Spin Liquid Research Articles

Review of honeycomb-based Kitaev materials with zigzag magnetic ordering.

The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long-range-ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-k magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single- and multi-k variants.

Classical and quantum spin liquids

Classical and quantum spin liquids

Antiferromagnetic order and possible quantum spin liquid in kagome antiferromagnet LuCu3(OH)6Br2[Br x (OH)1-x

Abstract Recent studies on the kagome lattice YCu3(OH)6+x X3-x (X = (Cl, Br)) have show promising evidence for the existence of a Dirac quantum spin liquid. We have synthesized a new compound LuCu3(OH)6Br2[Br x (OH)1-x ], which has two types of structures with two different space group, P 3 m1 and R 3. Type-I sample with the space group of P 3 m1 has undistorted Cu2+ kagome planes and orders magnetically below about 1.5 K. Type-II has a larger unit cell with the space group of R 3 and distorted kagome planes. No magnetic ordering is observed, and the low-temperature specific heat behaves like the Dirac quantum spin liquid, including the quadratic temperature dependence at zero field and an additional linear-T term under magnetic fields. By comparing the structures with YCu3(OH)6+x X3-x (X = Cl, Br), we show that the QSL ground state may have a deep connection with the J ⎔ - J - J' Heisenberg model on the kagome lattice.

Robust quantum spin liquid state in the presence of giant magnetic isotope effect in D3LiIr2O6

The deuterium isotope effect on the honeycomb iridate H3LiIr2O6, a quantum spin-orbit-entangled liquid, was examined by synthesizing D3LiIr2O6. The structural refinements indicate the different character of the interlayer OH and OD bonds, which results in a giant isotope effect on the magnetic interactions; the antiferromagnetic Curie-Weiss temperature |θCW| of D3LiIr2O6 increases to ~ 170 K from ~ 100 K of H3LiIr2O6. Nevertheless, the quantum liquid state is robust against the deuterium isotope exchange in contrast to the theoretical prediction that the Kitaev spin liquid is stable only for a limited phase space of magnetic interactions. The bond- and site disorders associated with disordered OD(H) bonds, in combination with Kitaev physics, may play a role in realizing the quantum liquid state.

Random Sampling Versus Active Learning Algorithms for Machine Learning Potentials of Quantum Liquid Water.

Training accurate machine learning potentials requires electronic structure data comprehensively covering the configurational space of the system of interest. As the construction of this data is computationally demanding, many schemes for identifying the most important structures have been proposed. Here, we compare the performance of high-dimensional neural network potentials (HDNNPs) for quantum liquid water at ambient conditions trained to data sets constructed using random sampling as well as various flavors of active learning based on query by committee. Contrary to the common understanding of active learning, we find that for a given data set size, random sampling leads to smaller test errors for structures not included in the training process. In our analysis, we show that this can be related to small energy offsets caused by a bias in structures added in active learning, which can be overcome by using instead energy correlations as an error measure that is invariant to such shifts. Still, all HDNNPs yield very similar and accurate structural properties of quantum liquid water, which demonstrates the robustness of the training procedure with respect to the training set construction algorithm even when trained to as few as 200 structures. However, we find that for active learning based on preliminary potentials, a reasonable initial data set is important to avoid an unnecessary extension of the covered configuration space to less relevant regions.

Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice

Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice

Ferromagnetic Semimetal and Charge-Density Wave Phases of Interacting Electrons in a Honeycomb Moiré Potential.

The exploration of quantum phases in moiré systems has drawn intense experimental and theoretical efforts. The realization of honeycomb symmetry has been a recent focus. The combination of strong interaction and honeycomb symmetry can lead to exotic electronic states such as fractional Chern insulator, unconventional superconductor, and quantum spin liquid. Accurate computations in such systems, with reliable treatment of long-ranged Coulomb interaction and approaching large system sizes to extract thermodynamic phases, are mostly missing. We study the two-dimensional electron gas on a honeycomb moiré lattice at quarter filling, using the fixed-phase diffusion MonteCarlo method. The ground state phases of this important model are determined in the parameter regime relevant to current experiments. With increasing moiré potential, the system transitions from a paramagnetic metal to an itinerant ferromagnetic semimetal then a charge-density-wave insulator.

Quantum Liquids He3 and He4 and Quantum Computing

L. D. Landau described the quantum liquids He3 and He4 at low temperature (below 3K) by applying the quasi particle approach called the quasi particles (elementary excitations) as “rotons”. We discuss in this paper how these physical materials may be candidates for building the processor of a quantum computer of type based on the quantum set theory of G. Takeuti.

Evidence of Dirac Quantum Spin Liquid in YbZn_{2}GaO_{5}.

The emergence of a quantum spin liquid (QSL), a state of matter that can result when electron spins are highly correlated but do not become ordered, has been the subject of a considerable body of research in condensed matter physics [1,2]. Spin liquid states have been proposed as hosts for high-temperature superconductivity [3] and can host topological properties with potential applications in quantum information science [4]. The excitations of most quantum spin liquids are not conventional spin waves but rather quasiparticles known as spinons, whose existence is well established experimentally only in one-dimensional systems; the unambiguous experimental realization of QSL behavior in higher dimensions remains challenging. Here, we investigate the novel compound YbZn_{2}GaO_{5}, which hosts an ideal triangular lattice of effective spin-1/2 moments with no detectable inherent chemical disorder. Thermodynamic and inelastic neutron scattering measurements performed on high-quality single crystal samples of YbZn_{2}GaO_{5} exclude the possibility of long-range magnetic ordering down to 0.06K, demonstrate a quadratic power law for the specific heat and reveal a continuum of magnetic excitations in parts of the Brillouin zone. Both low-temperature thermodynamics and inelastic neutron scattering spectra suggest that YbZn_{2}GaO_{5} is a U(1) Dirac QSL with spinon excitations concentrated at certain points in the Brillouin zone. We advanced these results by performing additional specific heat measurements under finite fields, further confirming the theoretical expectations for a Dirac QSL on the triangular lattice of YbZn_{2}GaO_{5}.

One-third magnetization plateau in Quantum Kagome antiferromagnet

The emergence of nontrivial quantum states from competing interactions is a central issue in quantum magnetism. In particular, for the realization of the quantum spin-liquid state, extensive studies have been conducted on frustrated systems, such as kagome antiferromagnets and Kitaev magnets. Novel quantum states in magnetic fields have remained elusive despite the prediction of rich physics. This can be attributed to material scarcity and the difficulty of precise measurements under ultra-high magnetic fields. Here, in this study, we develop the Kapellasite-type compound InCu3(OH)6Cl3, whose exchange interactions are in appropriate energy scale to comprehensively elucidate the magnetic properties of the frustrated S = 1/2 kagome antiferromagnet. The one-third magnetization plateau was clearly observed. Moreover, the large temperature-linear term in the heat capacity was observed in the magnetic fields, indicating the excitation of gapless quasiparticles in the vicinity of the plateau. These results shed light on the critical behaviors between quantum spin-liquid and -solid in kagome antiferromagnets under high magnetic fields.

Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Tunable Electron Correlation in Epitaxial 1T-TaS2 Spirals.

Tantalum disulfide (1T-TaS2), being a Mott insulator with strong electron correlation, is highlighted for diverse collective quantum states in the 2D lattice, including charge density wave (CDW), spin liquid, and unconventional superconductivity. The Mott physics embedded in the 2D triangular CDW lattice has raised debates on stacking-dependent properties because interlayer interactions are sensitive to van der Waals (vdW) spacing. However, control of interlayer distance remains a challenge. Here, spiral lattices in the epitaxial TaS2 spirals are studied to probe collective properties with tunable interlayer interactions. A scalable synthesis of epitaxial TaS2 spirals is presented. A more than 50%-increased interlayer spacing enables prototype decoupled monolayers for enhanced electronic correlation exhibiting Mott physics at room-temperature and a simplified system to explore collective properties in vdW materials.

Structured volume-law entanglement in an interacting, monitored Majorana spin liquid

Structured volume-law entanglement in an interacting, monitored Majorana spin liquid

Quantum spin-liquid in Ba3CuSb2O9 epitaxial thin films

Hexagonal perovskite materials are emerging quantum spin liquid (QSL) systems providing a fertile ground to realize novel quantum phenomena. The epitaxially grown thin films of such materials offer a compelling approach to utilize exotic quantum phases for device applications with better control over the structure. We fabricate the intriguing QSL triple perovskite Ba3CuSb2O9epitaxially onto a MgO (100) substrate by pulsed laser deposition technique as well as in bulk form for comparison. The presence of only (00l) parallel planes of Ba3CuSb2O9in x-ray diffraction validates the epitaxial growth of the thin film. Temperature-dependent magnetization of thin film reveals no magnetic ordering down to 400 mK, with a large antiferromagnetic Curie-Weiss temperature (θCW≈-11.68 K). This indicates strong magnetic frustration and QSL behaviour, similar to bulk Ba3CuSb2O9. The presence of magnetic correlations at low temperature (in the quantum spin liquid state) is further confirmed by analysing the low temperature magnetic isotherms. These experimental findings underscore the potential of this quantum material for its use in quantum technologies.

Emergence of Exotic Spin Texture in Supramolecular Metal Complexes on a 2D Superconductor.

Designer heterostructures have offered a very powerful strategy to create exotic superconducting states by combining magnetism and superconductivity. In this Letter, we use a heterostructure platform combining supramolecular metal complexes (SMCs) with a quasi-2D van der Waals superconductor NbSe_{2}. Our scanning tunneling microscopy measurements demonstrate the emergence of Yu-Shiba-Rusinov bands arising from the interaction between the SMC magnetism and the NbSe_{2} superconductivity. Using x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements, we show the presence of antiferromagnetic coupling between the SMC units. These result in the emergence of an unconventional 3×3 reconstruction in the magnetic ground state that is directly reflected in real space modulation of the Yu-Shiba-Rusinov bands. The combination of flexible molecular building blocks, frustrated magnetic textures, and superconductivity in heterostructures establishes a fertile starting point to fabricating tunable quantum materials, including unconventional superconductors and quantum spin liquids.

Exact Deconfined Gauge Structures in the Higher-Spin Yao-Lee Model: A Quantum Spin-Orbital Liquid with Spin Fractionalization and Non-Abelian Anyons.

The nonintegrable higher spin Kitaev honeycomb model has an exact Z_{2} gauge structure, which exclusively identifies quantum spin liquid in the half-integer spin Kitaev model. But its constraints for the integer-spin Kitaev model are much limited, and even trivially gapped insulators cannot be excluded. The physical implications of exact Z_{2} gauge structure, especially Z_{2} fluxes, in integer-spin models remain largely unexplored. In this Letter, we theoretically show that a spin-S Yao-Lee model [a spin-orbital model with SU(2) spin-rotation symmetry] possesses a topologically nontrivial quantum spin-orbital liquid ground state for any spin (both integer and half-integer spin) by constructing exact deconfined fermionic Z_{2} gauge charges. We further show that the conserved Z_{2} flux can also demonstrate the intriguing spin fractionalization phenomena in the non-Abelian topological order phase of the spin-1 Yao-Lee model. Its deconfined Z_{2} vortex excitation carries fractionalized spin-1/2 quantum number in the low-energy subspace, which is also a non-Abelian anyon. Our exact manifestation of spin fractionalization in an integer-spin model is rather rare in previous studies, and is absent in the Kitaev honeycomb model.

Compass-model physics on the hyperhoneycomb lattice in the extreme spin-orbit regime

The physics of spin-orbit entangled magnetic moments of 4d and 5d transition metal ions on a honeycomb lattice has been much explored in the search for unconventional magnetic orders or quantum spin liquids expected for compass spin models, where different bonds in the lattice favour different orientations for the magnetic moments. Realising such physics with rare-earth ions is a promising route to achieve exotic ground states in the extreme spin-orbit limit; however, this regime has remained experimentally largely unexplored due to major challenges in materials synthesis. Here we report the successful synthesis of powders and single crystals of β-Na2PrO3, with 4f1 Pr4+ jeff = 1/2 magnetic moments arranged on a hyperhoneycomb lattice with the same threefold coordination as the planar honeycomb. We find a strongly non-collinear magnetic order with highly dispersive gapped excitations that we argue arise from frustration between bond-dependent, anisotropic off-diagonal exchanges, a compass quantum spin model not explored experimentally so far. Our results show that rare-earth ions on threefold coordinated lattices offer a platform for the exploration of quantum compass spin models in the extreme spin-orbit regime, with qualitatively distinct physics from that of 4d and 5d Kitaev materials.

Floquet dynamical chiral spin liquid at finite frequency

Floquet dynamical chiral spin liquid at finite frequency

Spiral Spin Liquid in a Frustrated Honeycomb Antiferromagnet: A Single-Crystal Study of GdZnPO.

The frustrated honeycomb spin model can stabilize a subextensively degenerate spiral spin liquid with nontrivial topological excitations and defects, but its material realization remains rare. Here, we report the experimental realization of this model in the structurally disorder-free compound GdZnPO. Using a single-crystal sample, we find that spin-7/2 rare-earth Gd^{3+} ions form a honeycomb lattice with dominant second-nearest-neighbor antiferromagnetic and first-nearest-neighbor ferromagnetic couplings, along with easy-plane single-site anisotropy. This frustrated model stabilizes a unique spiral spin liquid with a degenerate contour around the K{1/3,1/3} point in reciprocal space, consistent with our experiments down to 30mK, including the observation of a giant residual specific heat. Our results establish GdZnPO as an ideal platform for exploring the stability of spiral spin liquids and their novel properties, such as the emergence of low-energy topological defects on the sublattices.

Quasi-One-Dimensional Spin Dynamics in a Molecular Spin Liquid System.

The molecular triangular lattice system, β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, is considered as a candidate material for the quantum spin liquid state, although ongoing debates arise from recent controversial results. Here, the results of electron spin resonance and muon-spin relaxation measurements on β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2} are presented. Both results indicate characteristic behaviors related to quasi-one-dimensional spin dynamics, whereas the direction of anisotropy found in electron spin resonance is in contradiction with previous theories. We succeed in interpreting the experiments by combining density-functional theory calculations and analysis of the effective model taking into account the multiorbital nature of the system. While the quantum-spin-liquid-like origin of β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2} was initially attributed to the magnetic frustration of the triangular lattice, it appears that the primary origin is a 1D spin liquid resulting from the dimensional reduction effect.