Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

Deciphering competing interactions of Kitaev-Heisenberg-Γ system in clusters: II. Dynamics of Majorana fermions

We perform a systematic and exact study of Majorana fermion dynamics in the Kitaev-Heisenberg-Γ model in a few finite-size clusters increasing in size up to twelve sites. We employ exact Jordan-Wigner transformations to evaluate certain measures of Majorana fermion correlation functions, which effectively capture matter and gauge Majorana fermion dynamics in different parameter regimes. An external magnetic field is shown to produce a profound effect on gauge fermion dynamics. Depending on certain non-zero choices of other non-Kitaev interactions, it can stabilise it to its non-interacting Kitaev limit. For all the parameter regimes, gauge fermions are seen to have slower dynamics, which could help build approximate decoupling schemes for appropriate mean-field theory. The probability of Majorana fermions returning to their original starting site shows that the Kitaev model in small clusters can be used as a test bed for the quantum speed limit.

Deciphering competing interactions of Kitaev-Heisenberg-Γ system in clusters: I. Static properties

Recently, the Kitaev-Heisenberg-Γ system has been used to explore various aspects of Kitaev spin liquid physics. Here, we consider a few small clusters of up to twelve sites and study them in detail to unravel many interesting findings due to the competition between all possible signs and various magnitudes of these interactions under the influence of an external magnetic field. When Heisenberg interaction is taken anti-ferromagnetic, one obtains plateaus in correlation functions where, surprisingly, the exact groundstate reduces to the eigenstate of Heisenberg interaction as well. On the other hand, for ferromagnetic Heisenberg interaction, its competition with Kitaev interaction results in non-monotonicity in the correlation functions. We discuss, in detail, the competing effects on low energy spectrum, flux operator, magnetization, susceptibility, and specific heat. Finally, we discuss how our findings could be helpful to explain some of the recent experimental and theoretical findings in materials with Kitaev interactions.

Cobalt-based pyroxenes: A new playground for Kitaev physics

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe[Formula: see text]O[Formula: see text] using a combination of neutron scattering, ab initio methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co[Formula: see text] ions. The extended Kitaev-Heisenberg model, including a significant anisotropic bond-dependent exchange term with [Formula: see text], is identified as the key descriptor of the magnetic interactions in SrCoGe[Formula: see text]O[Formula: see text]. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13 T) which shifts the system from a fragile antiferromagnetic ordering with [Formula: see text] K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended [Formula: see text] orbitals, emerge as a platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics.

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

Probing Majorana Wave Functions in Kitaev Honeycomb Spin Liquids with Second-Order Two-Dimensional Spectroscopy

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.

Giant Anisotropic Magnetoresistance in Few-Layer α-RuCl3 Tunnel Junctions

The spin-orbit-assisted Mott insulator α-RuCl3 is proximate to the coveted quantum spin liquid (QSL) predicted by the Kitaev model. In the search for the pure Kitaev QSL, reducing the dimensionality of this frustrated magnet by exfoliation has been proposed as a way to enhance magnetic fluctuations and Kitaev interactions. Here, we perform angle-dependent tunneling magnetoresistance (TMR) measurements on ultrathin α-RuCl3 crystals with various layer numbers to probe their magnetic, electronic, and crystal structures. We observe a giant change in resistance, as large as ∼2500%, when the magnetic field rotates either within or out of the α-RuCl3 plane, a manifestation of the strongly anisotropic spin interactions in this material. In combination with scanning transmission electron microscopy, this tunneling anisotropic magnetoresistance (TAMR) reveals that few-layer α-RuCl3 crystals remain in the high-temperature monoclinic phase at low temperatures. It also shows the presence of a zigzag antiferromagnetic order below the critical temperature TN ≃ 14 K, which is twice the one typically observed in bulk samples with rhombohedral stacking. Our work offers valuable insights into the relation between the stacking order and magnetic properties of this material, which helps lay the groundwork for creating and electrically probing exotic magnetic phases such as QSLs via van der Waals engineering.

Incommensurate charge super-modulation and hidden dipole order in layered kitaev material α-RuCl3

The magnetism of Kitaev materials has been widely studied, but their charge properties and the coupling to other degrees of freedom are less known. Here we investigate the charge states of α-RuCl3, a promising Kitaev quantum spin liquid candidate, in proximity to graphite. We discover that few-layered α-RuCl3 experiences a clear modulation of charge states, where a Mott-insulator to weak charge-transfer-insulator transition in the 2D limit occurs by means of heterointerfacial polarization. More notably, distinct signals of incommensurate charge and lattice super-modulations, regarded as an unconventional charge order, accompanied in the insulator. Our theoretical calculations have reproduced the incommensurate charge order by taking into account the antiferroelectricity of α-RuCl3 that is driven by dipole order in the internal electric fields. The findings imply that there is strong coupling between the charge, spin, and lattice degrees of freedom in layered α-RuCl3 in the heterostructure, which offers an opportunity to electrically access and tune its magnetic interactions inside the Kitaev compounds.

Spin-Mechanical Coupling in 2D Antiferromagnet CrSBr

Spin-mechanical coupling is vital in diverse fields including spintronics, sensing, and quantum transduction. Two-dimensional (2D) magnetic materials provide a unique platform for investigating spin-mechanical coupling, attributed to their mechanical flexibility and novel spin orderings. However, studying their spin-mechanical coupling presents challenges in probing mechanical deformation and thermodynamic property changes at the nanoscale. Here we use nano-optoelectromechanical interferometry to mechanically detect the phase transition and magnetostriction effect in multilayer CrSBr, an air-stable antiferromagnet with large magnon-exciton coupling. The transitions among antiferromagnetism, spin-canted ferromagnetism, and paramagnetism are visualized. Nontrivial magnetostriction coefficient 2.3 × 10-5 and magnetoelastic coupling strength on the order of 106 J/m3 have been found. Moreover, we demonstrate the substantial tunability of the magnetoelastic constant by nearly 50% via gate-induced strain. Our findings demonstrate the strong spin-mechanical coupling in CrSBr and pave the way for developing sensitive magnetic sensing and efficient quantum transduction at the atomically thin limit.

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

Field tuning Kitaev systems for spin fractionalization and topological order

The honeycomb Kitaev model describes aZ2spin liquid with topological order and fractionalized excitations consisting of gappedπ-fluxes and free Majorana fermions. Competing interactions, even when not very strong, are known to destabilize the Kitaev spin liquid. Magnetic fields are a convenient parameter for tuning between different phases of the Kitaev systems, and have even been investigated for potentially counteracting the effects of other destabilizing interactions leading to a revival of the topological phase. Here we review the progress in understanding the effects of magnetic fields on some of the perturbed Kitaev systems, particularly on fractionalization and topological order.

Evidence for electron-hole crystals in a Mott insulator

The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.

Periodic DFT calculations to compute the attributes of a quantum material: honeycomb ruthenium trichloride

Quantum spin liquids (QSLs) have become prominent materials of interest in the pursuit of fault-tolerant materials for quantum computing applications. This is due to the fact that these materials are theorized to host an interesting variety of quantum phenomena such as quasi-particles that may behave as anyons as a result of the high entangled nature of the spin states within the systems. Computing the electronic and magnetic properties of these materials is necessary in order to understand the underlying interactions of the materials. In this paper, the structural, electronic, and magnetic properties including lattice parameters, bandgap, Heisenberg coupling constants, and Curie temperatures for α-RuCl3, a promising candidate for the Kitaev QSL model, are computed using periodic density functional theory. Furthermore, various parameters of the calculations (i.e. functional choice, basis set, k-point density, and Hubbard correction) are varied in order to determine what effect, if any, the computational setup has on the computed properties. The results of this study indicate that PBE functional with Hubbard corrections of 1.5-2.5 eV with a k-point density of 3.0 points per Å-1 appear to be the best parameters to compute Heisenberg coupling constants for α-RuCl3. These parameters with the addition of spin orbit coupling works well for computing Curie temperatures for α-RuCl3. Distinct differences are noted in the computations of the bulk structure vs. monolayer structures, indicating that interactions between the layers play a role in the material properties and changes to the inter-layer spacing may result in interesting and unique magnetic properties that require further investigation.

Stacking Faults Enabled Second Harmonic Generation in Centrosymmetric van der Waals RhI3

Second harmonic generation (SHG) in van der Waals (vdW) materials has garnered significant attention due to its potential for integrated nonlinear optical and optoelectronic applications. Stacking faults in vdW materials are a typical kind of planar defect that introduces a degree of freedom to modulate the crystal symmetry and resultant SHG response. However, the physical origin and tunability of stacking-fault-governed SHG in vdW materials remain unclear. Here, taking the intrinsically centrosymmetric vdW RhI3 as an example, we theoretically reveal the origin of stacking-fault-governed SHG response, where the SHG response comes from the energetically favorable AC̅ stacking fault of which the electrical transitions along the high-symmetry paths Γ-M and Γ-K in the Brillion zone play the dominant role at 810 nm. Such a stacking-fault-governed SHG response is further confirmed via structural characterizations and SHG measurements. Furthermore, by applying hydrostatic pressure on RhI3, the correlation between structural evolution and SHG response is revealed with SHG enhancement up to 6.9 times, where the decreased electronic transition energies and higher momentum matrix elements due to the stronger interlayer interactions upon compression magnify the SHG susceptibility. This study develops a promising foundation for nonlinear nano-optics applications through the strategic design of stacking faults.

Two-Dimensional Cobalt(II) Benzoquinone Frameworks for Putative Kitaev Quantum Spin Liquid Candidates

The realization and discovery of quantum spin liquid (QSL) candidate materials are crucial for exploring exotic quantum phenomena and applications associated with QSLs. Most existing metal-organic two-dimensional (2D) quantum spin liquid candidates have structures with spins arranged on the triangular or kagome lattices, whereas honeycomb-structured metal-organic compounds with QSL characteristics are rare. Here, we report the use of 2,5-dihydroxy-1,4-benzoquinone (X2dhbq, X = Cl, Br, H) as the linkers to construct cobalt(II) honeycomb lattices (NEt4)2[Co2(X2dhbq)3] as promising Kitaev-type QSL candidate materials. The high-spin d7 Co2+ has pseudospin-1/2 ground-state doublets, and benzoquinone-based linkers not only provide two separate superexchange pathways that create bond-dependent frustrated interactions but also allow for chemical tunability to mediate magnetic coupling. Our magnetization data show antiferromagnetic interactions between neighboring metal centers with Weiss constants from -5.1 to -8.5 K depending on the X functional group in X2dhbq linkers (X = Cl, Br, H). No magnetic transition or spin freezing could be observed down to 2 K. Low-temperature susceptibility (down to 0.3 K) and specific heat (down to 0.055 K) of (NEt4)2[Co2(H2dhbq)3] were further analyzed. Heat capacity measurements confirmed no long-range order down to 0.055 K, evidenced by the broad peak instead of the λ-like anomaly. Our results indicate that these 2D cobalt benzoquinone frameworks are promising Kitaev QSL candidates with chemical tunability through ligands that can vary the magnetic coupling and frustration.

Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material displays competing magnetic interactions and features nonlinear optical responses with the capability of generating coherent photons. The incommensurate magnetic ground state of CaMnTeO6 with an unusually large spin rotation angle of 127°(1) indicates that the anisotropic interlayer exchange is strong and competing with the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) µB, extracted from low-temperature heat capacity and neutron diffraction measurements, is only 46% of the expected value of the static moment 3 µB. This reduction indicates the presence of strong quantum fluctuations in the half-integer spin S = 3/2 CaMnTeO6 magnet, which is rare. By comparing the spin-polarized band structure, chemical bonding, and physical properties of AMnTeO6 (A = Ca, Sr, Pb), how quantum-chemical interpretation can illuminate insights into the fundamentals of magnetic exchange interactions, providing a powerful tool for modulating spin dynamics with atomically precise control is demonstrated.

Gate-Controlled Anyon Generation and Detection in Kitaev Spin Liquids

Reliable manipulation of non-Abelian Ising anyons supported by Kitaev spin liquids may enable intrinsically fault-tolerant quantum computation. Here, we introduce a standalone scheme for both generating and detecting individual Ising anyons using tunable gate voltages in a heterostructure containing a non-Abelian Kitaev spin liquid and a monolayer semiconductor. The key ingredients of our setup are a Kondo coupling to stabilize an Ising anyon in the spin liquid around each electron in the semiconductor, and a large charging energy to allow control over the electron numbers in distinct gate-defined regions of the semiconductor. In particular, a single Ising anyon can be generated at a disk-shaped region by gate tuning its electron number to one, while it can be interferometrically detected by measuring the electrical conductance of a ring-shaped region around it whose electron number is allowed to fluctuate between zero and one. We provide concrete experimental guidelines for implementing our proposal in promising candidate materials like α-RuCl_{3}.

Engineering the Kitaev Spin Liquid in a Quantum Dot System

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.

Planar thermal Hall effect from phonons in a Kitaev candidate material

The thermal Hall effect has emerged as a potential probe of exotic excitations in spin liquids. In the Kitaev magnet α -RuCl3, the thermal Hall conductivityκ x y has been attributed to Majorana fermions, chiral magnons, or phonons. Theoretically, the former two types of heat carriers can generate a "planar"κ x y , whereby the magnetic field is parallel to the heat current, but it is unknown whether phonons also could. Here we show that a planarκ x y is present in another Kitaev candidate material, Na2Co2TeO6. Based on the striking similarity betweenκ x y and the phonon-dominated thermal conductivityκ x x , we attribute the effect to phonons. We observe a large difference inκ x y between different configurations of heat current and magnetic field, which reveals that the direction of heat current matters in determining the planarκ x y . Our observation calls for a re-evaluation of the planarκ x y observed inα -RuCl3.

Room Temperature Relaxometry of Single Nitrogen Vacancy Centers in Proximity to α-RuCl3 Nanoflakes

Nitrogen vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use the longitudinal relaxation time T1 of single NV centers to investigate the spin dynamics of nanometer-thin flakes of α-RuCl3 at room temperature. We observe a significant reduction in the T1 in the presence of α-RuCl3 in the proximity of NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal planes. Furthermore, the T1 time exhibits a monotonic increase with an applied magnetic field. We associate this trend with the alteration of the spin and charge noise in α-RuCl3 under an external magnetic field. These findings suggest that the influence of the spin dynamics of α-RuCl3 on the T1 of the NV center can be used to gain information about the material itself and the technique to be used on other 2D materials.

Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise

The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.

Vacancy Spectroscopy of Non-Abelian Kitaev Spin Liquids

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This "quasi-zero-voltage peak" is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material α-RuCl_{3}.

Rotational phase transitions in antifluorite-type osmate and iridate compounds

We present temperature-dependent single-crystal diffraction results on seven antifluorite-typeA2MeX6compounds withMe= Os or Ir: K2OsCl6,A2OsBr6withA= K, Rb, Cs and NH4, and K2IrX6withX= Cl and Br. The structural transitions in this family arise fromMeX6octahedron rotations that generate a rich variety of symmetries depending on the rotation axis and stacking schemes. In order to search for local distortions in the high-symmetry phase we perform refinements of anharmonic atomic displacement parameters with comprehensive data sets. Even at temperatures close to the onset of structural distortions, these refinements only yield a small improvement indicating only small anharmonic effects. The phase transitions in these antifluorites are essentially of displacive character. However, some harmonic displacement parameters are very large reflecting soft phonon modes with the softening covering large parts of the Brillouin zone. The occurrence of the rotational transitions in the antifluorite-type family can be remarkably well analyzed in terms of a tolerance factor of ionic radii.

Emergence of the isotropic Kitaev honeycomb latticeα-RuCl3and its magnetic properties

We present a comprehensive investigation of the crystal and magnetic structures of the van der Waals antiferromagnetα-RuCl3using single crystal x-ray and neutron diffraction. The crystal structure at room temperature is a monoclinic (C2/m). However, with decreasing temperature, a remarkable first-order structural phase transition is observed, leading to the emergence of a rhombohedral (R3-) structure characterized by three-fold rotational symmetry forming an isotropic honeycomb lattice. On further cooling, a zigzag-type antiferromagnetic order develops belowTN=6∼6.6K. The critical exponent of the magnetic order parameter was determined to beβ=0.11(1), which is close to the two-dimensional Ising model. Additionally, the angular dependence of the magnetic critical field of the zigzag antiferromagnetic order for the polarized ferromagnetic phase reveals a six-fold rotational symmetry within theab-plane. These findingsreflect the symmetry associated with the Ising-like bond-dependent Kitaev spin interactions and underscore the universality of the Kitaev interaction-dominated antiferromagnetic system.

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Incommensurate Spiral Spin Order in CaMn2Bi2 Observed via High-Pressure Neutron Diffraction

High-pressure neutron diffraction is employed to investigate the magnetic behavior of CaMn2Bi2 in extreme conditions. In contrast to antiferromagnetic ordering on Mn atoms reported at ambient pressure, our results reveal that at high pressure, incommensurate spiral spin order emerges due to the interplay between magnetism on the Mn atoms and strong spin-orbit coupling on the Bi atoms: sinusoidal spin order is observed at pressures as high as 7.4 GPa. First-principles calculations with a noncollinear spin orientation demonstrate band crossing behavior near the Fermi level as a result of strong hybridization between the d orbitals of Mn and the p orbitals of Bi atoms. Competing antiferromagnetic order is observed at different temperatures in the partially frustrated lattice. Theoretical models have been developed to investigate spin dynamics. This research provides a unique toolbox for conducting experimental and theoretical magnetic and spin dynamics studies of magnetic quantum materials via high-pressure neutron diffraction.

Theory of Moiré Magnetism in Twisted Bilayer α-RuCl3

Motivated by the recent developments in moiré superlattices of van der Waals magnets and the desire to control the magnetic interactions of α-RuCl3, here we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer α-RuCl3. Using a combination of first-principles calculations and atomistic simulations, we show that the stacking-dependent interlayer exchange gives rise to an array of magnetic phases that can be realized by controlling the twist angle. In particular, we discover a complex hexagonal domain structure in which multiple zigzag orders coexist. This multidomain order minimizes the interlayer energy while enduring the energy cost due to domain wall formation. Further, we show that quantum fluctuations can be enhanced across the phase transitions. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moiré superlattices can be exploited to tune quantum fluctuations and the magnetic ground state of α-RuCl3.

Electronic Structures of Kitaev Magnet Candidates RuCl3 and RuI3

Layered honeycomb magnets with strong atomic spin-orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α-RuCl3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α-RuBr3 and α-RuI3 with the same crystal structure. Here, we investigate correlated electronic structures of α-RuCl3 and α-RuI3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α-RuI3, and suggests a potential realization of correlated flat bands with strong spin-orbit coupling and a quantum spin-Hall insulating phase in α-RuI3.

Nonlocal Spin Correlation as a Signature of Ising Anyons Trapped in Vacancies of the Kitaev Spin Liquid

In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a Z_{2} flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this nonlocal spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the nonlocal correlation can be detected electrically via the measurement of nonlocal conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

Kondo screening in a Majorana metal

Kondo impurities provide a nontrivial probe to unravel the character of the excitations of a quantum spin liquid. In the S = 1/2 Kitaev model on the honeycomb lattice, Kondo impurities embedded in the spin-liquid host can be screened by itinerant Majorana fermions via gauge-flux binding. Here, we report experimental signatures of metallic-like Kondo screening at intermediate temperatures in the Kitaev honeycomb material α-RuCl3 with dilute Cr3+ (S = 3/2) impurities. The static magnetic susceptibility, the muon Knight shift, and the muon spin-relaxation rate all feature logarithmic divergences, a hallmark of a metallic Kondo effect. Concurrently, the linear coefficient of the magnetic specific heat is large in the same temperature regime, indicating the presence of a host Majorana metal. This observation opens new avenues for exploring uncharted Kondo physics in insulating quantum magnets.

Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Triple-q Order in Na_{2}Co_{2}TeO_{6} from Proximity to Hidden-SU(2)-Symmetric Point

In extended Heisenberg-Kitaev-Gamma-type spin models, hidden-SU(2)-symmetric points are isolated points in parameter space that can be mapped to pure Heisenberg models via nontrivial duality transformations. Such points generically feature quantum degeneracy between conventional single-q and exotic multi-q states. We argue that recent single-crystal inelastic neutron scattering data place the honeycomb magnet Na_{2}Co_{2}TeO_{6} in proximity to such a hidden-SU(2)-symmetric point. The low-temperature order is identified as a triple-q state arising from the Néel antiferromagnet with staggered magnetization in the out-of-plane direction via a 4-sublattice duality transformation. This state naturally explains various distinctive features of the magnetic excitation spectrum, including its surprisingly high symmetry and the dispersive low-energy and flat high-energy bands. Our result demonstrates the importance of bond-dependent exchange interactions in cobaltates, and illustrates the intriguing magnetic behavior resulting from them.

Ultrafast Spin Dynamics and Photoinduced Insulator-to-Metal Transition in α-RuCl3

Laser-induced ultrafast demagnetization is a phenomenon of utmost interest and attracts significant attention because it enables potential applications in ultrafast optoelectronics and spintronics. As a spin-orbit coupling assisted magnetic insulator, α-RuCl3 provides an attractive platform to explore the physics of electronic correlations and unconventional magnetism. Using time-dependent density functional theory, we explore the ultrafast laser-induced dynamics of the electronic and magnetic structures in α-RuCl3. Our study unveils that laser pulses can introduce ultrafast demagnetizations, accompanied by an out-of-equilibrium insulator-to-metal transition in a few tens of femtoseconds. The spin response significantly depends on the laser wavelength and polarization on account of the electron correlations, band renormalizations, and charge redistributions. These findings provide physical insights into the coupling between the electronic and magnetic degrees of freedom in α-RuCl3 and shed light on suppressing the long-range magnetic orders and reaching a proximate spin liquid phase for two-dimensional magnets on an ultrafast time scale.

Direct Visualization of the Charge Transfer in a Graphene/α-RuCl3 Heterostructure via Angle-Resolved Photoemission Spectroscopy

We investigate the electronic properties of a graphene and α-ruthenium trichloride (α-RuCl3) heterostructure using a combination of experimental techniques. α-RuCl3 is a Mott insulator and a Kitaev material. Its combination with graphene has gained increasing attention due to its potential applicability in novel optoelectronic devices. By using a combination of spatially resolved photoemission spectroscopy and low-energy electron microscopy, we are able to provide a direct visualization of the massive charge transfer from graphene to α-RuCl3, which can modify the electronic properties of both materials, leading to novel electronic phenomena at their interface. A measurement of the spatially resolved work function allows for a direct estimate of the interface dipole between graphene and α-RuCl3. Their strong coupling could lead to new ways of manipulating electronic properties of a two-dimensional heterojunction. Understanding the electronic properties of this structure is pivotal for designing next generation low-power optoelectronics devices.

Possible intermediate quantum spin liquid phase in α-RuCl3 under high magnetic fields up to 100 T

Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ-[Formula: see text] model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly fluctuating and highly entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultralow-temperature specific heat, muon spin relaxation (μSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, μSR, and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

Ba9RE2(SiO4)6 (RE = Ho-Yb): A Family of Rare-Earth-Based Honeycomb-Lattice Magnets

Rare-earth (RE)-based honeycomb-lattice materials with strong spin-orbit coupled Jeff = 1/2 moments have attracted great interest as a platform to realize the Kitaev quantum spin liquid (QSL) state. Herein, we report the discovery of a family of RE-based honeycomb-lattice magnets Ba9RE2(SiO4)6 (RE = Ho-Yb), which crystallize into the rhombohedral structure with the space group R3̅. In these serial compounds, magnetic RE3+ ions are arranged on a perfect honeycomb lattice within the ab-plane and stacked in the "ABCABC"-type fashion along the c-axis. All synthesized Ba9RE2(SiO4)6 (RE = Ho-Yb) polycrystals exhibit the dominant antiferromagnetic interaction and absence of magnetic order down to 2 K. In combination with the magnetization and electron spin resonance results, magnetic behaviors are discussed for the compounds with different RE ions. Moreover, the as-grown Ba9Yb2(SiO4)6 single crystals show large magnetic frustration with frustration index f = θCW/TN > 8 and no long-range magnetic ordering down to 0.15 K, being a possible QSL candidate material. These series of compounds are attractive for exploring the exotic magnetic phases of Kitaev materials with 4f electrons.

Gate-Tunable Renormalization of Spin-Correlated Flat-Band States and Bandgap in a 2D Magnetic Insulator

Emergent quantum phenomena in two-dimensional van der Waal (vdW) magnets are largely governed by the interplay between exchange and Coulomb interactions. The ability to precisely tune the Coulomb interaction enables the control of spin-correlated flat-band states, band gap, and unconventional magnetism in such strongly correlated materials. Here, we demonstrate a gate-tunable renormalization of spin-correlated flat-band states and bandgap in magnetic chromium tribromide (CrBr3) monolayers grown on graphene. Our gate-dependent scanning tunneling spectroscopy (STS) studies reveal that the interflat-band spacing and bandgap of CrBr3 can be continuously tuned by 120 and 240 meV, respectively, via electrostatic injection of carriers into the hybrid CrBr3/graphene system. This can be attributed to the self-screening of CrBr3 arising from the gate-induced carriers injected into CrBr3, which dominates over the weakened remote screening of the graphene substrate due to the decreased carrier density in graphene. Precise tuning of the spin-correlated flat-band states and bandgap in 2D magnets via electrostatic modulation of Coulomb interactions not only provides effective strategies for optimizing the spin transport channels but also may exert a crucial influence on the exchange energy and spin-wave gap, which could raise the critical temperature for magnetic order.

Disorder-Enriched Magnetic Excitations in a Heisenberg-Kitaev Quantum Magnet Na_{2}Co_{2}TeO_{6}

Using optical magnetospectroscopy, we investigate the magnetic excitations of Na_{2}Co_{2}TeO_{6} in a broad magnetic field range (0  T≤B≤17.5  T) at low temperature. Our measurements reveal rich spectra of in-plane magnetic excitations with a surprisingly large number of modes, even in the high-field spin-polarized state. Theoretical calculations find that the Na-occupation disorder in Na_{2}Co_{2}TeO_{6} plays a crucial role in generating these modes. Our Letter demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.

Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H3LiIr2O6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H3LiIr2O6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H3LiIr2O6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

Electronic Structure Manipulation of the Mott Insulator RuCl3 via Single-Crystal to Single-Crystal Topotactic Transformation

The core task for Mott insulators includes how rigid distributions of electrons evolve and how these induce exotic physical phenomena. However, it is highly challenging to chemically dope Mott insulators to tune properties. Herein, we report how to tailor electronic structures of the honeycomb Mott insulator RuCl₃ employing a facile and reversible single-crystal to single-crystal intercalation process. The resulting product (NH₄ )_0.5 RuCl₃ ⋅1.5 H₂ O forms a new hybrid superlattice of alternating RuCl₃ monolayers with NH₄ ⁺ and H₂ O molecules. Its manipulated electronic structure markedly shrinks the Mott-Hubbard gap from 1.2 to 0.7 eV. Its electrical conductivity increases by more than 10³ folds. This arises from concurrently enhanced carrier concentration and mobility in contrary to the general physics rule of their inverse proportionality. We show topotactic and topochemical intercalation chemistry to control Mott insulators, escalating the prospect of discovering exotic physical phenomena.

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.

Polar magnetism and chemical bond inα-RuCl3

The micaceous black allotrope of ruthenium trichloride is the subject of many recent experimental and theoretical studies. Even so, its structural and magnetic properties remain undecided; monoclinic, trigonal and rhombohedral space groups for the crystal structure have been proposed on the basis of various types of experiments. The magnetic structure is often discussed in the context of the Kitaev state, but inevitably they are inconclusive discussions in the absence of structural and magnetic space groups. Johnsonet alinfer a candidate for the magnetic structure (C_c2/m) from results gathered in an extensive set of experiments on an untwined sample ofα-RuCl₃(Johnsonet al2015Phys. Rev.B92235119). The proposed zigzag antiferromagnetic ground state of Ru ions does not respond to bulk magnetic probes, with optical rotation and all forms of dichroism prohibited by symmetry. Experimental techniques exploited by Johnsonet alincluded x-ray and magnetic neutron diffraction. Properties of the candidate magnetic structure not previously explored include polar magnetism that supports Ru Dirac multipoles, e.g. a ruthenium anapole that is also known as a toroidal dipole. In a general case, Dirac dipoles are capable of generating interactions between magnetic ions, as in an electrical Dzyaloshinskii-Moryia interaction (Kaplan and Mahanti 2011Phys. Rev.B83174432; Zhaoet al2021Nat. Mater.20341). Notably, the existence of Dirac quadrupoles in the pseudo-gap phases of cuprate superconductors YBCO and Hg1201 account for observed magnetic Bragg diffraction patterns. Dirac multipoles contribute to the diffraction of both x-rays and neutrons, and a stringent test of the magnetic structure C_c2/m awaits future experiments. From symmetry-informed calculations we show that, the magnetic candidate permits Bragg spots that arise solely from Dirac multipoles. Stringent tests of C_c2/m can also be accomplished by performing resonant x-ray diffraction with signal enhancement from the chlorineK-edge. X-ray absorption spectra published forα-RuCl₃possess a significant low-energy feature (Plumbet al2014Phys. Rev.B90041112(R)). Many experimental studies of other Cl-metal compounds concluded that identical features hallmark the chemical bond. Using a monoclinic C_c2/m structure, we predict the contribution to Bragg diffraction at the ClK-edge absorption. Specifically, the variation of intensity of Bragg spots with rotation of the sample about the reflection vector. The two principal topics of our studies, polar magnetism and the chemical bond in the black allotrope of ruthenium trichloride, are brought together in a minimal model of magnetic Ru ions in C_c2/m.

Ground-State Spin Dynamics in d1 Kagome-Lattice Titanium Fluorides

Many quantum magnetic materials suffer from structural imperfections. The effects of structural disorder on bulk properties are difficult to assess systematically from a chemical perspective due to the complexities of chemical synthesis. The recently reported S = 1/2 kagome lattice antiferromagnet, (CH₃NH₃)₂NaTi₃F₁₂, 1-Ti, with highly symmetric kagome layers and disordered interlayer methylammonium cations, shows no magnetic ordering down to 0.1 K. To study the impact of structural disorder in the titanium fluoride kagome compounds, (CH₃NH₃)₂KTi₃F₁₂, 2-Ti, was prepared. It presents no detectable structural disorder and only a small degree of distortion of the kagome lattice. The methylammonium disorder model of 1-Ti and order in 2-Ti were confirmed by atomic-resolution transmission electron microscopy. The antiferromagnetic interactions and band structures of both compounds were calculated based on spin-polarized density functional theory and support the magnetic structure analysis. Three spin-glass-like (SGL) transitions were observed in 2-Ti at 0.5, 1.4, and 2.3 K, while a single SGL transition can be observed in 1-Ti at 0.8 K. The absolute values of the Curie-Weiss temperatures of both 1-Ti (-139.5(7) K) and 2-Ti (-83.5(7) K) are larger than the SGL transition temperatures, which is indicative of geometrically frustrated spin glass (GFSG) states. All the SGL transitions are quenched with an applied field >0.1 T, which indicates novel magnetic phases emerge under small applied magnetic fields. The well-defined structure and the lack of structural disorder in 2-Ti suggest that 2-Ti is an ideal model compound for studying GFSG states and the potential transitions between spin liquid and GFSG states.

A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo₂(AsO₄)₂, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo₂(AsO₄)₂ is a promising QSL candidate.

Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3

The honeycomb magnet α-RuCl₃ has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κ_xy of Majorana fermions is predicted to be half-quantized. Half-quantization of κ_xy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κ_xy on α-RuCl₃ with the magnetic field B ∥ a (zigzag axis). In our experiment, κ_xy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κ_xy/T.

Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3

Layered α-RuCl₃ is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl₃, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit.

Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits

Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs—the result reproducibility crisis.

Coexistence of Two Spin Frustration Pathways in the Quantum Spin Liquid Ca10Cr7O28

Kagome antiferromagnetic lattices are of high interest because the geometric frustration is expected to give rise to highly degenerated ground states that may host exotic properties such as quantum spin liquid (QSL). Ca₁₀Cr₇O₂₈ has been reported to display all the features expected for a QSL. At present, most of the literature reports on samples synthesized with starting materials ratio CaO/Cr₂O₃ 3:1, which leads to a material with small amounts of CaCrO₄ and CaO as secondary phases; this impurity excess affects not only the magnetic properties but also the structural ones. In this work, samples with starting material ratios CaO/Cr₂O₃ 3:1, 2.9:1, 2.85:1, and 2.8:1 have been synthesized and studied by X-ray diffraction with Rietveld refinements, selected area electron diffraction measurements, high-resolution transmission electron microscopy (HRTEM), low-temperature magnetometry, and magnetic calorimetry. This result shows that a highly pure Ca₁₀Cr₇O₂₈ phase is obtained for a CaO/Cr₂O₃ ratio of 2.85:1 instead of the 3:1 usually reported; the incorrect stoichiometric ratio leads to a larger distortion of the corner-sharing triangular arrangement of magnetic ions Cr⁺⁵ with S = 1/2 in the Kagome lattice. In addition, our study reveals that there exists another frustration pathway which is an asymmetric zigzag spin ladder along the directions [211], [12–1], and [1–1–1], in which the Cr–Cr distances are shorter than in the Kagome layers.

This work represents the endeavor to ensure the correct stoichiometric composition of the quantum spin liquid material Ca₁₀Cr₇O₂₈. The synthesis and characterization addressed several nonstoichiometric samples, including impurities’ influence on the crystal structure and properties of Kagome and zigzag magnetic interaction. The characterization aspects of the compound are based on the X-ray diffraction data and Rietveld refinement. Further characterization could help us understand the nature of quantum material and aid in the additional development of quantum theories and technology.

Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na_{2}Co_{2}TeO_{6}

Na_{2}Co_{2}TeO_{6} is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging effective link in the ordered state. The presence of at least six nonoverlapping spin-wave branches is at odds with all models proposed to date. Above the ordering temperature, persisting dynamic correlations can be described by equal-time magnetic structure factors of a hexagonal cluster, which reveal the leading instabilities. Our result sets definitive constraints on theoretical models for Na_{2}Co_{2}TeO_{6} and provides new insight for the materialization of the Kitaev model.