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 a SVM bias parameter. For completeness we mention that the machine also picks up the leading $\sqrt{3} \times \sqrt{3}$ 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.
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.
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…
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.
The spin half Heisenberg antiferromagnet on the Kagome lattice, is mapped by Contractor Renormalization to a Spin-Pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low energy singlets observed numerically, and the non magnetic T-squared specific heat observed experimentally.
Low-energy degrees of freedom of a spin-1/2 kagome antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows to obtain quantitative description of the magnetothermodynamics of a quantum kagome antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.
Using an advanced Monte Carlo algorithm and high precision spin dynamics simulation, we investigated the dynamical behavior of the Heisenberg antiferromagnet on a kagome lattice at extremely low temperatures. We demonstrate that the detection and correct identification of propagating excitations depends crucially on the choice of coordinates and we show how modes are displaced in Fourier space if a single, global Cartesian coordinate system is chosen.
Classical Heisenberg antiferromagnets on two-dimensional kagome and three-dimensional hyperkagome lattices are investigated by Monte Carlo simulations. For both models the symmetry-breaking states at low temperatures are described by non-zero octupole moments or third-rank spin tensor order parameters. In the case of the two-dimensional kagome antiferromagnet, a sharp crossover into a coplanar state takes place at T_k ~ 0.004J, which we attribute to proliferation of fractional vortices. The three-dimensional model exhibits a first-order transition at T_c ~ 0.002J into a phase with critical spi…
An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.
The thermal order by disorder effect in magnetic field is studied for a classical Heisenberg antiferromagnet on the kagome lattice. Using analytical arguments we predict a unique H-T phase diagram for this strongly frustrated magnet: states with a coplanar and a uniaxial triatic order parameters respectively at low and high magnetic fields and an incompressible collinear spin-liquid state at a one-third of the saturation field. We also present the Monte Carlo data which confirm existence of these phases.
Asymmetric destruction of the one-third magnetization plateau upon heating is found in the spin-1/2 kagome Heisenberg antiferromagnets using the typical pure quantum state approach. The asymmetry originates from larger density of states of low-lying excited sates of $N_{\rm s}$ spin systems with magnetization $(1/3-2/N_{\rm s})$ than that of low-lying sates with magnetization $(1/3+2/N_{\rm s})$. The enhanced specific heat and entropy that reflect the larger density of states in the lower-field side of the plateau are detectable in candidate materials of the kagome antiferromagnets. We discuss…
We discuss the ground state and the low-lying excitations of the spin-half Heisenberg antiferromagnet on the two-dimensional square-kagome lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is known also for the Heisenberg antiferromagnet on the kagome and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet likely with a finite spin gap and with a large number of non-magnetic excitations within this gap. The magnetization versus field curve sho…
Low energy spectrum of the S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of exact diagonalization and the cluster expansion. The magnitude of the energy gap of the magnetic excitation is consistent with the recent experimental observation for \mpynn. In contrast to the $S=1/2$ KHAF, the non-magnetic excitations have finite energy gap comparable to the magnetic excitation. As a physical picture of the ground state, the hexagon singlet solid state is proposed and verified by variational analysis.
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 magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1/3 plateau are obtained by using the approximated state in the unit cell and compared with the nu- merical results of the exact diagonalization of 42 sites.
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 magnetization process of the S=1 and 1/2 kagome Heisenberg antiferromagnet is studied by means of the numerical exact diagonalization method. It is found that the magnetization curve at zero temperature has a plateau at 1/3 of the full magnetization. In the presence of $\sqrt{3} \times \sqrt{3}$ lattice distortion, this plateau is enhanced and eventually the ferrimagnetic state is realized. There also appear the minor plateaux above the main plateau. The physical origin of these phenomena is discussed.
The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The pres…
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…
We introduce a two dimensional network of corner-sharing triangles with square lattice symmetry. Properties of magnetic systems here should be similar to those on the kagome lattice. Focusing on the spin half Heisenberg quantum antiferromagnet, we generalise the spin symmetry group from SU(2) to SU(N). In the large N limit, we map the model exactly to the eight vertex model, solved by Baxter. We predict an exponential number of low-lying singlet states, a triplet gap, and a two-peak specific heat. In addition, the large N limit suggests a finite temperature phase transition into a phase with o…
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.
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order paramet…
We discuss the ground-state degeneracy of spin-$1/2$ kagome-lattice quantum antiferromagnets on magnetization plateaus by employing two complementary methods: the adiabatic flux insertion in closed boundary conditions and a 't Hooft anomaly argument on inherent symmetries in a quasi-one-dimensional limit. The flux insertion with a tilted boundary condition restricts the lower bound of the ground-state degeneracy on $1/9$, $1/3$, $5/9$, and $7/9$ magnetization plateaus under the $\mathrm{U(1)}$ spin-rotation and the translation symmetries: $3$, $1$, $3$, and $3$, respectively. This result motiv…
We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 \sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- re…
The ground state phase transitions in the distorted S=1 kagome Heisenberg antiferromagnet (KHAF) with single-site anisotropy D are studied by the numerical exact diagonalization method. For strong easy plane anisotropy, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and large-D state is realized. The quantum phase transition between these two states is analogous to the Haldane-large-D transition in the S=1 antiferromagnetic Heisenberg chain. The combined effect of the sqrt(3) times sqrt(3) lattice distortion and single site anisotropy is also investigated. The g…
We consider a spin-$\frac{1}{2}$ kagome-like chain with competing ferro- and antiferromagnetic anisotropic exchange interactions. The ground state phase diagram of this model consists of the ferromagnetic and ferrimagnetic phases. We study the ground state and the low-temperature properties on the phase boundary between these phases. The ground state on this phase boundary is macroscopically degenerate and consists of localized magnon states. We calculate the ground state degeneracy and corresponding residual entropy. The spontaneous magnetization has a jump on the phase boundary confirming th…
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…
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 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 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…
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 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…
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 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.
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…
The antiferromagnetism in $α$-Cu$_3$Mg(OH)$_6$Br$_2$ was studied by magnetic-susceptibility, specific-heat and neutron-diffraction measurements. The crystal structure consists of Cu$^{2+}$ kagome layers with Mg$^{2+}$ ions occupying the centers of the hexagons, separated by Br$^{1-}$ ions. The magnetic system orders antiferromagnetically at 5.4 K with the magnetic moments aligned ferromagnetically within the kagome planes. The ordered moment is 0.94 $μ_B$, suggesting little quantum and geometrical fluctuations. By comparing the magnetic and specific-heat properties with those of the haydeeite,…
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.
