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At least 91 records · Page 5

From bare to renormalized order parameter in gauge space: Structure and reactions

The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body (Nambu-Gorkov (NG), nuclear field theory (NFT)) spectroscopic amplitudes, is not immediately obvious. Restoration of spontaneous symmetry breaking and associated emergent generalised rigidity in gauge space provides the answer, and points to a new emergence: a physical sum rule resulting from the intertwining of structure and reaction processes and closely connected with the central role induced pairing interaction plays in structure together with the fact that successive transfer dominates Cooper pair tunneling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Switching of Hybrid Improper Ferroelectricity in Oxide Double Perovskites

In ABO 3 -type perovskite oxides with Pnma symmetry, rotation (Q R+ , a 0 a 0 c + ) and tilt (Q T , a – a – c 0 ) of BO 6 octahedra are the two primary order parameters. These order parameters establish an inherent trilinear coupling with anti-ferroelectric A-site displacement (Q AFE ) to form the low-symmetry phase. The symmetry is further lowered in double perovskite oxides (DPOs) due to A/A' cation ordering. It in turn makes these systems polar via hybrid improper ferroelectric mechanism, primarily driven by Q R+ and Q T . Naturally, it has been believed that functionalities such as polarization can also be switched by tuning these primary order parameters. However, mystery around finding switching mechanism still remains. Our study based on density functional theory calculations combined with finite-temperature molecular dynamics simulations shows that the polarization switching is a two-step process, driven by out-of-phase rotation (Q R– , a 0 a 0 c – when Q T = 0 or, a – a – b – when Q T ≠ 0). A series of polar DPOs such as KLnFeOsO 6 [Ln = Sm, Gd, Dy, Tm (lanthanides) and Y (rare earth)], all belonging to P2 1 symmetry, are considered in this investigation. The polarization switching P ($\overrightarrow{P}$) occurs at a very high temperature of ~1150 K through a phase transition, from a polar (P2 1 ) phase with $\overrightarrow{P}$(+) to $\overrightarrow{P}$(-) via a non-polar P4/n phase. The switching itself is metastable in nature. The switching (both polarization and spin state) is only observed for a very short period of time (~23 ps) that poses limitation on using such a mechanism in memory device realization. We demonstrate a concurrent heating–cooling procedure to overcome such shortcoming. In conclusion, simulations conducted at 600 K further imply that long lasting switching can be achieved, at least for 1.2 ns for 600 K, and ideally for an infinite time, if the material is heated just above the T c followed by rapid cooling to a temperature below T c .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations

We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. Furthermore, we analyze the effect of the system size on the ice Ih-liquid free energy differences, and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Capturing Nucleation at 4D Atomic Resolution

Nucleation plays a critical role in many physical and biological phenomena ranging from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases. However, nucleation is a challenging process to study especially in the early stage when several atoms/molecules start to form a new phase from its parent phase. Here, we advance atomic electron tomography to study early stage nucleation at 4D atomic resolution. Using FePt nanoparticles as a model system, we reveal that early stage nuclei are irregularly shaped, each has a core of a maximum order parameter, and an order parameter gradient points from the core to the boundary of the nucleus. We capture the structure and dynamics of the same nuclei undergoing growth, fluctuation, dissolution, merging and/or division, which are regulated by the distribution of the order parameter and its gradient. These experimental results differ from classical nucleation theory (CNT) and to explain them we propose an order parameter gradient model, which is more general and thermodynamically more favourable than CNT. We further corroborate this model using molecular dynamics simulations of heterogeneous and homogeneous nucleation in the liquid-solid phase transition of Pt. Here, we anticipate that the order parameter gradient model is applicable to different kinds of nucleation processes and our experimental method opens the door to study the structure and dynamics of materials with 4D atomic resolution.

74 ATOMIC AND MOLECULAR PHYSICS↗

Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking

In this article, we consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between classical long-range order of local order parameters and quantum order of long-range entanglement in the ground states, we study the topological point defects and textures of order parameters in such systems. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground states with a nonfluctuating order parameter, and provide a classification for their properties based on the inflation-restriction exact sequence. We highlight a few phenomena revealed by our theory framework. First, in the absence of intrinsic topological orders, we show a connection between the symmetry properties of point defects and textures to deconfined quantum criticality. Second, when the symmetry-breaking ground state has intrinsic topological orders, we show that the point defects can permute different anyons when braided around. They can also obey projective fusion rules in the sense that multiple vortices can fuse into an Abelian anyon, a phenomenon for which we coin “defect fractionalization.” Finally, we provide a formula to compute the fractional statistics and fractional quantum numbers carried by textures (skyrmions) in Abelian topological orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observing crystal nucleation in four dimensions using atomic electron tomography

Nucleation plays a critical role in many physical and biological phenomena that range from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases. However, nucleation is a challenging process to study in experiments, especially in the early stage when several atoms or molecules start to form a new phase from a parent phase. A number of experimental and computational methods have been used to investigate nucleation processes, but experimental determination of the three-dimensional atomic structure and the dynamics of early stage nuclei has been unachievable. Here we use atomic electron tomography to study early stage nucleation in four dimensions (4D: that is, including time) at atomic resolution. Using FePt nanoparticles as a model system, we find that early stage nuclei are irregularly shaped, each has a core of one to a few atoms with the maximum order parameter, and the order parameter gradient points from the core to the boundary of the nucleus. We capture the structure and dynamics of the same nuclei undergoing growth, fluctuation, dissolution, merging and/or division, which are regulated by the order parameter distribution and its gradient. These experimental observations are corroborated by molecular dynamics simulations of heterogeneous and homogeneous nucleation in liquid–solid phase transitions of Pt. Our experimental and molecular dynamics results differ from classical nucleation theory, indicating that a theory beyond this is needed to describe early stage nucleation at the atomic scale. Looking forward, we anticipate that the reported approach will open the door to the study of many fundamental problems in materials science, nanoscience, condensed matter physics and chemistry, such as phase transition, atomic diffusion, grain boundary dynamics, interface motion, defect dynamics and surface reconstruction with 4D atomic resolution.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Probing the pathway of an ultrafast structural phase transition to illuminate the transition mechanism in Cu 2 S

Disentangling the primary order parameter from secondary order parameters in phase transitions is critical to the interpretation of transition mechanisms in strongly correlated systems and quantum materials. Here in this work, we present a study of structural phase transition pathways in superionic Cu 2 S nanocrystals that exhibit intriguing properties. Utilizing ultrafast electron diffraction techniques sensitive to both the momentum-space and the time-domain, we distinguish the dynamics of crystal symmetry breaking and lattice expansion in this system. We are able to follow the transient states along the transition pathway, and so observe the dynamics of both the primary and secondary order parameters. Based on these observations, we argue that the mechanism of structural phase transition in Cu 2 S is dominated by the electron-phonon coupling. Lastly, this mechanism advances the understanding from previous results, where the focus was solely on dynamic observations of the lattice expansion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering

Here we propose an analytical Landau-Ginzburg (LG) theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include the electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the LG free energy density as a power expansion with respect to the charge density and other long-range order parameters as well as their spatial gradients and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes, and modulation periods obtained in this paper can be employed to guide the comprehensive physical explanation, deconvolution, and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dynamic Magnetic Features of the Mixed Ising System on the Bilayer Square Lattice

In order to study the dynamic magnetic features of the mixed spin-1 and spin-5/2 Ising system, we have used the mean-field theory (MFT) based on the Glauber-type stochastic dynamics on the bilayer square lattice (BSL). By employing the Master equation, dynamic equations describing the behavior of the system are derived. The average order parameters and dynamic order parameters are studied for different values of exchange interactions, oscillating magnetic field, and temperature. The complete dynamic phase diagrams (DPDs) are obtained for the ferromagnetic/ferromagnetic (FM/FM), ferromagnetic/antiferromagnetic (FM/AFM), and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions in the different planes, and the role of the interaction in the Hamiltonian on the DPDs is explored. It is found that the DPDs display richer dynamic behavior for this mixed Ising system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A generalized deep learning approach for local structure identification in molecular simulations

Identifying local structure in molecular simulations is of utmost importance. The most common existing approach to identify local structure is to calculate some geometrical quantity referred to as an order parameter. In simple cases order parameters are physically intuitive and trivial to develop (e.g., ion-pair distance), however in most cases, order parameter development becomes a much more difficult endeavor (e.g., crystal structure identification). Using ideas from computer vision, we adapt a specific type of neural network called a PointNet to identify local structural environments in molecular simulations. A primary challenge in applying machine learning techniques to simulation is selecting the appropriate input features. This challenge is system-specific and requires significant human input and intuition. In contrast, our approach is a generic framework that requires no system-specific feature engineering and operates on the raw output of the simulations, i.e., atomic positions. We demonstrate the method on crystal structure identification in Lennard-Jones (four different phases), water (eight different phases), and mesophase (six different phases) systems. The method achieves as high as 99.5% accuracy in crystal structure identification. The method is applicable to heterogeneous nucleation and it can even predict the crystal phases of atoms near external interfaces. We demonstrate the versatility of our approach by using our method to identify surface hydrophobicity based solely upon positions and orientations of surrounding water molecules. Our results suggest the approach will be broadly applicable to many types of local structure in simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase coexistence and electric-field control of toroidal order in oxide superlattices

Systems that exhibit phase competition, order parameter coexistence, and emergent order parameter topologies constitute a major part of modern condensed-matter physics. Here, by applying a range of characterization techniques, and simulations, we observe that in PbTiO 3 /SrTiO 3 superlattices all of these effects can be found. By exploring superlattice period-, temperature- and field-dependent evolution of these structures, we observe several new features. First, it is possible to engineer phase coexistence mediated by a first-order phase transition between an emergent, low-temperature vortex phase with electric toroidal order and a high-temperature ferroelectric a 1 /a 2 phase. At room temperature, the coexisting vortex and ferroelectric phases form a mesoscale, fibre-textured hierarchical superstructure. The vortex phase possesses an axial polarization, set by the net polarization of the surrounding ferroelectric domains, such that it possesses a multi-order-parameter state and belongs to a class of gyrotropic electrotoroidal compounds. Finally, application of electric fields to this mixed-phase system permits interconversion between the vortex and the ferroelectric phases concomitant with order-of-magnitude changes in piezoelectric and nonlinear optical responses. Here, our findings suggest new cross-coupled functionalities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter Q is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of Q cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of Q on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for Q, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. Finally, the analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.

36 MATERIALS SCIENCE↗

On the possibility to detect multipolar order in URu 2 Si 2 by the electric quadrupolar transition of resonant elastic x-ray scattering

Resonant elastic x-ray scattering is a powerful technique for measuring multipolar order parameters. In this paper, we theoretically and experimentally study the possibility of using this technique to detect the proposed multipolar order parameters in URu 2 Si 2 at the U- L 3 edge with the electric quadrupolar transition. Based on an atomic model, we calculate the azimuthal dependence of the quadrupolar transition at the U- L 3 edge. Our results illustrate the potential of this technique for distinguishing different multipolar order parameters. We then perform experiments on ultraclean single crystals of URu 2 Si 2 at the U- L 3 edge to search for the predicted signal, but do not detect any indications of multipolar moments within the experimental uncertainty. We also theoretically estimate the orders of magnitude of the cross section and the expected count rate of the quadrupolar transition and compare them to the dipolar transitions at the U- M 4 and U- L 3 edges, clarifying the difficulty in detecting higher order multipolar order parameters in URu 2 Si 2 in the current experimental setup.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗