Real-space Technique Research Articles

CP2 skyrmions and skyrmion crystals in realistic quantum magnets

Magnetic skyrmions are nanoscale topological textures that have been recently observed in different families of quantum magnets. These objects are called CP1 skyrmions because they are built from dipoles—the target manifold is the 1D complex projective space, CP1 ≅ S2. Here we report the emergence of magnetic CP2 skyrmions in a realistic spin-1 model, which includes both dipole and quadrupole moments. Unlike CP1 skyrmions, CP2 skyrmions can also arise as metastable textures of quantum paramagnets, opening a new road to discover emergent topological solitons in non-magnetic materials. The quantum phase diagram of the spin-1 model also includes magnetic field-induced CP2 skyrmion crystals that can be detected with regular momentum- (diffraction) and real-space (Lorentz transmission electron microscopy) experimental techniques.

Calculations of positron annihilation lifetime in solid based on finite difference and conjugate-gradient methods

We employ a real-space grids technique to calculate positron annihilation lifetimes with pseudopotentials. This method is based on the two-component of density functional theory (TCDFT), the Hamiltonian operator of the Kohn-Sham equation is discretized on a point grid by the finite difference method (FDM), the positron eigenstates are searched by the conjugate-gradient method (CG) and the positron Kohn-Sham equation is solved by a self-consistent iteration method. We show that the numerical results under this scheme for bulk and monovacancy of positron annihilation lifetimes are in reasonable agreement with the available experimental data. Furthermore, all the results of our calculations demonstrate the accuracy and efficiency of the method from different aspects.

A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives.

The somewhat elusive concept of aromaticity plays an undeniable role in the chemical narrative, often being considered the principal cause of the unusual properties and stability exhibited by certain skeletons. More recently, the concept of aromaticity has also been utilised to explain the modulation of the strength of non-covalent interactions (NCIs), such as hydrogen bonding (HB), paving the way towards the in silico prediction and design of tailor-made interacting systems. In this work, we try to shed light on this area by exploiting real space techniques, such as the Quantum Theory of Atoms in Molecules (QTAIM), the Interacting Quantum Atoms (IQA) approaches along with the electron delocalisation indicators Aromatic Fluctuation (FLU) and Multicenter (MCI) indices. The QTAIM and IQA methods have been proven capable of providing an unbiased and rigorous picture of NCIs in a wide variety of scenarios, whereas the FLU and MCI descriptors have been successfully exploited in the study of diverse aromatic and antiaromatic systems. We used a collection of simple archetypal examples of aromatic, non-aromatic and antiaromatic moieties within organic molecules to examine the changes in delocalisation and aromaticity induced by the Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB). We observed fundamental differences in the behaviour of systems containing the HB acceptor within and outside the ring, e.g., a destabilisation of the rings in the former as opposed to a stabilisation of the latter upon the formation of the corresponding molecular clusters. The results of this work provide a physically sound basis to rationalise the strengthening and weakening of AMHBs with respect to suitable non-cyclic non-aromatic references. We also found significant differences in the chemical bonding scenarios of aromatic and antiaromatic systems in the formation of AMHB. Altogether, our investigation provide novel, valuable insights about the complex mutual influence between hydrogen bonds and systems.

Decimation technique for open quantum systems: A case study with driven-dissipative bosonic chains

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data.

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

A super-resolution technique to analyze single-crystal inelastic neutron scattering measurements using direct-geometry chopper spectrometers.

Direct-geometry time-of-flight chopper neutron spectroscopy is instrumental in studying dynamics in liquid, powder, and single crystal systems. We report here that real-space techniques in optical imagery can be adapted to obtain reciprocal-space super resolution dispersion for phonon or magnetic excitations from single-crystal neutron spectroscopy measurements. The procedure to reconstruct super-resolution energy dispersion of excitations relies on an accurate determination of the momentum and energy-dependent point spread function and a dispersion correction technique inspired by an image disparity calculation technique commonly used in stereo imaging. Applying these methods to spinwave dispersion data from a virtual neutron experiment demonstrates ∼5-fold improvement over nominal energy resolution.

Ultrabroadband Nanocavity of Hyperbolic Phonon–Polaritons in 1D-Like α-MoO3

The exploitation of phonon-polaritons in nanostructured materials offers a pathway to manipulate infrared (IR) light for nanophotonic applications. Notably, hyperbolic phonon-polaritons (HP2) in polar bidimensional crystals have been used to demonstrate strong electromagnetic field confinement, ultraslow group velocities, and long lifetimes (up to ∼12 ps). Here we present nanobelts of α-phase molybdenum trioxide (α-MoO3) as a low-dimensional medium supporting HP2 modes in the mid- and far-IR ranges. Through real-space nanoimaging techniques with synchrotron and tunable laser IR light, we observe HP2 Fabry-Perot resonances that demonstrate distinct anisotropic propagation and frequency dependence. We remark an anisotropic propagation that critically depends on the frequency range. Our findings are supported by the convergence of experiment, theory, and numerical simulations. Our work shows that the low dimensionality of natural nanostructured crystals, like α-MoO3 nanobelts, provides an attractive platform to study polaritonic light-matter interactions and offers appealing cavity properties that could be harnessed in future designs of compact nanophotonic devices.

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba5SmSn3Nb7O30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

Direct visualization of nucleation intermediate state of magnetic skyrmion from helical stripes assisted by artificial surface pits

Magnetic skyrmion is a particle-like spin texture promising for future novel spintronic devices. For such applications, microscopic mechanism of nucleation of skyrmion is essential to control the unique spin texture. Although real-space visualization techniques with high spatial resolution could be powerful to investigate the mechanism at the nanometer length scale, a direct visualization of skyrmion nucleation process from the helical stripe state is still technically challenging because not only a high spatial resolution but also a high temporal resolution is required to resolve the transient state. Furthermore, the location of the intermediate state is likely to move along the stripe, which hampers a successful visualization. Here, taking advantage of the high spatial resolution of aberration-corrected differential phase contrast scanning transmission electron microscopy, we observe the nucleation of skyrmion from helical stripes in a thin plate of FeGe1-xSix (x ~ 0.05). By slowing down the kinetics with a careful control of both magnetic field and temperature, while pinning the helical stripe by artificial surface pits fabricated on the surface of the thin plate specimen, we directly visualize the nucleation intermediate state of skyrmion. We find the theoretically predicted antiskyrmion-like spin texture is actually created as the intermediate state during nucleation.

High-Quality All-Inorganic Perovskite CsPbBr3 Microsheet Crystals as Low-Loss Subwavelength Exciton-Polariton Waveguides.

Nanostructured all-inorganic metal halide perovskites have attracted considerable attention due to their outstanding photonic and optoelectronic properties. Particularly, they can exhibit room-temperature exciton-polaritons (EPs) capable of confining electromagnetic fields down to the subwavelength scale, enabling efficient light harvesting and guiding. However, a real-space nanoimaging study of the EPs in perovskite crystals is still absent. Additionally, few studies focused on the ambient-pressure and reliable fabrication of large-area CsPbBr3 microsheets. Here, CsPbBr3 orthorhombic microsheet single crystals were successfully synthesized under ambient pressure. Their EPs were examined using a real-space nanoimaging technique, which reveal EP waveguide modes spanning the visible to near-infrared spectral region. The EPs exhibit a sufficient long propagation length of over 16 μm and a very low propagation loss of less than 0.072 dB·μm-1. These results demonstrate the potential applications of CsPbBr3 microsheets as subwavelength waveguides in integrated optics.

Sn3B8O15: A Ternary Tin(II) Borate with Flexible [B8O18]12- Fundamental Building Block Formed by [B7O16]11- and [BO3]3- Groups.

Owing to the tendency to form the glass state in growing crystals in the ternary tin(II) borate system, hitherto, very few single crystals in ternary tin(II) borate were reported. In this paper, a single crystal of Sn3B8O15 was obtained via a high temperature solution method in a closed system. The structure features a flexible fundamental building block [B8O18]12- constructed by one [BO3]3- unit and one [B7O16]11- group that contains three hexatomic rings, which further connect to compose a two-dimensional 2∞[B8O15] layer structure. The connection mode and flexibility of the three hexatomic B-O rings were analyzed, verifying the structural diversity of the B-O configuration. Moreover, the synthesis, crystal structure, and various characterizations were comprehensively presented. Also, theoretical calculations were employed to discuss structure-property relationships, and we use the real-space atom-cutting techniques to explain the origin of the birefringence of Sn3B8O15.

Electric and antiferromagnetic chiral textures at multiferroic domain walls.

Chirality, a foundational concept throughout science, may arise at ferromagnetic domain walls1 and in related objects such as skyrmions2. However, chiral textures should also exist in other types of ferroic materials, such as antiferromagnets, for which theory predicts that they should move faster for lower power3, and ferroelectrics, where they should be extremely small and possess unusual topologies4,5. Here, we report the concomitant observation of antiferromagnetic and electric chiral textures at domain walls in the room-temperature ferroelectric antiferromagnet BiFeO3. Combining reciprocal and real-space characterization techniques, we reveal the presence of periodic chiral antiferromagnetic objects along the domain walls as well as a priori energetically unfavourable chiral ferroelectric domain walls. We discuss the mechanisms underlying their formation and their relevance for electrically controlled topological oxide electronics and spintronics.

(Invited) Opportunities and Challenges for in-Situ Synchrotron Characterization of All Solid State Batteries

The increasing demand for portable electronics, stationary storage, and electric vehicles is driving innovation in high-energy density batteries. Solid electrolytes that are strong enough to impede lithium dendrite growth may enable energy dense lithium metal anodes. Currently, the power densities of all-solid state batteries is limited because of ineffective ion transport and chemical and physical decomposition at solid|solid interfaces. Solid electrolytes consist of both intrinsic interfaces formed by grains, vacancies, and material junctions and extrinsic interfaces formed at solid|solid interfaces. The former involves transport between two ion conducting phases, and the latter involves ionic transport between an ion conducting phase and a mixed ion and electron conducting phase. The nature of ionic transport at intrinsic and extrinsic interfaces is important for mitigating chemical and structural instabilities. Extrinsic interface instabilities are responsible for high interfacial resistances. Examples of extrinsic interface instabilities include: (1) chemical decomposition and the formation of a solid electrolyte interphase at the electrode|electrolyte interface, (2) regions of excess and deficient lithium content, and (3) poor or delaminating-type contact at the interface which can contribute to non-uniform current distributions and localized degradation. In order to displace liquid electrolytes, new materials and engineering strategies need to be developed to negate these degradation pathways. New insight into the governing physics that occurs at these interfaces are critical for developing engineering strategies for the next generation of energy dense batteries [1,2]. However, buried solid|solid interfaces are notoriously difficult to observe with traditional bench-top and lab-scale experiments. In this talk I discuss opportunities for tracking phenomena and mechanisms in all solid state batteries in-situ using advanced synchrotron techniques. Synchrotron techniques that combine reciprocal and real space techniques are best equipped to track relevant phenomena with adequate spatial and temporal resolutions. [1] Shen, Fengyu, Marm B. Dixit, Xianghui Xiao, and Kelsey B. Hatzell. "Effect of pore connectivity on Li dendrite propagation within LLZO electrolytes observed with synchrotron X-ray tomography." ACS Energy Letters 3, no. 4 (2018): 1056-1061. [2] Dixit, Marm B., Matthew Regala, Fengyu Shen, Xianghui Xiao, and Kelsey B. Hatzell. "Tortuosity Effects in Garnet-Type Li7La3Zr2O12 Solid Electrolytes." ACS applied materials & interfaces 11, no. 2 (2018): 2022-2030.

Depletion layer dynamics of polyelectrolyte solutions under Poiseuille flow

Complex liquids flow through channels faster than expected, an effect attributed to the formation of low-viscosity depletion layers at the boundaries. Characterization of depletion layer length scale, concentration, and dynamics has remained elusive due in large part to the lack of suitable real-space experimental techniques. The short length scales associated with depletion layers have traditionally prohibited direct imaging. By overcoming this limitation via adaptations of stimulated emission depletion (STED) microscopy, we directly measure the concentration profile of polymer solutions at a nonadsorbing wall under Poiseuille flow. Using this approach, we 1) confirm the theoretically predicted concentration profile governed by entropically driven depletion, 2) observe depletion layer narrowing at low to intermediate shear rates, and 3) report depletion layer composition that approaches pure solvent at unexpectedly low shear rates.

Data Correction of Intensity Modulated Small Angle Scattering

To investigate long length scale structures using neutron scattering, real space techniques have shown certain advantages over the conventional methods working in reciprocal space. As one of the real space measurement techniques, spin echo modulated small angle neutron scattering (SEMSANS) has attracted attention, due to its relaxed constraints on sample environment and the possibility to combine SEMSANS and a conventional small angle neutron scattering instrument. In this report, we present the first implementation of SEMSANS at a pulsed neutron source and discuss important corrections to the data due to the sample absorption. These corrections allow measurements made with different neutron wavelengths and SEMSANS configurations to be overlaid and give confidence that the measurements provide an accurate representation of the density correlations in the sample.

Average and local strain fields in nanocrystals

This article presents a rigorous and self-consistent comparison of lattice distortion and deformation fields existing in energy-optimized pseudo-spherical gold nanoparticles obtained from real-space and powder diffraction strain analysis techniques. The changes in atomic positions resulting from energy optimization (relaxation) of ideally perfect gold nanoparticles were obtained using molecular dynamics modeling. The relaxed atomic coordinates were then used to compute the displacement, rotation and strain components in all unit cells within the energy-optimized (relaxed) particles. It was seen that all of these terms were distributed heterogeneously along the radial and tangential directions within the nanospheroids. The heterogeneity was largest in the first few atomic shells adjacent to the nanoparticle surface, where the continuity of crystal lattice vectors originating from the interior layers was broken because of local lattice rotations. These layers also exhibited maximum shear and normal strains. These (real-space) strain values were then compared with the average lattice strains obtained by refining the computed diffraction patterns of such particles. The results show that (i) relying solely on full-pattern refinement techniques for lattice strain analysis might lead to erroneous conclusions about the dimensionality and symmetry of deformation within relaxed nanoparticles; (ii) the lattice strains within such relaxed particles should be considered `eigenstrains' (`inherent strains') as defined by Mura [Micromechanics of Defects in Solids, (1991), 2nd ed., Springer]; and (iii) the stress/strain state within relaxed nanoparticles cannot be analyzed rigorously using the constitutive equations of linear elasticity.

Self-assembly of copper-free maltoheptaose-block-polystyrene nanostructured thin films in real and reciprocal space

The promising carbohydrate-based block copolymer maltoheptaose-block-polystyrene (MH-b-PS) has been used for high-performance memory transistors and next generation nanolithography. In order to realize the potential of MH-b-PS especially in microelectronic applications, we firstly improved its synthetic method for obtaining large amount of copper-free MH-b-PS. The main improvement relies on the removal of the residual copper catalyst by using a chelating resin. Then, the microphase separation of copper-free MH-b-PS in both thin film and bulk states under different solvent vapor annealing conditions were investigated comprehensively and compared with our previous report by using both real-space and reciprocal-space techniques. A phase transition of MH-b-PS from hexagonal close-packed horizontal cylinders to face-centered cubic were observed when increasing the amount of tetrahydrofuran in the mixture annealing solvent of tetrahydrofuran and H2O. More details about self-assembled MH-b-PS nanostructures were analyzed by comparing grazing incidence small angle X-ray scattering patterns with corresponding atomic force microscopy phase images.

Relaxation and domain formation in incommensurate two-dimensional heterostructures

We introduce configuration space as a natural representation for calculating the mechanical relaxation patterns of incommensurate two-dimensional (2D) bilayers, bypassing supercell approximations to encompass aperiodic relaxation patterns. The approach can be applied to a wide variety of 2D materials through the use of a continuum model in combination with a generalized stacking fault energy for interlayer interactions. We present computational results for small-angle twisted bilayer graphene and molybdenum disulfide (MoS$_2$), a representative material of the transition metal dichalcogenide (TMDC) family of 2D semiconductors. We calculate accurate relaxations for MoS$_2$ even at small twist-angle values, enabled by the fact that our approach does not rely on empirical atomistic potentials for interlayer coupling. The results demonstrate the efficiency of the configuration space method by computing relaxations with minimal computational cost for twist angles down to $0.05^\circ$, which is smaller than what can be explored by any available real space techniques. We also outline a general explanation of domain formation in 2D bilayers with nearly-aligned lattices, taking advantage of the relationship between real space and configuration space.

Application of video microscopy in experimental soft matter physics

Combining precise microscopic measurement with quantitative image analysis, video microscopy has become one of the most important, real-space experiment techniques to study the microscopic properties of soft matter systems. On the one hand, it provides a basic tool to observe and record the microscopic world. On the other hand, it offers a powerful experiment method to study the underlying physics of the microscopic world. In this paper, we review the development of the video microscopy, introduce the corresponding hardware and video processing software, and summarize the typical applications and recent progresses of video microscopy in colloidal suspensions. The future of the video microscopy in the soft condensed matter physics and interdisciplinary research is discussed.

Real-space Hopfield diagonalization of inhomogeneous dispersive media

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields, and we invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory can be naturally extended to the case of dissipative materials.