V. R. Shaginyan, A. Z. Msezane, M. Ya. Amusia, J. W. Clark, G. S. Japaridze, V. A. Stephanovich, Y. S. Leevik
In our review we focus on the quantum spin liquid, defining the thermodynamic, transport and relaxation properties of geometrically frustrated magnets (insulators) represented by herbertsmithite $\rm ZnCu_{3}(OH)_6Cl_2$.
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Exotic quantum spin liquid (QSL) is formed with such hypothetic particles as fermionic spinons carrying spin 1/2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental properties of QSL, forming strongly correlated Fermi system located at a fermion condensation quantum phase transition. These are in a good agreement with experimental data and allow us to detect the behavior of QSL as that observed in heavy fermion metals. We predict that the thermal resistivity of QSL under the application of magnetic fields at fixed temperature de…
We report on temperature dependence of the infrared reflectivity spectra of a single crystalline herbertsmithite in two polarizations --- parallel and perpendicular to the kagome plane of Cu atoms. We observe anomalous broadening of the low frequency phonons possibly caused by fluctuations in the exotic dynamical magnetic order of the spin liquid.
We present a theory of the dynamic magnetic susceptibility of quantum spin liquid. The obtained results are in good agreement with experimental facts collected on herbertsmithite ZnCu3(OH)6Cl2 and on heavy-fermion metals, and allow us to predict a new scaling in magnetic fields in the dynamic susceptibility. Under the application of strong magnetic fields quantum spin liquid becomes completely polarized. We show that this polarization can be viewed as a manifestation of gapped excitations when investigating the spin-lattice relaxation rate.
Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still to be discovered. We show that herbertsmithite ZnCu_3(OH)_6Cl_2 can be viewed as a strongly correlated Fermi system whose low temperature thermodynamic in magnetic fields is defined by a quantum critical spin liquid. Our calculations of its thermodynamic properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior which strongly resembles that observed in HF metals and 2D 3He.
We argue that neutron spectra in a short-range ordered Valence Bond state is dominated by two-spinon states localized in small spatial regions such as a pinwheel. These excitations lead to angle averaged dynamic structure factor that is spread over a wide frequency range up to about $2.5 J$, whereas its wavevector dependence at all frequencies remains very close to that of isolated dimers. These results are in excellent agreement with recent Neutron scattering data in the Herbertsmithite materials ZnCu$_3$(OH)$_6$Cl$_2$.
Based on experimental data and our theoretical analysis, we provide a strategy for unambiguous establishing of gapless quantum spin liquid state (QSL) in herbertsmithite and other materials. To clarify the nature of QSL, we recommend measurements of heat transport, low-energy inelastic neutron scattering and optical conductivity under the application of external magnetic field at low temperatures. We also suggest that artificially introduced inhomogeneity into $\rm ZnCu_{3}(OH)_6Cl_2$ can stabilize QSL, and serves as a test elucidating the contribution coming from impurities. We predict the re…
We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a mo…
We analyze recent heat capacity measurements in herbertsmithite $\rm ZnCu_3(OH)_6Cl_2$ single crystal samples subjected to strong magnetic fields. We show that the temperature dependence of specific heat $C_{mag}$ formed by quantum spin liquid at different magnetic fields $B$ resembles the electronic heat capacity $C_{el}$ of the HF metal $\rm YbRh_2Si_2$. We demonstrate that the spinon effective mass $M^*_{mag}\propto C_{mag}/T$ exhibits a scaling behavior like that of $C_{el}/T$. We also show that the recent measurements of $C_{mag}$ are compatible with those obtained on powder samples. Thes…
Recent terahertz conductivity measurements observed low-power-law frequency dependence of optical conduction within the Mott gap of the Kagome lattice spin-liquid candidate Herbertsmithite. We investigate mechanisms for this observed sub-gap conductivity for two possible scenarios in which the ground-state is described by: 1) a U(1) Dirac spin-liquid with emergent fermionic spinons or 2) a nearly critical Z2 spin-liquid in the vicinity of a continuous quantum phase transition to magnetic order. We identify new mechanisms for optical-absorption via magneto-elastic effects and spin- orbit coupli…
Despite tremendous investigations, a quantum spin liquid state realized in spin-1/2 kagome Heisenberg antiferromagnet remains largely elusive. In herbertsmithite ZnCu$_3$(OH)$_6$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. Our results are highlighted by the …
Low energy inelastic neutron scattering on single crystals of the kagome spin liquid compound ZnCu3(OD)6Cl2 (Herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers E < 0.8 meV (~J/20). The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wavevectors (1 0 0) and (0 0 3/2), which is consistent with antiferromagnetic correlations between pairs of nearest neighbor Cu impurities on adjacent triangular (Zn) interlay…
Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the three-fold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establi…
Recently Han et al. have provided an analysis of the observed behavior of $\rm ZnCu_{3}(OH)_6Cl_2$ Herbertsmithite based on a separation of the contributions to its thermodynamic properties due to impurities from those due to the kagome lattice. The authors developed an impurity model to account for the experimental data and claimed that it is compatible with the presence of a small spin gap in the kagome layers. We argue that the model they advocate is problematic, conflicting with the intrinsic properties of $\rm ZnCu_{3}(OH)_6Cl_2$ as observed and explained in recent experimental and theore…
It has been suggested that the nearest-neighbour (NN) antiferromagnetic Heisenberg (HAF) model on the Kagome lattice may be a good starting point to understand the quantum spin-liquid (QSL) behaviour discovered in Herbertsmithite. We investigate possible QSL phases in the presence of experimentally relevant spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya and Ising interactions, as well as second-neighbour antiferromagnetic Heisenberg interactions. We use the projective symmetry group analysis within the slave-fermion framework of QSL phases and systematically classi…
A quantum spin liquid (QSL) is a state of matter in which magnetic spins interact strongly, but quantum fluctuations inhibit long-range magnetic order even at zero temperature. A QSL has been predicted to have a host of exotic properties, including fractionalized excitations and long-range quantum entanglement. Despite the numerous theoretical studies, experimental realization of a QSL has proved to be challenging due to the lack of candidate materials. The triangular organic salts EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu2(CN)3, and kagome ZnCu3(OH)6Cl2 (Herbertsmithite) have recently emerged a…
Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here, we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.
We report thermal conductivity measurements on single crystals of herbertsmithite, over a wide range of temperatures (0.05-120 K) in magnetic fields up to 15 T. We also report measurements of the thermal Hall effect, found to be vanishingly small. At high temperatures, in the paramagnetic regime, the thermal conductivity has a negligible field dependence. Upon cooling and the development of correlations, the onset of a clear monotonic field dependence below about 20 K signals a new characteristic temperature scale that may reflect the subtle crossover towards the quantum spin liquid regime. De…
Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied, and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2…
A novel Kagome uud-ddu spin order in Heisenberg spin-1/2 Clinoatacamite Cu$_4$(OH)$_6$Cl$_2$, the parent compound of Herbertsmithite
本研究在自旋液体候选材料Herbertsmithite的母体斜氯铜矿中，发现了零场下新型二维uud-ddu非共面Kagome自旋序，明确了其两级磁转变行为，解决了相关神秘磁相的疑难问题。
Electron correlation effects and spin-liquid state in the Herbertsmithite Kagome lattice
本文利用实空间变分量子蒙特卡罗方法，结合共振价键波函数，研究Herbertsmithite Kagome体系中Zn掺杂浓度对电子关联效应的影响，并探讨了由长程关联能驱动的量子自旋液体态的形成机制。
Combinatorial exploration of quantum spin liquid candidates in the herbertsmithite material family
本文用密度泛函理论对 herbertsmithite 家族的阳离子和卤素取代物进行组合筛选，依据结构、热力学、合成可行性及层畸变选出量子自旋液体候选材料。
Herbertsmithite and Zn-doped barlowite are two compounds for experimental realization of twodimensional gapped kagome spin liquid. Theoretically, it has been proposed that charge doping a quantum spin liquid gives rise to exotic metallic states, such as high-temperature superconductivity. However, one recent experiment about herbertsmithite with successful Li-doping shows surprisingly the insulating state even under the heavy doped scenario, which can hardly be explained by many-body physics. Using first-principles calculation, we performed a comprehensive study about the Li intercalated dopin…
Synthetic barlowite, Cu4(OH)6BrF, has emerged as a new quantum spin liquid (QSL) host, containing kagome layers of S=1/2 Cu2+ ions separated by interlayer Cu2+ ions. Similar to synthetic herbertsmithite, ZnCu3(OH)6Cl2, it has been reported that Zn2+ substitution for the interlayer Cu2+ induces a QSL ground state. Here we report a scalable synthesis of single crystals of Cu4(OH)6BrF. Through x-ray, neutron, and electron diffraction measurements coupled with magic angle spinning 19F and 1H NMR spectroscopy, we resolve the previously reported positional disorder of the interlayer Cu2+ ions and fi…
To capture the high-field magnetization process of herbertsmithite (ZnCu3(OH)6Cl2), Faraday rotation (FR) measurements were carried out on a single crystal in magnetic fields of up to 190 T. The magnetization data evaluated from the FR angle exhibited a saturation behavior above 150 T at low temperatures, which was attributed to the 1/3 magnetization plateau. The overall behavior of the magnetization process was reproduced by theoretical models based on the nearest-neighbor Heisenberg model. This suggests that herbertsmithite is a proximate kagome antiferromagnet hosting an ideal quantum spin …
The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity $χT^α$ with $α\simeq 0.66$ can be expressed as a universal function of $H/T$ or $ω/T$. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum crit…
Nearest-neighbor interacting S = 1/2 spins on the ideal Kagomé lattice are predicted to form a variety of novel quantum entangled states, including quantum spin-liquid (SL) and valence bond solid (VBS) phases. In real materials, the presence of additional perturbative spin interactions may further expand the variety of entangled states, which recent theoretical analyses show are identifiable through the spontaneous loss of particular discrete point group symmetries. Here we comprehensively resolve the ground state point group symmetries of the prototypical Kagomé SL candidate ZnCu$_3$(OH)$_6$C…
Spinon mediation of witness spin dynamics in herbertsmithite
研究通过自旋噪声光谱探测赫伯特斯密特石中自旋子介导的见证自旋动力学，发现其行为与量子自旋液体中的自旋子传播一致，并揭示了自旋玻璃相的临界温度。
Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of spin liquids, the measured dynamic structure factor reveals an excitation continuum which is remarkably flat as a function of frequency and has almost no momentum dependence along several high-symmetry directions. Here we show that many experimentally observed features can be explained by the presence of topological viso…
Barlowite $Cu_4(OH)_6FBr$ is a newly found mineral containing $Cu^{2+}$ kagome planes. Despite similarities in many aspects to Herbertsmithite $Cu_3Zn(OH)_6Cl_2$, the well-known quantum spin liquid (QSL) candidate, intrinsic Barlowite turns out not to be a QSL, possibly due to the presence of $Cu^{2+}$ ions in between kagome planes that induce interkagome magnetic interaction [PRL, 113, 227203 (2014)]. Using first-principles calculation, we systematically study the feasibility of selective substitution of the interkagome Cu ions with isovalent nonmagnetic ions. Unlike previous speculation of u…
Arguably the most favorable situation for spins to enter the long-sought quantum spin liquid (QSL) state is when they sit on a kagome lattice. No consensus has been reached in theory regarding the true ground state of this promising platform. The experimental efforts, relying mostly on one archetypal material ZnCu$_3$(OH)$_6$Cl$_2$, have also led to diverse possibilities. Apart from subtle interactions in the Hamiltonian, there is the additional degree of complexity associated with disorder in the real material ZnCu$_3$(OH)$_6$Cl$_2$ that haunts most experimental probes. Here we resort to heat…
Realizing a quantum spin liquid (QSL) ground state in a real material is a leading issue in condensed matter physics research. In this pursuit, it is crucial to fully characterize the structure and influence of defects, as these can significantly affect the fragile QSL physics. Here, we perform a variety of cutting-edge synchrotron X-ray scattering and spectroscopy techniques, and we advance new methodologies for site-specific diffraction and L-edge Zn absorption spectroscopy. The experimental results along with our first-principles calculations address outstanding questions about the local an…
The structural-magnetic models of 25 AFM kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2) - a perspective spin liquid - have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is…
We report measurements of the specific heat and magnetization of single crystal samples of the spin-1/2 kagome compound ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ (herbertsmithite), a promising quantum spin-liquid candidate, in high magnetic fields and at low temperatures. The magnetization was measured up to $μ_{0}H$ = 55 T at $T$ = 0.4 K, showing a saturation of the weakly interacting impurity moments in fields above $\sim10$ T. The specific heat was measured down to $T < 0.4$ K in magnetic fields up to 18 T, revealing $T$-linear and $T$-squared contributions. The $T$-linear contribution is surprisingly l…
We report 17O NMR measurements in the S=1/2 Cu2+ kagome antiferromagnet Herbertsmithite ZnCu3(OH)6Cl2 down to 45mK in magnetic fields ranging from 2T to 12T. While Herbertsmithite displays a gapless spin-liquid behavior in zero field, we uncover an instability toward a spin-solid phase at sub-kelvin temperature induced by an applied magnetic field. The latter phase shows largely suppressed moments $\lesssim 0.1\muB$ and gapped excitations. The H-T phase diagram suggests the existence of a quantum critical point at the small but finite magnetic field mu0 Hc=1.55(25)T. We discuss this finding in…
Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics. We show that the herbertsmithite ZnCu3(OH)6Cl2 can be viewed as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermion metals with one exception: it resists the flow of electric charge. We demonstrate that herbertsmithite's low temperature properties are defined by a strongly correlated quantum spin liquid made with such hypothetic particles as fermionic spinons which carry spin 1/2 and no charge. Our calculations of its thermodynamic and relaxation pro…
The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets. But the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite ZnCu$_{3}$(OD)$_{6}$FBr and herbertsmithite ZnCu$_{3}$(OD)$_{6}$Cl$_2$ do not exhibit long range order, and they are considered the best realizations of t…
New physics can emerge in magnetic materials where quantum fluctuations are enhanced due to reduced dimensionality and strong frustration. One long sought example is the resonating-valence-bond (RVB) state, where atomic magnetic moments are strongly correlated but do not order or freeze even in the limit of T -> 0. The RVB ground state does not break conventional symmetries, such as lattice translation or spin-rotation. The realization of such a quantum spin liquid in two-dimensions would represent a new state of matter. It is believed that spin liquid physics plays a role in the phenomenon of…
In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the S = 1/2 kagome lattice Heisenberg antiferromagnet. This state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite (ZnCu3(OH)6Cl2). Here, we study the properties of this ASL in more detail, using both the low-energy effective field theory and Gutzwiller-projected wavefunctions. We identify the competing orders of the ASL -- among them we find a set of magnetic orders lying at the M-points of the Brillouin zone, the q = 0 magnetic ordered state, the "Hastings…
We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4). We investigate in detail the spin dynamics on well characterized samples in zero and applied longitudinal fields and propose a low T defect based interpretation to explain the unconventional dynamics observed in the quantum spin liquid phase.
Theory of the Spinon-Mediated Witness Spin Glass in Herbertsmithite
本文建立含单一自由参数的理论模型，解释赫伯茨mithite中由QSL自旋子介导的见证自旋玻璃现象，匹配多类实验数据，预测Z₂与U(1)型QSL的中子散射差异及高浓度下的相变，为区分QSL类型提供测试方法。
A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J \simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need t…
The effect of the quenched bond-randomness on the ordering of the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice is investigated by means of an exact-diagonalization method. When the randomness exceeds a critical value, the ground state of the model exhibits a transition within the non-magnetic state into the randomness-relevant gapless spin-liquid state. Implications to the S=1/2 kagome-lattice antiferromagnet herbertsmithite is discussed.
Magnetic susceptibility, NMR, muSR, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphous with the herbertsmithite mineral, is a gapless spin liquid with frustrated interactions showing unusual dynamic short-range correlations of non-coplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to thermodynamical data. The experimental data are compared to theoretical calculations using the Schwinger-boson approach.
The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^α$, where $α$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liq…
Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor $S(\mathbf{q},ω)$ of spin liquid states on the kagome lattice. Spin-1 excited states in spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). FSL and RSL have low energy peaks in $S(\mathbf{q},ω)$ at $K$ points in the ext…
The ground state of the simple Heisenberg nearest-neighbor quantum kagome antiferromagnetic model is a magnetically disordered spin liquid, yet various perturbations may lead to fundamentally different states. Here we disclose the origin of magnetic ordering in the structurally-perfect kagome material YCu$_3$(OH)$_6$Cl$_3$, which is free of the widespread impurity problem. {\it Ab-initio} calculations and modeling of its magnetic susceptibility reveal that, similar to the archetypal case of herbertsmithite, the nearest-neighbor exchange is by far the dominant isotropic interaction. Dzyaloshins…
Herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$, is a two dimensional kagomé lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$rd electron doping. Here we report the topochemical synthesis of electron-doped ZnLi$_x$Cu$_3$(OH)$_6$Cl$_2$ from $x$ = 0 to $x$ = 1.8 ($3/5$th per Cu$^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we…
The electrodynamic response of the organic spin-liquid candidate $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ has been measured in an extremely wide energy range ($10^{-13}$ to 2 eV) as a function of temperature (5 to 300 K). Below the Mott gap, excitations from the un-gapped spinon continuum cause a considerable contribution to the infrared conductivity, as suggested by the U(1) gauge theory. At THz frequencies we can identify a power-law behavior $σ(ω) \propto ω^β$ with two distinct exponents $β$ that change from 0.9 to 1.3 at low temperatures. The corresponding crossover scales with temperature: $\hbar…
The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with non-negligible Dzyaloshinskii-Moriya interaction~(DMI). A well established phase transition to the $\mathbf q=0$ long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in inelastic neutron scattering experiment by Han et al (…
We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac sp…
We address the problem of a lightly doped spin-liquid through a large-scale density-matrix renormalization group (DMRG) study of the $t$-$J$ model on a Kagome lattice with a small but non-zero concentration, $δ$, of doped holes. It is now widely accepted that the undoped ($δ=0$) spin 1/2 Heisenberg antiferromagnet has a spin-liquid groundstate. Theoretical arguments have been presented that light doping of such a spin-liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal (FL$^\ast$). Instead, we infer that the doped holes form an insulating cha…
Recent discoveries in neutron scattering experiments for Kapellasite and Herbertsmithite as well as theoretical calculations of possible spin liquid phases have revived interest in magnetic phenomena on the kagome lattice. We study the quantum phase diagram of the S=1/2 Heisenberg kagome model as a function of nearest neighbor coupling J1 and second neighbor coupling J2. Employing the pseudofermion functional renormalization group, we find four types of magnetic quantum order (q=0 order, cuboc order, ferromagnetic order, and Sqrt{3}x\Sqrt{3} order) as well as extended magnetically disordered r…
Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly, these compounds are strongly correlated electron systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates. First we consider the inorganic material Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$ and related compounds, which crystallize in a …
The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of great debate. We conducted 17-O single crystal NMR measurements of the S=1/2 kagome lattice in herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrate that the intrinsic local spin susceptibility $χ_{kagome}$ deduced from the 17-O NMR frequency shift asymptotes to zero below temperature T ~ 0.03 J, where J ~ 200 K is the Cu-Cu super-exc…
The spin-1/2 kagomé Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagomé Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the int…
We present a Raman spectroscopic investigation of the Herbertsmithite ZnCu3(OH)6Cl2, the first realization of a Heisenberg s=1/2 antiferromagnet on a perfect kagome lattice. The magnetic excitation spectrum of this compound is dominated by two components, a high temperature quasi elastic signal and a low temperature, broad maximum. The latter has a linear low energy slope and extends to high energy. We have investigated the temperature dependence and symmetry properties of both signals. Our data agree with previous calculations and point to a spin liquid ground state.
The intrinsic magnetic susceptibility and local magnetization of the near-kagome quantum magnet vesignieite, Cu3BaV2O8(OH)2, are presented as measured using 51V NMR. The NMR line shift gives an accurate measurement of the intrinsic susceptibility of the kagome sites which closely resembles that of the quantum spin liquid herbertsmithite [A. Olariu et al. Phys. Rev. Lett. 100, 087202 (2008)]. It is therefore surprising that, at Tc ~ 9 K, a transition to a heterogeneous ground state is observed. A gradual wipeout of half the NMR intensity indicates a slowly fluctuating spin liquid component and …
We study dynamical spin structure factor (DSSF) of S = 1/2 Heisenberg model on the kagome lattice (KAFM) by means of density-matrix renormalization group. By comparison with the well-defined magnetic ordered state and chiral spin liquid sitting nearby in the phase diagram, the KAFM with the nearest-neighbor interaction shows distinct dynamical response behaviors. First of all, the DSSF displays important spectral intensity predominantly at low frequency region around Q = M point in momentum space, and shows a broad spectral distribution at high frequency region for momenta along the boundary o…
We compute the real-space spin correlations and frquency and wave-vector resolved dynamic structure factors $S(\vec q,ω)$ for the nearest-neighbor Kagome-Lattice Heisenberg Antiferromagnet (KLHM) at finite temperatures using Numerical Linked Cluster Expansion (NLCE) method. A triangle-based NLCE is used to calculate frequency moments of the dynamic structure factors in the thermodynamic limit, which show excellent convergence for $T> J/4$. A Gaussian approximation and the fluctuation-dissipation relation are used to to reconstruct the frequency dependence. We find that some features of the low…
Herbertsmithite, ZnCu3(OH)6Cl2, is the prototype candidate for a spin liquid behavior on a geometrically perfect kagome lattice. Its discovery and the absence of any evidence for spin-freezing down to the lowest probed temperature to-date enable one to explore the properties of kagome-related physics in an unprecedented temperature range. We review its properties and discuss some open issues. A tentative comparison to models is also performed.
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