A three-dimensional system of interacting spins typically develops static long-range order when it is cooled. If the spins are quantum (S = 1/2), however, novel quantum paramagnetic states may appear. The most highly sought state among them is the resonating valence bond (RVB) state in which every pair of neighboring quantum spins form entangled spin singlets (valence bonds) and the singlets are quantum mechanically resonating amongst all the possible highly degenerate pairing states. Here we provide experimental evidence for such quantum paramagnetic states existing in frustrated antiferromagnets, ZnxCu4-x(OD)6Cl2, where the S = 1/2 magnetic Cu2+ moments form layers of a two-dimensional kagome lattice. We find that in Cu4(OD)6Cl2, where distorted kagome planes are weakly coupled to each other, a dispersionless excitation mode appears in the magnetic excitation spectrum below ~ 20 K, whose characteristics resemble those of quantum spin singlets in a solid state, known as a valence bond solid (VBS), that breaks translational symmetry. Doping nonmagnetic Zn2+ ions reduces the distortion of the kagome lattice, and weakens the interplane coupling but also dilutes the magnetic occupancy of the kagome lattice. The VBS state is suppressed and for ZnCu3(OD)6Cl2 where the kagome planes are undistorted and 90% occupied by the Cu2+ ions, the low energy spin fluctuations in the spin liquid phase become featureless.
We prepared a powder sample of edwardsite Cd2Cu3(SO4)2(OH)6 4H2O, which is a new candidate compound for the spin-1/2 kagome antiferromagnet, and studied its magnetic properties by magnetic susceptibility and heat capacity measurements. Edwardsite has a deformed kagome lattice with an average antiferromagnetic interaction of 51 K between nearby spins and shows an antiferromagnetic order accompanied by a small ferromagnetic moment below 4.3 K. The weak ferromagnetism is likely due to spin canting caused by sizable Dzyaloshinsky-Moriya interactions, which may stabilize the long-range magnetic ord…
We investigate the connection between highly frustrated kagome based Hamiltonians and a recently synthesized family of materials containing Ti3+ S=1/2 ions. Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs2NaTi3F12 and Cs2KTi3F12. We determine magnetization curves in excellent agreement with experimental observations. Our calculations successfully clarify the relationship between the experimental observations and the magnetization-plateau…
We give a physical picture of the low-energy sector of the spin 1/2 Heisenberg Kagome antiferromagnet (KAF). It is shown that Kagome lattice can be presented as a set of stars which are arranged in a triangular lattice and contain 12 spins. Each of these stars has two degenerate singlet ground states which can be considered in terms of pseudospin. As a result of interaction between stars we get Hamiltonian of the Ising ferromagnet in magnetic field. So in contrast to the common view there is a long range order in KAF consisting of definite singlet states of the stars.
In the context of the $S=1$ kagome antiferromagnet Na$_2$Ti$_3$Cl$_8$, we respond to the comment by Khomskii et al. [D.I. Khomskii, T. Mizokawa and S.V. Streltsov, Phys. Rev. Lett. 127, 049701 (2021)] on previous work by Paul et al. [A. Paul, C.-M. Chung, T. Birol, and H. J. Changlani, Phys. Rev. Lett. 124, 167203 (2020)].
We investigate the low temperature magnetic properties of a $S=\frac{5}{2}$ Heisenberg kagomé 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 $T_{\rm N}=1.3$ K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below $T^* \sim 5$ K. A moderate $^{31}$P NMR line broadening reveals the development of anisotropic short-range correlations within the plateau phase concomitantly with a gapless spin-latti…
Y{0.5}$Ca{0.5}BaCo4O7 contains kagome layers of Co ions, whose spins are strongly coupled according to a Curie-Weiss temperature of -2200 K. At low temperatures, T = 1.2 K, our diffuse neutron scattering study with polarization analysis reveals characteristic spin correlations close to a predicted two-dimensional coplanar ground state with staggered chirality. The absence of three dimensional long-range AF order proves negligible coupling between the kagome layers. The scattering intensities are consistent with high spin S=3/2 states of Co2+ in the kagome layers and low spin S=0 states for Co3…
Coupling between spin and lattice degrees of freedom are important in geometrically frustrated magnets where they can lead to degeneracy lifting and novel orders. We show that moderate spin-lattice couplings in triangular and Kagome antiferromagnets can induce complex colinear magnetic orders. When classical Heisenberg spins on the triangular lattice are coupled to Einstein phonons, a rich variety of phases emerge, including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magneto-electric material CuFeO$_2$. In addition we predict magne…
A polycrystalline sample of vesignieite BaCu3V2O8(OH)2 comprising a nearly ideal kagome lattice composed of Cu2+ ions carrying spin 1/2 has been synthesized and studied by magnetization and heat capacity measurements. Magnetic susceptibility shows a neither long range order, a spin glass transition nor a spin gap down to 2 K, in spite of a moderately strong antiferromagnetic interaction of J/kB = 53 K between nearest-neighbor spins. A broad peak observed at a temperature corresponding to 0.4J in intrinsic magnetic susceptibility indicates a marked development of the short-range order. The grou…
We investigate the $S=1/2$ quantum spin antiferromagnets on the triangular and Kagome lattices in magnetic field, using the numerical exact diagonalization. Particularly we focus on an anomalous magnetization behavior of each system at 1/3 of the saturation magnetization. The critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, on the Kagome lattice.
The search for the resonating valence bond (RVB) state continues to underpin many areas of condensed matter research. The RVB is made from the dimerisation of spins on different sites into fluctuating singlets, and was proposed by Anderson to be the reference state from which the transition to BCS superconductivity occurs. Little is known about the state experimentally, due to the scarcity of model materials. Theoretical work has put forward the S = 1/2 kagome antiferromagnet (KAFM) as a good candidate for the realization of the RVB state. In this paper we introduce a new model system, the S =…
A brief review is provided of earlier work on the low temperature phases of $S=1$ kagome and triangular lattice antiferromagnets in which there is sufficiently strongly single-ion anisotropy $D$ that dominates over the antiferromagnetic exchange $J$.
The kagome lattice, consisting of interconnected triangles and hexagons uniquely, is an excellent model system for study frustrated magnetism, electronic correlation and topological electronic structure. After an intensive investigation on frustrated magnetism in insulating magnetic kagome lattices, the interplay between charge and spin degrees of freedom via spin-orbital coupling in metallic systems (kagome metals) has become an attractive topic recently. Here, we study centrosymmetric YMn6Sn6 with Mn kagome lattice. We discover that it exhibits giant topological Hall effect near room tempera…
The jarosite family of minerals contain antiferromagnetically coupled Fe3+ ions that make up the kagome network. This geometric arrangement of the Fe3+ ions causes magnetic frustration that results in exotic electronic ground states, e.g. spin glasses and spin liquids. Synthesic research into jarosites has focused on producing near perfect stoichiometry to eliminate possible magnetic disorder. An new oxidative synthesis method has been devel-oped for the potassium, sodium, rubidium and ammonium jarosites that leads to high Fe coverage. We show through the identification of a meta-stable interm…
We present the crystal structure and magnetic properties of Y$_{3}$Cu$_{9}$(OH)$_{19}$Cl$_{8}$, a stoichiometric frustrated quantum spin system with slightly distorted kagome layers. Single crystals of Y$_{3}$Cu$_{9}$(OH)$_{19}$Cl$_{8}$ were grown under hydrothermal conditions. The structure was determined from single crystal X-ray diffraction and confirmed by neutron powder diffraction. The observed structure reveals two different Cu-positions leading to a slightly distored kagome layer in contrast to the closely related YCu$_{3}$(OH)$_{6}$Cl$_{3}$. Curie-Weiss behavior at high-temperatures w…
We investigate the zero-temperature phase diagram of the nearest-neighbor kagome antiferromagnet in the presence of Dzyaloshinksii-Moriya interaction. We develop a theory for the transition between Z2 spin liquids with bosonic spinons and a phase with antiferromagnetic long-range order. Connections to recent numerical studies and experiments are discussed.
Dynamics of classical Heisenberg spins, ${\bf S}_i=({\bf s}_i,S_{iz})$, on the Kagomé lattice has been studied. An ideal Heisenberg Kagomé antiferromagnet is known to remain disordered down to T=0 due to the macroscopic degeneracy of the ground state. Through the study, however, we find that ${\bf S}_i$ and their planar components ${\bf s}_i$ behave in a qualitatively different way and especially planar spins (${\bf s}_i$) show the exotic glass-like transition in the very low temperature $T\sim 0.003J$ ($J$: spin exchange). The glassy behaviors of ${\bf s}_i$ would be found to be driven by the…
The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".
The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S=1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.
We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.
We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system…
A clear thermal Hall signal ($κ_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagomé antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2\cdot 0.6$H$_2$O). We found that $κ_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J \sim 0.1$. In particular, $κ_{xy}$ values of Ca kapellasite and those of another kagomé antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $κ_{xy}$ fo…
Within the t-J model, we study the electronic properties of the doped antiferromagnet on the kagome lattice based on the framework of the self-consistent mean-field theory. At the half-filling, the spin-liquid ground-state energy per site of the kagome antiferromagnet is Eg/NJ=-0.859, which is in very good agreement with the numerical estimates. Away from the half-filling, the electron photoemission spectroscopy and density of states are discussed, and the results indicate that there is a gap in the normal-state of the system.
The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.
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…
The recent NMR experiments on ZnCu3(OH)6Cl2 motivate our study of the effect of non- magnetic defects on the antiferromagnetic spin-1/2 kagome lattice. We use exact diagonalization methods to study the effect of two such defects on finite size systems. Our results, obtained without adjustable parameters, are in good quantitative agreement with recent Oxygen 17 NMR data. They provide support for the experimental interpretation of the presence of defects within the kagome layers due to Zn/Cu substitutions. Our results also show that disorder effects become relevant at lower temperatures, raising…
We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings Jhexagon, J and J', and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear Q = 0 magnetic phase, two unusual non-collinear coplanar Q = (1/3,1/3) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-di…
We propose a general non-perturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective Generalized Quantum Dimer Models. We develop the formal lattice independent frame and establish some important results on (i) the locality of the generated Hamiltonians (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian - shown to capture the essential properties and provide deep insights on the mic…
Herbertsmithite (ZnCu3(OH)6Cl2) is often discussed as the best realization of the highly frustrated antiferromagnetic kagome lattice known so far. We employ density functional theory calculations to determine eight exchange coupling constants of the underlying Heisenberg Hamiltonian. We find the nearest neighbour coupling J1 to exceed all other couplings by far. However, next-nearest neighbour kagome layer couplings of 0.019 J1 and interlayer couplings of up to -0.035 J1 slightly modify the perfect antiferromagnetic kagome Hamiltonian. Interestingly, the largest interlayer coupling is ferromag…
In this Letter, we identify a noncoplanar chiral spin texture on the distorted kagomé-lattice antiferromagnets induced by the presence of a magnetic field applied perpendicular to the distorted kagomé plane. The noncoplanar chiral spin texture has a nonzero scalar spin chirality similar to a chiral quantum spin liquid with broken time-reversal symmetry. In the noncoplanar regime we observe nontrivial topological magnetic excitations and thermal Hall response through the emergent field-induced scalar spin chirality in contrast to collinear ferromagnets in which the Dzyaloshinskii-Moriya (DM) sp…
We argue that the S=1/2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For $D<D_c$ the system is in a moment-free phase and for $D>D_c$ the system develops antiferromagnetic long-range order. The quantum critical point is found to be $D_c \simeq 0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu$_3(OH)$_6$Cl$_3$ may be in a quantum critical region controlled by this fixed point.
We have studied the effect of the Dzyaloshinskii-Moriya interaction on kagome Heisenberg anti-ferromagnet using Schwinger boson mean field theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ansätze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and…
We have successfully synthesized S = 1/2 kagome antiferromagnets MCu3(OH)6Cl2 (M = Ni and Co) by hydrothermal method with rotating pressure vessel. Structural characterization shows that both compounds have the similar crystal structure as ZnCu3(OH)6Cl2 with R-3m symmetry. Similar to ZnCu3(OH)6Cl2, the compounds show no obvious hysteresis at 2 K. A spin glass transition is found in both NiCu3(OH)6Cl2 and CoCu3(OH)6Cl2 at low temperatures (6.0 and 3.5 K respectively) by AC susceptibility measurements. It indicates no long-range magnetic order and a strong spin frustration. The substitution of Z…
Dynamical magnetic correlations in the geometrically frustrated Nd$\_3$Ga$\_5$SiO$\_{14}$ compound were probed by inelastic neutron scattering on a single crystal. A scattering signal with a ring shape distribution in reciprocal space and unprecedented dispersive features was discovered. Comparison with calculated static magnetic scattering from models of correlated spins suggests that the observed phase is a spin liquid inherent to an antiferromagnetic kagomé-like lattice of anisotropic Nd moments.
An effective spin-orbit Hamiltonian is derived for a spin-1/2 trimerized kagome antiferromagnet in the second-order of perturbation theory in the ratio of two coupling constants. Low-energy singlet states of the obtained model are mapped to a quantum dimer model on a triangular lattice. The quantum dimer model is dominated by dimer resonances on a few shortest loops of the triangular lattice. Characteristic energy scale for the dimer model constitutes only a small fraction of the weaker exchange coupling constant.
The ground state of the S=1/2 Heisenberg antiferomagnet on kagome can be viewed as a collection of fermionic spinons bound into small, heavy singlet pairs. Low-energy magnetic excitations in this system correspond to breaking the pairs into individual spinons. We calculate the structure factor for inelastic neutron scattering from independent spinon pairs.
We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$ to investigate the possibility of a dispersionless zero-energy excitation associated with rotation of spins along the chains. The observed spectra indeed exhibit such an excitation with strong intensity at low energy, as well as dispersive excitations with weak intensity at high energy. Combining the measurements with calculations from linear spin-wave theory reveals that NaBa$_{2}$Mn$_{3}$F$_{11}$ is a good realization of the classical kagome anti…
The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.
The spin wave excitations of the ideal S=5/2 Kagome lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted "zero energy mode," verifying a fundamental prediction for the Kagome lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low temperature magnetization and spin structure.
Motivated by recent experiments on ZnCu$_3$(OH)$_6$Cl$_2$, we study the inhomogeneous Knight shifts (local susceptibilities) of spin 1/2 Kagome antiferromagnet in the presence of nonmagnetic impurities. Using high temperature series expansion, we calculate the local susceptibility and its histogram down to about T=0.4J. At low temperatures, we explore a Dirac spin liquid proposal and calculate the local susceptibility in the mean field and beyond mean field using Gutzwiller projection, finding the overall picture to be consistent with the NMR experiments.
By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning…
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
Spin dynamics of the spin-1/2 kagome lattice antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$ was studied using high-resolution, time-of-flight inelastic neutron scattering. The flat mode, a characteristic of the frustrated kagome antiferromagnet, and the low-energy dispersive mode, which is dominated by magnons, can be well described by the linear spin-wave theory. However, the theory fails to describe three weakly dispersive modes between 9 and 14 meV. These modes could be attributed to two-spinon bound states, which decay into free spinons away from the zone center and at a high temperature, giving r…
We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin-chains (exchange J) that are weakly coupled via intermediate "dangling" spins (exchange J'). Using one-dimensional bosonization, renormalization group methods, and current algebra techniques the ground state is determined in the limit J'<<J. We find that the dangling spins and chain spins form a spiral with O(1) and O(J'/J) static moments, respectively, atop of which the chain spins exhibit a smaller O[(J'/J)^2] antiferromagnetica…
We construct a phenomenological Z_2 lattice gauge theory to describe the spin-liquid state of the S=1/2 kagome Heisenberg antiferromagnet in the sector with zero total spin. The model is a natural generalization of the Misguich-Serban-Pasquier Hamiltonian with added interactions that are strongly constrained by lattice symmetries. We are able to reproduce qualitatively many of the characteristic features observed in recent numerical studies. We also make connections to the previous works along similar lines.
We report the crystal structure and unconventional magnetic ordering of Cs_2Cu_3CeF_{12}, which is composed of buckled kagome lattice of Cu^{2+} ions. The exchange network in the buckled kagome lattice is fairly anisotropic, so that the present spin system can be divided into two subsystems: alternating Heisenberg chains with strong antiferromagnetic exchange interactions and dangling spins. Although the direct exchange interactions between neighboring spins were found to be all antiferromagnetic, ferromagnetic magnetic ordering of the dangling spins was observed. Magnetization exhibits a plat…
The dc-magnetization of the unique S=1/2 kagome antiferromagnet Herbertsmithite has been measured down to 0.1K. No sign of spin freezing is observed in agreement with former muSR and ac-susceptibility results. The low temperature magnetic response is dominated by a defect contribution which exhibits a new energy scale $\simeq 1$ K, likely reflecting the coupling of the defects. The defect component is saturated at low temperature by H>8T applied magnetic fields which enables us to estimate an upper bound for the non saturated intrinsic kagome susceptibility at T=1.7K.
We investigate the effect of geometrical frustration on the $H$--$T$ phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large scale Monte Carlo simulations. For the kagome antiferromagnet thermal fluctuations are unable to lift completely degeneracy and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagom…
Spin-1/2 Heisenberg model on kagome lattice is a typical frustrated quantum spin system. A basic structure of kagome lattice is also present in kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translati…
Topological magnon insulators in insulating Kagomé ferromagnets have been extensively studied in a series of papers. It has been established that Dzyaloshinskii-Moriya interaction (DMI) is the key ingredient to observe a nontrivial topological magnon with edge modes. However, insulating antiferromagnets on the Kagomé lattice are frustrated systems considered as a playground for studying quantum spin liquid physics. In these systems the DMI can induce a coplanar but noncollinear magnetic orders with a $\mathbf{q}=0$ propagating wavevector. We show that topological magnon bands are absent in thi…
We propose in this work an effective field theory description of the chiral spin liquid state in Heisenberg spin system on kagomé lattice.To this end, we derive the low-energy effective theory of kagomé (isotropic) Heisenberg antiferromagnet around its ordered ground states found numerically and show that quantum fluctuations induced by further neighbor spin exchanges are equally strong as those from first neighbor.We use a chiral order parameter theory to argue for the occurrence of finite temperature chiral symmetry breaking transition into chiral ordered state in kagomé antiferromagnet with…
Density matrix renormalization group (DMRG) calculations on large systems (up to 3096 spins) indicate that the ground state of the Heisenberg model on a 3-chain Kagome strip is spontaneously dimerized. This system has degenerate ground states and a gap to triplet and singlet excitations. These results are in direct contradiction with recent results of Azaria et al (Phys. Rev. Lett. 81, 1694 (1998)) and suggest a need for a reexamination of the underlying field theory.
Magnetic excitations in the spin-$\frac{1}{2}$ distorted kagome lattice antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$, which has an ordered ground state owing to the strong Dzyaloshinskii-Moriya interaction, were studied using inelastic neutron scattering. Although the spin-wave dispersion can be qualitatively understood in terms of linear spin-wave theory (LSWT), the excitation energies are renormalized by a factor of approximately 0.6 from those calculated by LSWT, almost irrespective of the momentum transfer. This inadequacy of LSWT, which is attributed to quantum fluctuations, provides evidence o…
We investigated the crystal structure of Rb$_2$Cu$_3$SnF$_{12}$ and its magnetic properties using single crystals. This compound is composed of Kagome layers of corner-sharing CuF$_{6}$ octahedra with a 2a x 2a enlarged cell as compared with the proper Kagome layer. Rb$_2$Cu$_3$SnF$_{12}$ is magnetically described as an $S$=1/2 modified Kagome antiferromagnet with four kinds of neighboring exchange interaction. From magnetic susceptibility and high-field magnetization measurements, it was found that the ground state is a disordered singlet with the spin gap, as predicted from a recent theory. …
Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagomé lattice has long-range spin order of the $\sqrt{3}\times\sqrt{3}$ type (modulo gradual orientation fluctuations of the spins' plane). I start from the effective quartic Hamiltonian for the soft (out of plane) spin fluctuation modes, and treat as a perturbation those terms which depend on the discrete coplanar state. Soft mode correlations, which become the coefficients of a discrete effective Hamiltonian, are estimated analytically.
Impurities, which are inherently present in any real material, may play an important role in the magnetism of frustrated spin systems with spin-liquid ground states. We address the impurity issue in quantum kagome antiferromagnets by investigating ZnCu$_3$(OH)$_6$SO$_4$ (Zn-brochantite) by means of muon spin spectroscopy. We show that muons couple to the impurity magnetism, originating from Cu-Zn intersite disorder, and that the impurities are highly correlated with the kagome spins, allowing us to probe the intrinsic kagome physics via a Kondo-like effect. The low-temperature plateau in local…
The anyonic excitations of a spin-liquid can feature fractional quantum numbers under space-group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice chiral spin liquid. We provide a method to detect these fractional quantum numbers in…
We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The SU(3)-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be -1.410(2) and establish the presence of a spin gap.
The spin-$\frac{1}{2}$ kagome antiferromagnet is an archetypal frustrated system predicted to host a variety of exotic magnetic states. We show using neutron scattering measurements that deuterated vesignieite BaCu$_{3}$V$_{2}$O$_{8}$(OD)$_{2}$, a fully stoichiometric $S=1/2$ kagome magnet with $<$1% lattice distortion, orders magnetically at $T_{\mathrm{N}}=9$K into a multi-k coplanar variant of the predicted triple-k octahedral structure. We find this structure is stabilized by a dominant antiferromagnetic 3$^{\mathrm{rd}}$-neighbor exchange $J_3$ with minor 1$^{\mathrm{st}}$- or 2$^{\mathrm…
The antiferromagnetic Heisenberg model on an anisotropic kagome lattice may be a good minimal model for real magnetic systems as well as a limit from which the isotropic case can be better understood. We therefore study the nearest-neighbor Heisenberg antiferromagnet on an anisotropic kagome lattice in a magnetic field. Such a system should be well described by weakly interacting spin chains, and we motivate a general form for the interaction by symmetry considerations and by perturbatively projecting out the inter-chain spins. In the spin 1/2 case, we find that the system exhibits a quantum p…
