Kagome Heisenberg Antiferromagnet Research Articles

Emergent Spin-Gapped Magnetization Plateaus in a Spin-1/2 Perfect Kagome Antiferromagnet.

The two-dimensional spin-1/2 kagome Heisenberg antiferromagnet is believed to host quantum spin liquid (QSL) states with no magnetic order, but its ground state remains largely elusive. An important outstanding question concerns the presence or absence of the 1/9 magnetization plateau, where exotic quantum states, including topological ones, are expected to emerge. Here we report the magnetization of a recently discovered kagome QSL candidate YCu_{3}(OH)_{6.5}Br_{2.5} up to 57T. Above 50T, a clear magnetization plateau at 1/3 of the saturation moment of Cu^{2+} ions is observed, supporting that this material provides an ideal platform for the kagome Heisenberg antiferromagnet. Remarkably, we found another magnetization plateau around 20T, which is attributed to the 1/9 plateau. The temperature dependence of this plateau reveals the presence of the spin gap. The observation of 1/9 and 1/3 plateaus highlights the emergence of novel states in quantum spin systems.

The dilute 3D and three site dimer Heisenberg antiferromagnet: review of some magnetic properties.

Many properties of the spin–½ kagome Heisenberg antiferromagnet remains controversial and receiving continuous attention from theorists and experimentalists due to their fascinating magnetic properties and high heterogeneity coax by the geometrical frustration. In this research we seek and compare the results obtained in our recent article [1] with that of Napel[2] where we elucidate some of the identified magnetic behaviour using the spin–½ Heisenbeg model with the application of Exact Diagonalization and classical Monte-Carlo simulation on three site dimer and 3D simple cubic lattice simulation. The results obtained shows excellent agreement in both papers reviewed with [1] establishing firmly the FM to AFM transition, having a clear transition point referred to mixed phased [2].

Possible chiral spin liquid state in the S = 1/2 kagome Heisenberg model

The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a 3×3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}\ imes \\sqrt{3}$$\\end{document} magnetically ordered phase and two valence-bond crystal phases.

Frustrated magnetism of the spin-1 kagome antiferromagnet β-BaNi3(VO4)2(OH)2

We propose the newly synthesized β-BaNi3(VO4)2(OH)2 (space group: ) as a candidate for the spin-1 kagome Heisenberg antiferromagnet (KHA). The compound features a uniform kagome lattice of Ni2+ (S = 1) ions with a large interlayer distance. High-field measurements at low temperatures reveal a susceptibility local minimum at ∼9 T, resembling a 1/3 magnetization plateau as predicted by the pure S = 1 KHA model. Below ∼6 K, approximately 1% of the spins exhibit spin-glass order, which may be attributed to the nanocrystalline grain size of ∼50 nm. Despite the antiferromagnetic exchange coupling strength of ∼7 K, the majority of spins remain disordered down to ∼0.1 K as indicated by the observed power-law behaviors in magnetic specific heat . Our results demonstrate that the low-energy magnetic excitations in β-BaNi3(VO4)2(OH)2 are gapless, which contradicts the current theoretical expectations of the ideal model.

Nature of the 1/9-magnetization plateau in the spin- 12 kagome Heisenberg antiferromagnet

The nature of the 1/9-magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3 quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\times\sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\times\sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1 conformal field theory.

Chiral spin liquids on the kagome lattice with projected entangled simplex states

The infinite projected entangled simplex state (iPESS), a type of tensor network (TN) state, has been used successfully for simulating and characterizing {\it non-chiral} spin liquids on the kagome lattice. Here, we demonstrate that iPESS also provides a faithful representation of a {\it chiral} spin liquid (CSL) on the same lattice, namely the ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet with a scalar chirality. By classifying local tensors according to SU$(2)$ and point group symmetries, we construct a chiral ansatz breaking reflection $P$ and time reversal $T$ symmetries while preserving $PT$. The variational TN states are shown to host, for bond dimension $D\ge 8$, a chiral gapless entanglement spectrum following SU$(2)_1$ conformal field theory. The correlation function shows a small weight long-range tail complying with the prediction of the TN bulk-edge correspondence. %{\color{red}With more constraints included, the chiral ansatz is reduced to a non-chiral one which preserves full point group symmetries due to an emergent {\it tensor conservation law} and is of relevance to the ground state at the Heisenberg point. Lastly, by simulations in the complete ansatz family we discuss the transition from the non-chiral spin liquid to the CSL induced by the scalar chirality term.} We identify a non-chiral manifold spanned by only a subset of symmetric tensors where a new emergent {\it tensor conservation law} is realized. This allows us to both probe the stability of the non-chiral spin liquid and discuss its transition to CSL induced by a scalar chirality term.

The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet

The search for the experimental evidence of quantum spin liquid (QSL) states is critical but extremely challenging, as the quenched interaction randomness introduced by structural imperfection is usually inevitable in real materials. YCu3(OH)6.5Br2.5 (YCOB) is a spin-1/2 kagome Heisenberg antiferromagnet (KHA) with strong coupling of 〈J1〉 ~ 51 K but without conventional magnetic freezing down to 50 mK ~ 0.001〈J1〉. Here, we report a Br nuclear magnetic resonance (NMR) study of the local spin susceptibility and dynamics on the single crystal of YCOB. The temperature dependence of NMR main-line shifts and broadening can be well understood within the frame of the KHA model with randomly distributed hexagons of alternate exchanges, compatible with the formation of a randomness-induced QSL state at low temperatures. The in-plane spin fluctuations as measured by the spin-lattice relaxation rates (1/T1) exhibit a weak temperature dependence down to T ~ 0.03〈J1〉. Our results demonstrate that the majority of spins remain highly fluctuating at low temperatures despite the quenched disorder in YCOB.

Universal scaling of specific heat in the S=12 quantum kagome antiferromagnet herbertsmithite

Despite tremendous investigations, a quantum spin liquid (QSL) state realized in a spin-1/2 kagome Heisenberg antiferromagnet remains largely elusive. In herbertsmithite $\mathrm{Zn}{\mathrm{Cu}}_{3}{(\mathrm{O}\mathrm{H})}_{6}{\mathrm{Cl}}_{2}$, a quantum spin liquid candidate on the perfect kagome lattice, precisely characterizing the intrinsic physics of the kagome layers is extremely challenging due to the presence of interlayer Cu/Zn antisite disorder within its crystal structure. Here we measured the specific heat and thermal conductivity of single-crystal herbertsmithite in magnetic fields with high resolution. Strikingly, intrinsic magnetic specific heat contribution arising from the kagome layers exhibits excellent scaling collapse as a function of $T/H$ (temperature/magnetic field). In addition, no residual linear term in the thermal conductivity $\ensuremath{\kappa}/T(T\ensuremath{\rightarrow}0)$ is observed in zero and applied magnetic fields, indicating the absence of itinerant gapless excitations. These results capture a new essential feature of the QSL state of the kagome layers; localized orphan spins are induced by exchange bond randomness, surrounded by a nonitinerant QSL.

Strain tuning of highly frustrated magnets: Order and disorder in the distorted kagome Heisenberg antiferromagnet

Strain applied to a condensed-matter system can be used to engineer its excitation spectrum via artificial gauge fields or it may tune the system through transitions between different phases. Here we demonstrate that strain tuning of the ground state of otherwise highly degenerate frustrated systems can induce novel phases, both ordered and disordered. For the classical Heisenberg antiferromagnet on the kagome lattice, we show that weak triaxial strain reduces the degeneracies of the system, leading to a classical spin liquid with noncoplanar configurations, while stronger strain drives the system into a highly unconventional state which displays signatures of both spin-glass behavior and magnetic long-range order. We provide experimentally testable predictions for the magnetic structure factor, characterize the ground-state degeneracies and the excitation spectrum, and analyze the influence of sample shape and boundaries. Our paper opens the way to strain engineering of highly frustrated magnets.

Gapless spin liquid behavior in a kagome Heisenberg antiferromagnet with randomly distributed hexagons of alternate bonds

We demonstrate that the new single crystal of YCu$_3$[OH(D)]$_{6.5}$Br$_{2.5}$ (YCOB) is a kagome Heisenberg antiferromagnet (KHA) without evident orphan spins ($\ll$ 0.8\%). The site mixing between polar OH$^-$ and non-polar Br$^-$ causes local distortions of Cu-O-Cu exchange paths, and gives rise to 70(2)\% of randomly distributed hexagons of alternate bonds ($\sim$ $J_1-\Delta J$ and $J_1+\Delta J$) and the rest of almost uniform hexagons ($\sim$ $J_1$) on the kagome lattice. Simulations of the random exchange model with $\Delta J$/$J_1$ = 0.7(1) show good agreement with the experimental observations, including the weak upturn seen in susceptibility and the slight polarization in magnetization. Despite the average antiferromagnetic coupling of $J_1$ $\sim$ 60 K, no conventional freezing is observed down to $T$ $\sim$ 0.001$J_1$, and the raw specific heat exhibits a nearly quadratic temperature dependence below 1 K $\sim$ 0.02$J_1$, phenomenologically consistent with a gapless (spin gap $\leq$ 0.025$J_1$) Dirac quantum spin liquid (QSL). Our result sheds new light on the theoretical understanding of the randomness-relevant gapless QSL behavior in YCOB, as well as in other relevant materials.

Classical Spin Liquid State in the S=5/2 Heisenberg Kagome Antiferromagnet Li_{9}Fe_{3}(P_{2}O_{7})_{3}(PO_{4})_{2}.

We investigate the low temperature magnetic properties of a S=5/2 Heisenberg kagome antiferromagnet, the layered monodiphosphate Li_{9}Fe_{3}(P_{2}O_{7})_{3}(PO_{4})_{2}, using magnetization measurements and ^{31}P nuclear magnetic resonance. An antiferromagnetic-type order sets in at T_{N}=1.3 K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below T^{*}∼5 K. A moderate ^{31}P NMR line broadening reveals the development of anisotropic short-range correlations concomitantly with a gapless spin-lattice relaxation time T_{1}∼k_{B}T/ℏS, which may point to the presence of a semiclassical nematic spin-liquid state predicted for the Heisenberg kagome antiferromagnetic model or to the persistence of the zero-energy modes of the kagome lattice under large magnetic fields.

Motif magnetism and quantum many-body scars

We generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite energy density eigenstates are thermal. However, some systems, such as many-body localized systems and systems with quantum many-body scars, violate ETH and have high-energy athermal eigenstates. In systems with scars, most eigenstates thermalize, but a few atypical scar states do not. Scar states can give rise to a periodic revival when time-evolving particular initial product states, which can be detected experimentally. Recently, a family of spin Hamiltonians was found with magnetically ordered 3-colored eigenstates that are quantum many-body scars [Lee et al. Phys. Rev. B 101, 241111(2020)]. These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet. In this work, we introduce a generalized family of $n$-colored Hamiltonians with "spiral colored" eigenstates made from $n$-spin motifs such as polygons or polyhedra. We show how these models can be realized in many different lattice geometries and provide numerical evidence that they can exhibit quantum many-body scars with periodic revivals that can be observed by time-evolving simple product states. The simple structure of these Hamiltonians makes them promising candidates for future experimental studies of quantum many-body scars.

The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial D 3h spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and an SVM bias parameter. For completeness we mention that the machine also picks up the leading correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.

Magnon Crystallization in the Kagome Lattice Antiferromagnet.

We present numerical evidence for the crystallization of magnons below the saturation field at nonzero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or, equivalently, flatband multimagnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon crystal is expected to be generic for spin models in dimension D>1 where flatband multimagnon ground states break translational symmetry.

Quantum-classical crossover in the spin- 12 Heisenberg-Kitaev kagome magnet

The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrizaton: i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram, and ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy $K$. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.

Chemistry of the spin- 12 kagome Heisenberg antiferromagnet

We believe that a necessary first step in understanding the ground state properties of the spin-${\scriptstyle\frac{1}{2}}$ kagome Heisenberg antiferromagnet is a better understanding of this model's very large number of low energy singlet states. A description of the low energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular when these turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all the low energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all the low energy states promise more robust predictions than methods that only refine a fraction of these states.

Effect of perturbations on the kagome S=12 antiferromagnet at all temperatures

The ground state of the $S=\frac{1}{2}$ kagome Heisenberg antiferromagnet is now recognized as a spin liquid, but its precise nature remains unsettled, even if more and more clues point towards a gapless spin liquid. We use high-temperature series expansions (HTSEs) to extrapolate the specific heat ${c}_{V}(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ over the full temperature range, using an improved entropy method with a self-determination of the ground-state energy per site ${e}_{0}$. Optimized algorithms give HTSE coefficients up to unprecedented orders (20 in $1/T$) and as exact functions of the magnetic field. Three extrapolations are presented for different low-$T$ behaviors of ${c}_{V}$: exponential (for a gapped system), and linear or quadratic (for two different types of gapless spin liquids). We study the effects of various perturbations to the Heisenberg Hamiltonian: Ising anisotropy, Dzyaloshinskii-Moriya interactions, second- and third-neighbor interactions, and randomly distributed magnetic vacancies. We propose an experimental determination of $\ensuremath{\chi}(T=0)$, which could be nonzero, from ${c}_{V}$ measurements under different magnetic fields.

Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2

Spin liquids are exotic phases of quantum matter challenging Landau's paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. While well-established for 1D quantum antiferromagnets, in higher dimension where quantum fluctuations are less acute, realizing and understanding such states represent major issues, both theoretical and experimental. In this respect the simplest nearest-neighbor Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key-issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature Nuclear Magnetic Resonance (NMR) contrast experiments on high quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$. We firmly conclude that this material does not harbor any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet.

Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb–Schultz–Mattis and Oshikawa–Yamanaka–Affleck theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the S = 1/2 kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a two-fold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at 1/3. Our results are in broad agreement with numerical and experimental studies.

Quantum spin liquid at finite temperature: Proximate dynamics and persistent typicality

Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $\alpha$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $\omega$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $\omega$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids.