Lattice Symmetry Research Articles

Pressure and chemical doping induced phase transition and phonon dynamics of multiferroic Bi5Ti3FeO15 ceramics

The external pressure and doping effect have been studied on the lattice structure of multiferroic Bi5Ti3−2xFe1+xNbxO15 (BTFNx) ceramics. Based on the x-ray diffraction and the Raman spectroscopic evidence, it is confirmed that the doping-induced lattice deformation is closely related to the concentrations of the Nb5+ and Fe3+ ions. The Bi5Ti3FeO15 (BTF) ceramic transits from orthorhombic (O, A21am) - O and tetragonal (T) - T (I4/mmm) with pressure, showing the intermediate phase coexistence at a wide pressure range of 4.5–14.8 GPa, while for BTFN0.6 ceramics, it is O (Fmm2) - O and T - T(I4/mmm) having the phase coexistence at 6–18 GPa. The ionic substitution, phase diagram and the evolution of phonon, lattice symmetry, and stability of BTFNx ceramics have been systematically observed and studied under the internal and external factors. Our work provides a comprehensive understanding of the structural and physical functionality for the development and optimization of multiferroic four-layer compounds BTF material systems.

Metallic ruthenium ilmenites: First-principles study of MgRuO3 and CdRuO3

Ilmenites ABO3 provide a platform for electron correlation and magnetism on alternatively stacked honeycomb layers of edge-sharing AO6 or BO6 octahedra. When A and B are 3d transition metals, strong electron correlation makes the systems Mott insulators showing various magnetic properties, while when B is Ir with 5d electrons, competition between electron correlation and spin–orbit coupling realizes a spin–orbital coupled Mott insulator as a potential candidate for quantum spin liquids. Here, we theoretically investigate intermediate 4d ilmenites, ARuO3 with A = Mg and Cd, which have recently been synthesized and shown to be metallic, unlike the 3d and 5d cases. By using first-principles calculations, we optimize the lattice structures and obtain the electronic band structures. We show that MgRuO3 exhibits strong dimerization on RuO6 honeycomb layers, leading to the formation of bonding and anti-bonding bands for one of the three t2g orbitals; the lattice symmetry is lowered from R3̄ to P1̄, and the Fermi surfaces are composed of the other two t2g orbitals. In contrast, we find that CdRuO3 has a lattice structure close to R3̄, and all three t2g orbitals contribute almost equally to the Fermi surfaces. A comparison of our results with other Ru honeycomb materials, such as Li2RuO3, indicates that the metallic ruthenium ilmenites stand on a subtle balance among electron correlation, spin–orbit coupling, and electron–phonon coupling.

Plastic phase transitions in tris(hydroxymethyl)aminomethane perchlorate.

Organic crystal materials with metal-free feature and intrinsically low molecular mass are highly desirable for applications in flexible smart devices. Here, we reported a plastic crystal, tris(hydroxymethyl)aminomethane perchlorate (Tris-HClO4), which crystallizes in the R3̄ space group at room temperature and undergoes plastic phase transition at 369 K, showing a large entropy gain of 70.5 J mol-1 K-1, much higher than its fusion entropy gain (12.9 J mol-1 K-1). PXRD measurement indicates that it has cubic lattice symmetry in the high-temperature phase. Moreover, it exhibits excellent dielectric permittivity switching properties and robust cyclic stability. This work could be the pathway for chemical designing multifunctional switchable materials with the motive of combining the idea of symmetry breaking and plastic phase transition.

Uniaxial-strain tuning method in study of iron-based superconductors

In the study of quantum materials, introducing pressure and strain that can change lattice parameters and symmetry is an effective experimental method for manipulating the electronic properties of the system. In measurements under hydrostatic pressure or in-plane epitaxial strain, the changes in lattice parameters will lead to significant changes in the electronic structure, thereby triggering off novel quantum phenomena and phase transitions. By comparison, the in-plane uniaxial strain, which has been widely employed in recent years, not only changes lattice parameters, but also directly destroys and controls the symmetry of the system, thereby affecting the electronic ordering state and even collective excitation of the system. This article provides a comprehensive overview of the basic concepts of uniaxial strain, the development of experimental methods, and some research progress in using these methods to regulate superconductivity and electronic nematicity in iron-based superconductors. This review contains six sections. Section 1 focuses on a genetral introduction for the uniaxial strain techque and the arrangement of this paper. Section 2 is devoted to the basic concepts and formulas related to elastic moduli and the decomposition of uniaxial strain into irreducible symmetric channels under <i>D</i><sub>4<i>h</i></sub> point group. Section 3 gives iron-based superconductors (FeSCs) and discusses the uniaxial-pressure detwinning method and related research progress. Section 4 introduces the establishment of the elastoresistance as a probe of the nematic susceptibility and discusses the key researches in this direction. Section 5 describes the research progress of the effects of uniaxial strain on superconductivity and nematicity. In sections 4 and 5, key experimental techniques, such as elastoresistance, are discussed in detail. Section 6 extends the discussion to several types of quantum materials suitable for uniaxial-strain tuning method beyond the FeSCs. Finally, we provide a brief summary and outlook on the uniaxial strain tuning technique. Overall, this review article provides valuable resources for the beginners in the field of FeSC and those who are interested in using uniaxial strain to modulate the electronic properties of quantum materials. By summarizing recent advancements and experimental techniques, this review hopes to inspire further research and innovation in studying electronic materials under uniaxial strain.

Elastically Isotropic Open-Cell Lattice Metamaterials with Superior Stiffness

Elastically Isotropic Open-Cell Lattice Metamaterials with Superior Stiffness

Performance of a deep convolutional neural network to classify crystal structures using selected area electron beam diffraction patterns containing lattice defect information.

A deep convolutional neural network (DCNN) architecture ResNet has been tested to verify its ability to handle selected area electron diffraction pattern (SADP) datasets carrying information on lattice defects including strains, thermal lattice vibrations, point defects, dislocations, and twin boundaries. The disordered states of the crystal lattices in the presence of these defects were predicted by ab initio molecular dynamics simulations, first principles geometry optimizations, and lattice manipulation operations in an effort to establish a possible dataset augmentation strategy for the improvement of classification performance of the ResNet. Using the disordered lattice information originating from the defects, test dataset SADPs were generated by simulating electron diffraction in transmission electron microscopy. The ResNet, pre-trained using SADPs from defect-free materials, showed decreasing but acceptable classification accuracies with increasing degrees of lattice disorder regarding the lattice vibrations and point defects. When tested using the diffraction patterns for strained lattices, the ResNet responded to the changing lattice symmetry when strain levels are relatively high suggesting that it has capability to discern different symmetries induced by large strains. However, the ResNet failed to recognize lattice structure when dislocations and twin boundaries were considered. It is suggested that DCNN architectures be trained over various scenarios including changes in the image feature characteristics in the diffraction patterns related to defects in future developments for improved general classification performances.

Anomalous intense emission of the 5D0/7F4 transition for reddish-orange light-emitting and fluorescent probe for multiple lattice sites in β-PbF2:Eu3+/K+ oxyfluoride glass ceramics

K+ ions as charge compensating ions doped into the fluorite lattice, vigorously regulating the lattice symmetry around rare earth ions, achieving luminescence efficiency enhancement and spectral broadening of rare earth ions.

Electronic Lieb lattice signatures embedded in two-dimensional polymers with a square lattice.

Exotic band features, such as Dirac cones and flat bands, arise directly from the lattice symmetry of materials. The Lieb lattice is one of the most intriguing topologies, because it possesses both Dirac cones and flat bands which intersect at the Fermi level. However, the synthesis of Lieb lattice materials remains a challenging task. Here, we explore two-dimensional polymers (2DPs) derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice (sql) as potential electronic Lieb lattice materials. By systematically varying the linker length (ZnPc-xP), we found that some ZnPc-xP exhibit a characteristic Lieb lattice band structure. Interestingly though, fes bands are also observed in ZnPc-xP. The coexistence of fes and Lieb in sql 2DPs challenges the conventional perception of the structure-electronic structure relationship. In addition, we show that manipulation of the Fermi level, achieved by electron removal or atom substitution, effectively preserves the unique characteristics of Lieb bands. The Lieb Dirac bands of ZnPc-4P shows a non-zero Chern number. Our discoveries provide a fresh perspective on 2DPs and redefine the search for Lieb lattice materials into a well-defined chemical synthesis task.

Tailoring on Rotational Symmetry of Liquid Crystal Domain Lattices

AbstractRotational symmetry is ubiquitous in nature. However, self‐assemblies of soft condensed matter such as liquid crystals (LCs) are entropy‐driven, making the tailoring of rotational symmetry challenging. Here, an approach is proposed to control the rotational symmetry of LC domain lattices based on the anchoring condition predesign and the orientational‐order inheritance during the nematic‐smectic phase transition. By this means, periodic and quasiperiodic LC textures with Ci symmetry (i = 2–6) determined by the preset alignment lattices are realized, and verified by symmetries of diffraction patterns. Topological analysis is carried out to disclose distinct evolutions of orders between disclination line textures and defect wall textures of different rotational symmetries. The influences of anchoring conditions, phase transitions, and mechanical stress on the self‐assembly of LCs, as well as the underlying mechanisms and dynamics, are investigated. This work realizes controllable rotational symmetry for large‐area self‐organized LCs and brings new insights to soft condensed matter.

Deciphering the structural heterogeneity behaviors of (K, Na)NbO[formula omitted]-based piezoelectric ceramics with multi-scale analyses

Inducing local structural heterogeneity is one of the most attractive strategies to enhance the piezoelectricity in lead-free piezoceramics, while the underlying mechanisms have not been well clarified, such as phase coexistence and domain boundary. Here, we mainly focus on analyzing the structure evolution mechanism of 0.96(K0.48Na0.52)(Nb1−xSbx)O3-0.04(Bi0.5Ag0.5)ZrO3 (0≤x≤0.1) (KNN) lead-free piezoelectric ceramics to study the intrinsic structural contributions from chemical modifying and/or alloy replacement. We explore the relation between structural characteristics and physical functionality by combining macro-spectral and micro-heterogeneity characterizations. It was found that Raman- and infrared-active phonon evolutions with respect to the motion of oxygen octahedron reveal the enhanced lattice symmetry when x increases to 0.06, along with the upswing optical electronic transitions. Moreover, we clarify the local heterogeneous structure of ceramics in terms of the spatial distribution of phonon traits on the micron scale accompanied with the atom-resolution polar vector state. The detected nanoscale atomic displacement clusters are directly related to the excellent polarization properties. Additionally, the phonon thermodynamics evolution was investigated in a wide temperature range of 80-720 K with unpolarized and polarized geometries. The detailed phase transition evolution and rhombohedral–orthorhombic–tetragonal multi-phase coexistence have been confirmed with Sb incorporation. The present work boosts the understanding of the compound-structure-functionality relation of KNN-based heterophase coexistent system, which could promote the development of the promising high-performance piezoelectric materials.

Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm.

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.

Interplay of spin and orbital ordering in a frustrated spinel chromite

Geometric Spin Frustration, when sufficiently strong, provides a platform for novel spin textures with emergent phenomena, such as ferroelectricity. This article investigates NiCr2O4, a spinel chromite co-hosting the frustration of Cr3+ spins with orbital frustration of Ni2+ ions, with the latter expected to eradicate the spin frustration by lowering lattice symmetry. Detailed experiments unveil an intriguing reentrant-spin-glass-like behavior alongside the previously known canted ferrimagnetism. Our analysis focuses on the ordering of Cr3+ spins at two distinct sublattices, with one contributing to canted ferrimagnetism, while the other exhibits a local (spin-frustrated) texture, potentially inducing spin-glass behavior. Density functional theory calculations corroborate the experimental findings, establishing as the ground state of NiCr2O4. This study presents new prospects for ferroelectricity driven by exchange striction in orbitally ordered spinel chromites.

Nonlinear and Emissive {[MIII(CN)6]3-···Polyresorcinol} (M = Fe, Co, Cr) Cocrystals Exhibiting an Ultralow Frequency Raman Response.

Optically active functional noncentrosymmetric architectures might be achieved through the combination of molecules with inscribed optical responses and species of dedicated tectonic character. Herein, we present the new series of noncentrosymmetric cocrystal salt solvates (PPh4)3[M(CN)6](L)n·msolv (M = Cr(III), Fe(III), Co(III); L = polyresorcinol coformers, multiple hydrogen bond donors: 3,3',5,5'-tetrahydroxy-1,19-biphenyl, DiR, n = 2, or 5'-(3,5-dihydroxyphenyl)-3,3″,5,5″-tetrahydroxy-1,19:3',1″-terphenyl, TriRB, n = 1) denoted as MDiR and MTriRB, respectively. The hydrogen-bonded subnetworks {[M(CN)6]3-;Ln}∞ of dmp, neb, or dia topology are formed through structural matching between building blocks within supramolecular cis-bis(chelate)-like {[M(CN)6]3-;(H2L)2(HL)2} or tris(chelate)-like {[M(CN)6]3-;(H2L)3} fragments. The quantum-chemical analysis demonstrates the mixed electrostatic and covalent character of these interactions, with their strength clearly enhanced due to the negative charge of the hydrogen bond acceptor metal complex. The corresponding interaction energy is also dependent on the geometry of the contact and size matching of its components, rotational degree of freedom and extent of the π-electron system of the coformer, and overall fit to the molecular surroundings. Symmetry of the crystal lattices is correlated with the local symmetry of coformers and {complex;(coformer)n} hydrogen-bonded motifs characterized by the absence of the inversion center and mirror plane. All compounds reveal second-harmonic generation activity and photoluminescence diversified by individual UV-vis spectral characteristics of the components, and interesting low-frequency Raman scattering spectra within the subterahertz spectroscopic domain. Vibrational (infrared/Raman), UV-vis electronic absorption (experimental and calculated), and 57Fe Mössbauer spectra together with electrospray ionization mass spectrometry (ESI-MS) data are provided for the complete description of our systems.

Multi-band topological valley modes of flexural waves in micro-perforated phononic plates

To develop phononic topological insulators (PTIs) with time reversal invariance, phononic crystals (PCs) are elaborately configurated to ensure the lattice symmetry and meanwhile to open the complete band gap. Particularly, a multi-band PTI requires more complex architecture than its single-band counterpart, leading to extra difficulty in implementation and poor manufacturability of PCs. Here, we present a straightforward and generic design strategy, to realize multi-band PTIs in micro-perforated phononic plates. Rather than using complex surface-mounted or embedded scatterers, the novel phononic plate is micro-perforated with a type of fan-shaped split-ring resonators (SRRs), the multi-modal resonances of which under constrained lattice symmetry induce multiple Dirac degeneracies in flexural-wave dispersions at different frequency scales. The multi-band topological phase transitions are observed, and triple topological band gaps are caused when rotating micro-perforated slots properly. Experimental results agree well with numerical simulation results, both demonstrating triband valley edge-state propagation of flexural waves. In addition, we also prove that the developed valley PTIs enable the second-order corner modes of flexural waves within the corresponding topological band gaps. Parametric studies further reveal that the emergence of the valley-shaped Dirac degeneracy bands in the developed PTI is insensitive to the plate thickness and slots parameters, and more than three Dirac cones exist in flexural-wave dispersions. The developed micro-perforated plates with SRRs provides a convenient platform for enabling multi-band PTIs with various symmetries, facilitating applications of multi-frequency topological effects of elastic waves in a cost-effective way.

Effective Mechanical Properties of Periodic Cellular Solids with Generic Bravais Lattice Symmetry via Asymptotic Homogenization.

In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais's lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in Python with a proposed fast-nearest neighbour algorithm to accurately estimate the periodic boundary conditions of the discretized representative volume element of the lattice unit cell. Convergence studies are performed, and numerical errors caused by both voxel meshing and periodic boundary condition approximation processes are discussed in detail. It is found that the numerical error in periodicity approximation is cyclically dependent on the number of divisions performed during the meshing process and, thus, is minimized with a refined voxel mesh. Validation studies are performed by comparing the elastic properties of 2D hexagon lattices with orthogonal and non-orthogonal bases. The developed methodology was also applied to derive the effective properties of several lattice topologies, and variation of their anisotropic macroscopic properties with relative densities is presented as material selection charts.

Large off-diagonal magnetoelectricity in a triangular Co2+-based collinear antiferromagnet

Magnetic toroidicity is an uncommon type of magnetic structure in solid-state materials. Here, we experimentally demonstrate that collinear spins in a material with R-3 lattice symmetry can host a significant magnetic toroidicity, even parallel to the ordered spins. Taking advantage of a single crystal sample of CoTe6O13 with an R-3 space group and a Co2+ triangular sublattice, temperature-dependent magnetic, thermodynamic, and neutron diffraction results reveal A-type antiferromagnetic order below 19.5 K, with magnetic point group -3′ and k = (0,0,0). Our symmetry analysis suggests that the missing mirror symmetry in the lattice could lead to the local spin canting for a toroidal moment along the c axis. Experimentally, we observe a large off-diagonal magnetoelectric coefficient of 41.2 ps/m that evidences the magnetic toroidicity. In addition, the paramagnetic state exhibits a large effective moment per Co2+, indicating that the magnetic moment in CoTe6O13 has a significant orbital contribution. CoTe6O13 embodies an excellent opportunity for the study of next-generation functional magnetoelectric materials.

LnPO4:Eu3+ nanoparticles: Role of host lattices on physiochemical and luminescent properties

LnPO4:Eu3+ (Ln = La, Gd and Y) nanoparticles (NPs) were prepared at low temperatures via a urea-based thermal decomposition method. X-ray diffraction pattern revealed a hexagonal single phase, high purity with an average crystalline size of 13.9, 14.89, and 18.7 nm for LaPO4:Eu, GdPO4:Eu, and YPO4:Eu NPs, respectively. Bandgap energies were calculated based on the measure absorption spectra are to be values 5.14, 5.03, and 4.90 eV for the LaPO4:Eu, GdPO4:Eu, and YPO4:Eu NPs, respectively. A comparative study suggested that the excitation and emission transitions were significantly higher in the GdPO4:Eu NPs and in comparison to the LaPO4:Eu and YPO4:Eu NPs. It implies the impact of the crystallinity, host lattice, and crystal symmetry, in which doped Eu3+-ion replaces the host cation and distorts the crystal symmetry.

Vectorial active matter on the lattice: polar condensates and nematic filaments

We introduce a novel lattice-gas cellular automaton (LGCA) for compressible vectorial active matter with polar and nematic velocity alignment. Interactions are, by construction, zero-range. For polar alignment, we show the system undergoes a phase transition that promotes aggregation with strong resemblance to the classic zero-range process. We find that above a critical point, the states of a macroscopic fraction of the particles in the system coalesce into the same state, sharing the same position and momentum (polar condensate). For nematic alignment, the system also exhibits condensation, but there exist fundamental differences: a macroscopic fraction of the particles in the system collapses into a filament, where particles possess only two possible momenta. Furthermore, we derive hydrodynamic equations for the active LGCA model to understand the phase transitions and condensation that undergoes the system. We also show that generically the discrete lattice symmetries—e.g. of a square or hexagonal lattice—affect drastically the emergent large-scale properties of on-lattice active systems. The study puts in evidence that aligning active matter on the lattice displays new behavior, including phase transitions to states that share similarities to condensation models.

Isotropic exchange-bias in twinned epitaxial Co/Co3O4 bilayer

Exchange bias (EB) is a unidirectional anisotropy caused by interface coupling between a ferromagnet and an antiferromagnet. It causes a preferential direction of magnetization in the ferromagnet, which manifests as a shift of the hysteresis loop along the magnetic field axis. Here, we demonstrate a large EB of over 1000 Oe at 20 K in a twinned Co(111)/Co3O4(111) thin film epitaxially grown on sapphire(0001) with sixfold rotational lattice symmetry, which is among the highest values reported for Co/Co1−yO systems. In such systems, the effect intensity is largest along the magnetic easy axes, which usually results in an anisotropy of the EB in epitaxial interfaces. However, we observed identical EB values for 0°, 15°, and 30° angles between the magnetic field and the nearest Co[002] magnetic easy axes. The measurements imply a relaxation of the magnetization to the nearest easy axis, suggesting increasingly isotropic EB fields with higher orders of rotational lattice symmetry.

Symmetry-Engineering-Induced In-Plane Polarization Enhancement in Ta2NiS5/CrOCl van der Waals Heterostructure

Van der Waals (vdW) interfaces can be formed via layer stacking regardless of the lattice constant or symmetry of the individual building blocks. Herein, we constructed a vdW interface of layered Ta2NiS5 and CrOCl, which exhibited remarkably enhanced in-plane anisotropy via polarized Raman spectroscopy and electrical transport measurements. Compared with pristine Ta2NiS5, the anisotropy ratio of the Raman intensities for the B2g, 2Ag, and 3Ag modes increased in the heterostructure. More importantly, the anisotropy ratios of conductivity and mobility in the heterostructure increased by one order of magnitude. Specifically speaking, the conductivity ratio changed from ~2.1 (Ta2NiS5) to ~15 (Ta2NiS5/CrOCl), while the mobility ratio changed from ~2.7 (Ta2NiS5) to ~32 (Ta2NiS5/CrOCl). Such prominent enhancement may be attributed to the symmetry reduction caused by lattice mismatch at the heterostructure interface and the introduction of strain into the Ta2NiS5. Our research provides a new perspective for enhancing artificial anisotropy physics and offers feasible guidance for future functionalized electronic devices.