Atomic-scale observation of structural and electronic orders in the layered compound α-RuCl3

Machine Learning for Optical Scanning Probe Nanoscopy

The ability to perform nanometer-scale optical imaging and spectroscopy is key to deciphering the low-energy effects in quantum materials, as well as vibrational fingerprints in planetary and extraterrestrial particles, catalytic substances, and aqueous biological samples. These tasks can be accomplished by the scattering-type scanning near-field optical microscopy (s-SNOM) technique that has recently spread to many research fields and enabled notable discoveries. Herein, it is shown that the s-SNOM, together with scanning probe research in general, can benefit in many ways from artificial-intelligence (AI) and machine-learning (ML) algorithms. Augmented with AI- and ML-enhanced data acquisition and analysis, scanning probe optical nanoscopy is poised to become more efficient, accurate, and intelligent.

Atomically Unveiling an Atlas of Polytypes in Transition-Metal Trihalides

Transition-metal trihalides MX₃ (M = Cr, Ru; X = Cl, Br, and I) belong to a family of novel two-dimensional (2D) magnets that can exhibit topological magnons and electromagnetic properties, thus affording great promises in next-generation spintronic devices. Rich magnetic ground states observed in the MX₃ family are believed to be strongly correlated to the signature Kagome lattice and interlayer van der Waals coupling raised from distinct stacking orders. However, the intrinsic air instability of MX₃ makes their direct atomic-scale analysis challenging. Therefore, information on the stacking-registry-dependent magnetism for MX₃ remains elusive, which greatly hinders the engineering of desired phases. Here, we report a nondestructive transfer method and successfully realize an intact transfer of bilayer MX₃, as evidenced by scanning transmission electron microscopy (STEM). After surveying hundreds of MX₃ thin flakes, we provide a full spectrum of stacking orders in MX₃ with atomic precision and calculated their associated magnetic ground states, unveiled by combined STEM and density functional theory (DFT). In addition to well-documented phases, we discover a new monoclinic C2/c phase in the antiferromagnetic (AFM) structure widely existing in MX₃. Rich stacking polytypes, including C2/c, C2/m, R3̅, P3₁12, etc., provide rich and distinct magnetic ground states in MX₃. Besides, a high density of strain soliton boundaries is consistently found in all MX₃, combined with likely inverted structures, allowing AFM to ferromagnetic (FM) transitions in most MX₃. Therefore, our study sheds light on the structural basis of diverse magnetic orders in MX₃, paving the way for modulating magnetic couplings via stacking engineering.

Exploring Physics of Ferroelectric Domain Walls in Real Time: Deep Learning Enabled Scanning Probe Microscopy

The functionality of ferroelastic domain walls in ferroelectric materials is explored in real-time via the in situ implementation of computer vision algorithms in scanning probe microscopy (SPM) experiment. The robust deep convolutional neural network (DCNN) is implemented based on a deep residual learning framework (Res) and holistically nested edge detection (Hed), and ensembled to minimize the out-of-distribution drift effects. The DCNN is implemented for real-time operations on SPM, converting the data stream into the semantically segmented image of domain walls and the corresponding uncertainty. Further the pre-defined experimental workflows perform piezoresponse spectroscopy measurement on thus discovered domain walls, and alternating high- and low-polarization dynamic (out-of-plane) ferroelastic domain walls in a PbTiO₃ (PTO) thin film and high polarization dynamic (out-of-plane) at short ferroelastic walls (compared with long ferroelastic walls) in a lead zirconate titanate (PZT) thin film is reported. This work establishes the framework for real-time DCNN analysis of data streams in scanning probe and other microscopies and highlights the role of out-of-distribution effects and strategies to ameliorate them in real time analytics.

Direct observation of the Mottness and p-d orbital hybridization in the epitaxial monolayer α-RuCl3

α-RuCl₃, a promising material to accomplish the Kitaev honeycomb model, has attracted enormous interest recently. Mottness and p-d bonds play vital roles in generating Kitaev interactions and underpinning the potential exotic states of quantum magnets, and the van der Waals monolayer is considered to be a better platform to approach a two-dimensional Kitaev model than the bulk. Here, we worked out the growth art of an α-RuCl₃ monolayer on a graphite substrate and studied its electronic structure, particularly the delicate orbital occupations, through scanning tunneling microscopy and spectroscopy. An in-plane lattice expansion of 2.67 ± 0.83% is observed and the pronounced t_2g-p_π and e_g-p_σ hybridization are visualized. The Mott nature is unveiled by an ∼0.6 eV full gap at the Fermi level located inside the t_2g-p_π manifold which is further verified by the density functional theory calculations. The monolayer phase of α-RuCl₃ fulfills the a priori criteria of recent theoretical predictions of tuning the relevant properties in this material and provides a novel platform to explore the Kitaev physics.

Layer dependent magnetism and topology in monolayer and bilayers ReX3(XBr, I)

The realization of robust intrinsic ferromagnetism in two-dimensional materials with the possibility to support topologically non-trivial states has provided the fertile ground for novel physics and next-generation spintronics and quantum computing applications. In this contribution, we investigated the formation of topological states and magnetism in monolayer and bilayer systems of ReX₃(X= Br, I), with PBE, ACBN0 (self-consistent Hubbard-U), excluding/including van der Waals (vdW) corrections and/or spin-orbit coupling. Bulk ReX₃(X= Br, I) is predicted to crystallize in space groupR3¯(#148), similar to CrI₃, with monolayer exfoliation energies that are comparable or less than that of graphite. The topological character of the monolayer and bilayer systems of ReX₃(X= Br, I) is derived from anomalous Hall conductivity computations. Topologically non-trivial states in ReX₃(X= Br, I) are absent in the Hubbard-Ucomputations if vdW interactions are included, a prediction that is attributed to the large Hubbard-Udifference between the chemical constituents, ΔU∼ 1.5-1.6 eV, and a significant ∼2.0%-3.6% compressive in-plane strain introduced by vdW interactions. In contrast to the fragile and likely absent topological states in ReX₃(X= Br, I), magnetic properties are robust and independent of the level of theory: ferromagnetic monolayers are coupled antiferromagnetically to bilayers, with an energy separation between ferromagnetic and antiferromagnetic bilayer spin configurations that could be as low as 0.02 meV/Re (f= 4.8 GHz), well within the microwave range. This suggests that layer dependent magnetism in ReX₃(X= Br, I) may support a microwave controllable magnetic qubit, consisting of a superposition of antiferromagnetic and ferromagnetic bilayer states.

Exploring order parameters and dynamic processes in disordered systems via variational autoencoders

We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on atomic positions are available. This approach is predicated on the synergy of two concepts, the parsimony of physical descriptors and general rotational invariance of noncrystalline solids, and is implemented using a rotationally invariant extension of the variational autoencoder applied to semantically segmented atom-resolved data seeking the most effective reduced representation for the system that still contains the maximum amount of original information. This approach allowed us to explore the dynamic evolution of electron beam-induced processes in a silicon-doped graphene system, but it can be also applied for a much broader range of atomic scale and mesoscopic phenomena to introduce the bottom-up order parameters and explore their dynamics with time and in response to external stimuli.

Chemistry of Quantum Spin Liquids

Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Electrical Access to Ising Anyons in Kitaev Spin Liquids

We show that spin-spin correlations in a non-Abelian Kitaev spin liquid are associated with a characteristic inhomogeneous charge density distribution in the vicinity of Z_{2} vortices. This density profile and the corresponding local electric fields are observable, e.g., by means of surface probe techniques. Conversely, by applying bias voltages to several probe tips, one can stabilize Ising anyons (Z_{2} vortices harboring a Majorana zero mode) at designated positions, where we predict a clear Majorana signature in energy absorption spectroscopy.

Probing Charge Accumulation at SrMnO3/SrTiO3 Heterointerfaces via Advanced Electron Microscopy and Spectroscopy

The last three decades have seen a growing trend toward studying the interfacial phenomena in complex oxide heterostructures. Of particular concern is the charge distribution at interfaces, which is a crucial factor in controlling the interface transport behavior. However, the study of the charge distribution is very challenging due to its small length scale and the intricate structure and chemistry at interfaces. Furthermore, the underlying origin of the interfacial charge distribution has been rarely studied in-depth and is still poorly understood. Here, by a combination of aberration-corrected scanning transmission electron microscopy (STEM) and spectroscopy techniques, we identify the charge accumulation in the SrMnO₃ (SMO) side of SrMnO₃/SrTiO₃ heterointerfaces and find that the charge density attains the maximum of 0.13 ± 0.07 e^-/unit cell (uc) at the first SMO monolayer. Based on quantitative atomic-scale STEM analyses and first-principle calculations, we explore the origin of interfacial charge accumulation in terms of epitaxial strain-favored oxygen vacancies, cationic interdiffusion, interfacial charge transfer, and space-charge effects. This study, therefore, provides a comprehensive description of the charge distribution and related mechanisms at the SMO/STO heterointerfaces, which is beneficial for the functionality manipulation via charge engineering at interfaces.

Majorana-Mediated Spin Transport in Kitaev Quantum Spin Liquids

We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with zigzag edges using the time-dependent Majorana mean-field theory. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the S=1/2 spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system despite the presence of a nonzero spin gap. We also demonstrate that this phenomenon can be observed in the system with small Heisenberg interactions using the exact diagonalization.

Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism

The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interactions can be yielded by the synergy of spin-orbit coupling and electron correlations for specific electron configuration and lattice geometry, which is known as the Jackeli-Khaliullin mechanism. Based on this mechanism, there has been a fierce race for the materialization of the Kitaev spin liquid over the last decade, but the candidates have been still limited mostly to 4d- and 5d-electron compounds including cations with the low-spind5electron configuration, such as Ir4+and Ru3+. Here we discuss recent efforts to extend the material perspective beyond the Jackeli-Khaliullin mechanism, by carefully reexamining the two requisites, formation of thejeff= 1/2 doublet and quantum interference between the exchange processes, for not onlyd- but alsof-electron systems. We present three examples: the systems including Co2+and Ni3+with the high-spind7electron configuration, Pr4+with thef1-electron configuration, and polar asymmetry in the lattice structure. In particular, the latter two are intriguing since they may realize the antiferromagnetic Kitaev interactions, in contrast to the ferromagnetic ones in the existing candidates. This partial overview would stimulate further material exploration of the Kitaev spin liquids and its topological properties due to fractional excitations.

Modular Design via Multiple Anion Chemistry of the High Mobility van der Waals Semiconductor Bi4O4SeCl2

Making new van der Waals materials with electronic or magnetic functionality is a chemical design challenge for the development of two-dimensional nanoelectronic and energy conversion devices. We present the synthesis and properties of the van der Waals material Bi₄O₄SeCl₂, which is a 1:1 superlattice of the structural units present in the van der Waals insulator BiOCl and the three-dimensionally connected semiconductor Bi₂O₂Se. The presence of three anions gives the new structure both the bridging selenide anion sites that connect pairs of Bi₂O₂ layers in Bi₂O₂Se and the terminal chloride sites that produce the van der Waals gap in BiOCl. This retains the electronic properties of Bi₂O₂Se while reducing the dimensionality of the bonding network connecting the Bi₂O₂Se units to allow exfoliation of Bi₄O₄SeCl₂ to 1.4 nm height. The superlattice structure is stabilized by the configurational entropy of anion disorder across the terminal and bridging sites. The reduction in connective dimensionality with retention of electronic functionality stems from the expanded anion compositional diversity.

Sub-gap optical response in the Kitaev spin-liquid candidate α-RuCl3

We report detailed optical experiments on the layered compound α-RuCl₃ focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of THz and spin-orbital excitations via a study of temperature and symmetry-induced changes. The optical studies are complemented by thermal expansion experiments. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. A complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Orbital excitations, which cannot be explained based on recent models, and an electronic excitation, which appears in a narrow temperature range just across the structural phase transition. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition and a change of the stacking sequence, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of a single molecular layer determines the eigenfrequencies of most of these excitations. Only one mode at THz frequencies, which becomes suppressed in the high-temperature monoclinic phase and one phonon mode experience changes in symmetry and stacking. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (<1 eV) electronic structure of the ruthenium 4d ⁵ electrons in α-RuCl₃.

Antiferromagnetic spin-frustrated layers of corner-sharing Cu4 tetrahedra on the kagome lattice in volcanic minerals Cu5O2(VO4)2(CuCl), NaCu5O2(SeO3)2Cl3, and K2Cu5Cl8(OH)4·2H2O

The objective of the present work was to analyze the possibility of realization of quantum spin liquids in three volcanic minerals-averievite (Cu₅O₂(VO₄)₂(CuCl)), ilinskite (NaCu₅O₂(SeO₃)₂Cl₃), and avdononite (K₂Cu₅Cl₈(OH)₄·2H₂O)-from the crystal chemistry point of view. Based on the structural data, the sign and strength of magnetic interactions have been calculated and the geometric frustrations serving as the main reason of the existence of spin liquids have been investigated. According to our calculations, the magnetic structures of averievite and ilinskite are composed of antiferromagnetic (AFM) spin-frustrated layers of corner-sharing Cu₄ tetrahedra on the kagome lattice. However, the direction of nonshared corners of tetrahedra is different in them. The oxygen ions centering the OCu₄ tetrahedra in averievite and ilinskite provide the main contribution to the formation of AFM interactions along the tetrahedra edges. The local electric polarization in averievite and the possibility of spin configuration fluctuations due to vibrations of tetrahedra-centering oxygen ions have been discussed. The existence of structural phase transitions accompanied with magnetic transitions was assumed in ilinskite because of the effect of a lone electron pair by Se⁴⁺ ions. As was demonstrated through comparison of averievite and avdoninite, at the removal of centering oxygen ions from tetrahedra, the magnetic structure of the pyrochlore layer present in averievite transformed into an openwork curled net with large cells woven from corner-sharing open AFM spin-frustrated tetrahedra ('butterflies') in avdoninite.

Pressure tuning of charge ordering in iron oxide

A Verwey-type charge-ordering transition in magnetite at 120 K leads to the formation of linear units of three iron ions with one shared electron, called trimerons. The recently-discovered iron pentoxide (Fe₄O₅) comprising mixed-valent iron cations at octahedral chains, demonstrates another unusual charge-ordering transition at 150 K involving competing formation of iron trimerons and dimerons. Here, we experimentally show that applied pressure can tune the charge-ordering pattern in Fe₄O₅ and strongly affect the ordering temperature. We report two charge-ordered phases, the first of which may comprise both dimeron and trimeron units, whereas, the second exhibits an overall dimerization involving both the octahedral and trigonal-prismatic chains of iron in the crystal structure. We link the dramatic change in the charge-ordering pattern in the second phase to redistribution of electrons between the octahedral and prismatic iron chains, and propose that the average oxidation state of the iron cations can pre-determine a charge-ordering pattern.

The charge order transition of commonly known magnetite has only recently been unraveled. Here, the measurement of the low-temperature high-pressure phase diagram of a related material (Fe₄O₅) elucidates the interplay of average oxidation state and charge-ordering phenomena in the iron oxide family.

Electrical Transport Signature of the Magnetic Fluctuation-Structure Relation in α-RuCl3 Nanoflakes

The small gap semiconductor α-RuCl₃ has emerged as a promising candidate for quantum spin liquid materials. Thus far, Raman spectroscopy, neutron scattering, and magnetization measurements have provided valuable hints for collective spin behavior in α-RuCl₃ bulk crystals. However, the goal of implementing α-RuCl₃ into spintronic devices would strongly benefit from the possibility of electrically probing these phenomena. To address this, we first investigated nanoflakes of α-RuCl₃ by Raman spectroscopy and observed similar behavior as in the case of the bulk material, including the signatures of possible fractionalized excitations. In complementary experiments, we investigated the electrical charge transport properties of individual α-RuCl₃ nanoflakes in the temperature range between 120 and 290 K. The observed temperature-dependent electrical resistivity is consistent with variable range hopping behavior and exhibits a transition at about 180 K, close to the onset temperature observed in our Raman measurements. In conjunction with the established relation between structure and magnetism in the bulk, we interpret this transition to coincide with the emergence of fractionalized excitations due to the Kitaev interactions in the nanoflakes. Compared to the bulk samples, the transition temperature of the underlying structural change is larger in the nanoflakes. This difference is tentatively attributed to the dimensionality of the nanoflakes as well as the formation of stacking faults during mechanical exfoliation. The demonstrated devices open up novel perspectives toward manipulating the Kitaev-phase in α-RuCl₃ via electrical means.

Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb

We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points [Formula: see text] and [Formula: see text] are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.

Electronic and magnetic properties of monolayer α-RuCl3: a first-principles and Monte Carlo study

Recent experiments revealed that monolayer α-RuCl₃ can be obtained by a chemical exfoliation method and exfoliation or restacking of nanosheets can manipulate the magnetic properties of the materials. Thermal variations of magnetization and specific heat curves indicate that monolayer α-RuCl₃ exhibits a phase transition between ordered and disordered phases at the Curie temperature of 14.21 K.

Models and materials for generalized Kitaev magnetism

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃), three-dimensional Kitaev materials (β- and γ-Li₂IrO₃), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Antiferromagnetic Resonance and Terahertz Continuum in α-RuCl_{3}

We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.