Weak ferromagnetic exchange and anomalous specific heat in ZnCu3(OH)6Cl2

Experimental evidence for a plethora of low energy spin excitations in the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2 may be understandable in terms of an extended Fermi surface of spinons coupled to a U(1) gauge field. We carry out variational calculations to examine the possibility that such a state may be energetically viable. A Gutzwiller-projected wave function reproduces the dimerization of a kagome strip found previously by the density matrix renormalization group. Application to the full kagome lattice shows that the inclusion of a small ferromagnetic next-nearest-neighbor interaction favors a ground state with a spinon Fermi surface.     

Field-induced freezing of a quantum spin liquid on the kagome lattice

We report (17)O NMR measurements in the S=1/2 (Cu(2+)) kagome antiferromagnet Herbertsmithite ZnCu(3)(OH)(6)Cl(2) down to 45 mK in magnetic fields ranging from 2 to 12 T. 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 ?0.1 μ(B) and gapped excitations. The H-T phase diagram suggests the existence of a quantum critical point at the small but finite magnetic field μ(0)H(c)=1.55(25) T. We discuss this finding in light of the perturbative Dzyaloshinskii-Moriya interaction which was theoretically proposed to sustain a quantum critical regime for the quantum kagome Heisenberg antiferromagnet model.     

Magnetic susceptibility of the Kagome antiferromagnet ZnCu3(OH)6Cl2

We analyze the experimental data for the magnetic susceptibility of the material ZnCu3(OH)6Cl2 in terms of the Kagome Lattice Heisenberg model (KLHM), discussing possible role of impurity spins, dilution, exchange anisotropy, and both out-of-plane and in-plane Dzyloshinski-Moriya (DM) anisotropies, with explicit theoretical calculations using the numerical linked cluster method and exact diagonalization. The high-temperature experimental data are well described by the pure Heisenberg model with J=170 K. We show that the sudden upturn in the susceptibility around T=75 K is due to DM interactions. We also observe that at intermediate temperatures, below T=J, our calculated susceptibility for KLHM fits well with a power law T(-0.25).     

Dzyaloshinsky-Moriya anisotropy in the spin-1/2 kagome compound ZnCu3(OH)6Cl2

We report the determination of the Dzyaloshinsky-Moriya interaction, the dominant magnetic anisotropy term in the kagome spin-1/2 compound ZnCu3(OH)6Cl2. Based on the analysis of the high-temperature electron spin resonance (ESR) spectra, we find its main component |Dz|=15(1) K to be perpendicular to the kagome planes. Through the temperature dependent ESR linewidth, we observe a building up of nearest-neighbor spin-spin correlations below approximately 150 K.     

63Cu, 35Cl, and 1H NMR in the S=1/2 Kagome lattice ZnCu3(OH)6Cl2

ZnCu(3)(OH)(6)Cl(2) (S=1/2) is a promising new candidate for an ideal Kagome Heisenberg antiferromagnet, because there is no magnetic phase transition down to approximately 50 mK. We investigated its local magnetic and lattice environments with NMR techniques. We demonstrate that the intrinsic local spin susceptibility decreases toward T=0, but that slow freezing of the lattice near approximately 50 K, presumably associated with OH bonds, contributes to a large increase of local spin susceptibility and its distribution. Spin dynamics near T=0 obey a power-law behavior in high magnetic fields.     

(17) O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)(6)Cl(2)

We report, through 17O NMR, an unambiguous local determination of the intrinsic kagome lattice spin susceptibility as well as that created around nonmagnetic defects arising from natural Zn/Cu exchange in the S=1/2 (Cu2+) herbertsmithite ZnCu3(OH)6Cl2 compound. The issue of a singlet-triplet gap is addressed. The magnetic response around a defect is found to markedly differ from that observed in nonfrustrated antiferromagnets. Finally, we discuss our relaxation measurements in the light of Cu and Cl NMR data and suggest a flat q dependence of the excitations.     

Modified kagome physics in the natural spin-1/2 kagome lattice systems: kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2

The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are spin 1/2 systems with an ideal kagome geometry. Based on electronic structure calculations, we develop a realistic model which includes couplings across the kagome hexagons beyond the original kagome model that are intrinsic in real kagome materials. Exact diagonalization studies for the derived model reveal a strong impact of these couplings on the magnetic ground state. Our predictions could be compared to and supplied with neutron scattering, thermodynamic data, and NMR data.     

External magnetic field effects on a distorted kagome antiferromagnet

We report bulk magnetization, and elastic and inelastic neutron scattering measurements under an external magnetic field H on the weakly coupled distorted kagome system, Cu2(OD)3Cl. Our results show that the ordered state below 6.7 K is a canted antiferromagnet and consists of large antiferromagnetic ac components and smaller ferromagnetic b components. By first-principles calculations and linear spin wave analysis, we present a simple spin Hamiltonian with nonuniform nearest neighbor exchange interactions resulting in a system of coupled spin trimers with a single-ion anisotropy that can qualitatively reproduce the spin dynamics of Cu2(OD)3Cl.     

Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2

We have performed thermodynamic and neutron scattering measurements on the S=1/2 kagomé lattice antiferromagnet ZnCu3(OH)6Cl2. The susceptibility indicates a Curie-Weiss temperature of theta CW approximately = -300 K; however, no magnetic order is observed down to 50 mK. Inelastic neutron scattering reveals a spectrum of low energy spin excitations with no observable gap down to 0.1 meV. The specific heat at low-T follows a power law temperature dependence. These results suggest that an unusual spin liquid state with essentially gapless excitations is realized in this kagomé lattice system.     

Magnetic ground state of an experimental S=1/2 kagome antiferromagnet

We present a detailed analysis of the heat capacity of a near-perfect S=1/2 kagome antiferromagnet, zinc paratacamite Zn(x)Cu(4-x)(OH)(6)Cl(2), as a function of stoichiometry x-->1 and for fields of up to 9 T. We obtain the heat capacity intrinsic to the kagome layers by accounting for the weak Cu2+/Zn2+ exchange between the Cu and the Zn sites, which was measured independently for x=1 using neutron diffraction. The evolution of the heat capacity for x=0.8...1 is then related to the hysteresis in the magnetic susceptibility. We conclude that for x>0.8 zinc paratacamite is a spin liquid without a spin gap, in which unpaired spins give rise to a macroscopically degenerate ground state manifold with increasingly glassy dynamics as x is lowered.     

Nested cluster algorithm for frustrated quantum antiferromagnets

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.     

Detection of XY behavior in weakly anisotropic quantum antiferromagnets on the square lattice

We consider the Heisenberg antiferromagnet on the square lattice with S=1/2 and very weak easy-plane exchange anisotropy; by means of the quantum Monte Carlo method, based on the continuous-time loop algorithm, we find that the thermodynamics of the model is highly sensitive to the presence of tiny anisotropies and is characterized by a crossover between isotropic and planar behavior. We discuss the mechanism underlying the crossover phenomenon and show that it occurs at a temperature which is characteristic of the model. The expected Berezinskii-Kosterlitz-Thouless transition is observed below the crossover: a finite range of temperatures consequently opens for experimental detection of noncritical 2D XY behavior. Direct comparison is made with uniform susceptibility data relative to the S=1/2 layered antiferromagnet Sr2CuO2Cl2.     

Magnetic susceptibility and specific heat of the spin-${\frac{1}{2}}$ Heisenberg model on the kagome lattice and experimental data on ZnCu3(OH)6Cl2

We compute the magnetic susceptibility and specific heat of the spin- Heisenberg model on the kagome lattice with high-temperature expansions and exact diagonalizations. We compare the results with the experimental data on ZnCu₃(OH)₆Cl₂ obtained by Helton et al. [Phys. Rev. Lett. 98, 107204 (2007)]. Down to k_BT/J≃0.2, our calculations reproduce accurately the experimental susceptibility, with an exchange interaction J≃190 K and a contribution of 3.7% of weakly interacting impurity spins. The comparison between our calculations of the specific heat and the experiments indicate that the low-temperature entropy (below ~20 K) is smaller in ZnCu₃(OH)₆Cl₂ than in the kagome Heisenberg model, a likely signature of other interactions in the system.     

Theoretical investigation of the oxidation pathways of the Cl-initiated reaction of 2-methyl-3-buten-2-ol

The mechanism and products of the reaction of 2-methyl-3-buten-2-ol (MBO232) with Cl atoms in the presence of O₂ have been elucidated by performing high-level quantum chemistry calculations. The geometries of the reactants, intermediates, transition states, and products are optimized at the MP2(full)/6-311G(d,?p) level, and their single-point energies are refined at the CCSD(T)/6-311?+?G(d,?p) level. The potential energy surface profiles have been constructed at the CCSD(T)/6-311?+?G(d,?p)//MP2(full)/6-311G(d,?p)?+?0.95?×?ZPE level of theory, and the possible channels involved in the reaction are also discussed. The calculations indicate that the reaction predominantly proceeds via the addition of Cl atoms to the double bond rather than the direct abstraction of the H atoms in MBO232. The nascent adducts (CH₃)₂C(OH)CHCH₂Cl (IM1) and (CH₃)₂C(OH)CHClCH₂ (IM2) do not undergo subsequent isomerization and dissociation reactions, but rather react with O₂. The theoretical results show that the major products are CH₂ClCHO and CH₃C(O)CH₃ for the reaction of MBO232?+?Cl in the presence of O₂, which is in good agreement with the experimental finding.     

Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice

We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu(3)(OH)(6)Cl(2).     

Quantum magnetism in the paratacamite family: towards an ideal kagomé lattice

We report muon spin rotation measurements on the S=1/2 (Cu2+) paratacamite ZnxCu4-x(OH)6Cl2 family. Despite a Weiss temperature of approximately -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.     

High-energy magnon dispersion and multimagnon continuum in the two-dimensional Heisenberg antiferromagnet

We use quantum Monte Carlo simulations and numerical analytic continuation to study high-energy spin excitations in the two-dimensional S = 1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse (x) and longitudinal (z) dynamic spin structure factors Sx,z(q,omega) at q = (pi,0) and (pi/2, pi/2). Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at (pi,0) is 10% lower than at (pi/2, pi/2). We also discuss the transverse and longitudinal multimagnon continua and their relevance to neutron scattering experiments.     

Theory of Néel and valence-bond solid phases on the kagome lattice of Zn paratacamite

Recently, neutron scattering data on powder samples of Zn paratacamite, ZnxCu4-x(OH)6Cl2, with small Zn concentration has been interpreted as evidence for valence-bond solid and Néel ordering [S.-H. Lee, Nat. Mater. 6, 853 (2007)10.1038/nmat1986]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence-bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and x-ray scattering experiments that can test our predictions.     

Spin waves in the frustrated kagomé lattice antiferromagnet KFe3(OH)6(SO4)2

The spin wave excitations of the S=5/2 kagomé 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 kagomé 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.