of freedom. Sizable departures from familiar thermal behavior arise at energy scales comparable to 𝜌 and could have testable experimental consequences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB 6 and LaB 6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB 6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB 2 . LaB 6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB 6 ’s greater Fermi-level (E f ) density of states and higher electron–phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB 6 , hybridize with π B–B bonds and bring this π-system lower in energy than the σ B–B bonds otherwise at E f . This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB 6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB 6 . These phonons in YB 6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB 6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB 6 , introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB 6 and YB 6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Science & Technology - Other Topics↗

Phonon dispersion throughout the iron spin crossover in ferropericlase

Ferropericlase (Fp), (Mg 1– x Fex)O, is the second most abundant phase in the Earth's lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), $\textit{S}$ = 2, to low spin (LS), $\textit{S}$ = 0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermoelastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasiharmonic approximation. Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio density-functional theory $+U_{sc}$ calculations. We address vibrational modes associated with isolated and (second-)nearest-neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient, while optical modes are the most affected. In this work, we show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Metastable piezoelectric group-IV monochalcogenide monolayers with a buckled honeycomb structure

Multiple two-dimensional materials are being naïvely termed stable on the grounds of displaying phonon dispersions with no negative frequencies and of not collapsing on molecular dynamics calculations at fixed volume. But, if these phases do not possess the smallest possible structural energy, how does one understand and establish their actual meta stability? To answer this question, twelve two-dimensional group-IV monochalcogenide monolayers (SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, and PbTe) with a buckled honeycomb atomistic structure—belonging to symmetry group P3m1—displaying an out-of-plane intrinsic electric polarization are shown to be metastable by three independent methods. First, we uncover a coordination-preserving structural transformation from the low-buckled honeycomb structure onto the lower-energy Pnm2 1 (or Pmmn for PbS, PbSe, and PbTe) phase to estimate energy barriers E B that must be overcome during such structural transformation. Using the curvature of the local minima and E B as inputs to Kramers escape formula, large escape times are found, implying the structural metastability of the buckled honeycomb phase (with the exception of PbS and PbSe, these phases display escape times ranging from 700 years to multiple times the age of the universe and can be considered “stable” for practical purposes in that relative sense). The second demonstration is provided by phonon dispersion relations that include the effect of long-range Coulomb forces and display no negative vibrational modes. The third and final demonstration of structural metastability is furnished by room-temperature ab initio molecular dynamics for selected compounds. Here, the magnitude of the electronic band gap evolves with chemical composition. Different from other binary two-dimensional compounds such as transition metal dichalcogenide monolayers and hexagonal boron nitride monolayers which only develop an in-plane piezoelectric response, the twelve group-IV monochalcogenide monolayers with a buckled honeycomb structure also display out-of-plane piezoelectric properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fyn–Saracatinib Complex Structure Reveals an Active State-like Conformation

Fyn is a Src-family tyrosine kinase implicated in synaptic dysfunction and neuroinflammation across multiple neurodegenerative disorders, including Alzheimer’s disease (AD) and Parkinson’s disease (PD). Saracatinib (AZD0530) is a potent Src-family inhibitor that has been explored as a repurposed therapeutic; however, its clinical utility is limited by poor kinase selectivity caused by high sequence conservation within Src-family ATP-binding sites. Here, we combine surface plasmon resonance (SPR) and X-ray crystallography to define saracatinib recognition by the Fyn kinase domain (KD). SPR single-cycle kinetics shows that saracatinib binds the isolated Fyn KD and full-length Fyn with low-nanomolar affinity, whereas dasatinib binds with subnanomolar affinity and markedly slower dissociation. We determined the crystal structure of the Fyn KD-saracatinib complex at 2.22 Å resolution. The kinase adopts an active-like conformation with the DFG motif and αC-helix in the ‘in’ state and a conserved β3 αC Lys-Glu salt bridge. Saracatinib occupies the adenine and ribose pockets, and engages the hinge through direct and water-mediated hydrogen bonding while complementing a hydrophobic back pocket by van der Waals contacts. Comparison with reported saracatinib-bound structures of other kinases suggests that the active-state geometry observed for Fyn creates a pocket not observed in inactive-like complexes, providing a structural handle for designing Fyn-selective inhibitors. Comparison with all saracatinib-bound kinase co-structures currently available in the PDB (ALK2 and PKMYT1) indicates a conserved monodentate hinge binding mode but kinase-dependent αC-helix conformations, providing a structural rationale for designing Fyn-selective analogues.

AZD0530↗

Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (Ca x Sr 1–x ) 3 Rh 4 Sn 13 , where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd 2 Re 2 O 7 , to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC–revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of 5d 2 Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

36 MATERIALS SCIENCE↗

Development of deflector mode for spin-resolved time-of-flight photoemission spectroscopy

Spin- and angle-resolved photoemission spectroscopy (“spin-ARPES”) is a powerful technique for probing the spin degree-of-freedom in materials with nontrivial topology, magnetism, and strong correlations. Spin-ARPES faces severe experimental challenges compared to conventional ARPES attributed to the dramatically lower efficiency of its detection mechanism, making it crucial for instrumentation developments that improve the overall performance of the technique. Here in this paper, we demonstrate the functionality of our spin-ARPES setup based on time-of-flight spectroscopy and introduce our recent development of an electrostatic deflector mode to map out spin-resolved band structures without sample rotation. We demonstrate the functionality by presenting the spin-resolved spectra of the topological insulator Bi2Te3 and describe in detail the spectrum calibrations based on numerical simulations. By implementing the deflector mode, we minimize the need for sample rotation during measurements, hence improving the overall efficiency of experiments on small or inhomogeneous samples.

47 OTHER INSTRUMENTATION↗

Numerical Simulation Studies of Ultrasonic De-Icing for Heating, Ventilation, Air Conditioning, and Refrigeration Structures

Ice accumulation on heating, ventilation, air conditioning, and refrigeration (HVACR) structures presents significant operational challenges. These challenges include reduced efficiency, increased energy consumption, and potential damage to equipment. Traditional de-icing methods, such as chemical treatments, mechanical scraping, or heating-based techniques, are often labor-intensive, costly, and environmentally harmful. Here, this study uniquely investigates ultrasonic de-icing as an energy-efficient alternative for HVACR applications, focusing on the specific structural geometries found in these systems. A comprehensive numerical simulation framework was developed using finite element analysis to explore ultrasonic wave propagation across four distinct HVACR structures. Key parameters such as ultrasonic frequency, power levels, and the number and placement of actuators were examined for their impact on ice detachment efficiency. Results from simulations on a plate structure reveal that ultrasonic excitation can propagate effectively across large areas (at least 150 × 150 mm), enhancing the de-icing coverage. Lower frequency (e.g., 30 to 45 kHz) excitation results in greater displacement, improving de-icing performance, while increased actuator numbers with the same total power input also enhance effectiveness. Two actuators seem sufficient for the de-icing of a 300 × 300 mm plate. For tube-and-fin structures, specific high-power ultrasonic frequencies selectively excite the fin plates, demonstrating efficient ice removal when actuated on the tube. However, optimal performance requires careful design of actuator placement and vibration modes to accommodate the irregular shapes of these structures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

High Pressure–Temperature Study of MgF 2 , CaF 2 , and BaF 2 by Raman Spectroscopy: Phase Transitions and Vibrational Properties of AF 2 Difluorides

The phase transition of AF 2 difluorides strongly depends on pressure, temperature, and cationic radius. Here, we have investigated the phase transition of three difluorides, including MgF 2 , CaF 2 , and BaF 2 , at simultaneously high pressures and temperatures using Raman spectroscopy and X-ray diffraction in externally heated diamond anvil cells up to 55 GPa at 300–700 K. Rutile-type difluoride MgF 2 with a small cationic radius undergoes a transition to the CaCl 2 -type phase at 9.9(1) GPa and 300 K, to the HP-PdF 2 -type phase at 21.0(2) GPa, and to the cotunnite-type phase at 44.2(2) GPa. The phase transition pressure to the HP-PdF 2 and cotunnite structure at 300 K for our single crystal was found to be higher than that in previous studies using polycrystalline samples. Elevating the temperature increases the transition pressure from rutile- to the CaCl 2 -type phase but has a negative influence on the transition pressure when MgF 2 transforms from the HP-PdF 2 - to cotunnite-type phase. Meanwhile, the transition pressure from the CaCl 2 - to HP-PdF 2 -type phase for MgF 2 was identified to be independent of the temperature. Raman peaks suspected to belong to the α-PbO 2 -type phase were observed at 14.6–21.0(1) GPa and 400–700 K. At 300 K, difluorides CaF 2 and BaF 2 in the fluorite structure with larger cationic radii transform to the cotunnite-type phase at 9.6(3) and 3.0(3) GPa at 300 K, respectively, and BaF 2 further undergoes a transition to the Ni 2 In-type phase at 15.5(4) GPa. For both CaF 2 and BaF 2 , elevating the temperature leads to a lower transition pressure from fluorite- to the cotunnite-type phase but has little influence on the transition to the Ni 2 In structure. Raman data provide valuable insights for mode Grüneisen parameters. We note that the mode Grüneisen parameters for both difluorides and dioxides vary linearly with the cation radius. Further calculations for the mode Grüneisen parameters at high pressures for MgF 2 , CaF 2 , and BaF 2 yield a deeper understanding of the thermodynamic properties of the difluorides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theory of finite-temperature two-dimensional structural transformations in group-IV monochalcogenide monolayers

An account of two-dimensional (2D) structural transformations in 2D ferroelectrics predicts an evolution from a structure with Pnm 2 1 symmetry into a structure with square P4/nmm symmetry and is consistent with experimental evidence, while another argues for a transformation into a structure with rectangular Pnmm symmetry. An analysis of the assumptions made in these models is provided here, and six fundamental results concerning these transformations are contributed as follows: (i) Softened phonon modes produce rotational modes in these materials. (ii) The transformation to a structure with P4/nmm symmetry occurs at the lowest critical temperature T c . (iii) The hypothesis that one unidirectional optical vibrational mode underpins the 2D transformation is unwarranted. (iv) Being successively more constrained, a succession of critical temperatures ( T c < T c ' < T c " ) occurs in going from molecular dynamics calculations with the NPT and NVT ensembles onto models with unidirectional oscillations. (v) The choice of exchange-correlation functional impacts the estimate of the critical temperature. (vi) Importantly, the correct physical picture of these transformations is one in which rotational modes confer a topological character to the 2D transformation via the proliferation of vortices.

2d ferroelectrics↗

Lamellar fluctuations melt ferroelectricity.

We consider a standard Ginzburg-Landau model of a ferroelectric whose electrical polarization is coupled to gradients of elastic strain. At the harmonic level, such flexoelectric interaction is known to hybridize acoustic and optic phonon modes and lead to phases with modulated lattice structures that precede the state with spontaneously broken inversion symmetry. Here, we use the self-consistent phonon approximation to calculate the effects of thermal and quantum polarization fluctuations on the bare hybridized modes to show that such long-range modulated order is unstable at all temperatures. We discuss the implications for the nearly ferroelectric SrTiO3 and KTaO3, and we propose that these systems are melted versions of an underlying modulated state that is dominated by nonzero momentum thermal fluctuations except at the very lowest temperatures.

Guzman-Verri, G. G.↗