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.     

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.     

(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.     

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.     

X-ray absorption investigation of the site occupancies of the copper element in nominal Cu_3Zn(OH)_6FBr

With Zn substitution to the three-dimensional antiferromagnetically ordered barlowite Cu_4(OH)_6 FBr,Cu_3 Zn(OH)_6 FBr shows no magnetic phase transition down to 50 mK,and the system is suggested to be a two-dimensional kagome quantum spin liquid [Chin.Phys.Lett.34 077502(2017)].A key issue to identify such phase diagram is the exact chemical formula of the substituted compound.With Cu L-edge x-ray absorption spectrum(XAS) combined with the MultiX XAS calculations,we evaluate the Cu concentration in a nominal Cu_3 Zn(OH)_6 FBr sample.Our results show that although the Cu concentration is 2.80,close to the expected value,there is 34% residual Cu occupation in intersite layers between kagome layers.Thus the Zn substitution of the intersite layers is not complete,and likely it intrudes the kagome layers.     

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.     

Gapped Spin-1/2 Spinon Excitations in a New Kagome Quantum Spin Liquid Compound Cu_3Zn(OH)_6FBr

We report a new kagome quantum spin liquid candidate Cu_3 Zn(OH)_6 FBr, which does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature(~200 K). A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from~(19)F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fractionalization in the fractional quantum Hall state.     

Kapellasite: a kagome quantum spin liquid with competing interactions

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu_{3}Zn(OH)_{6}Cl_{2}, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20?mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.     

Spin-liquid state in the S=1/2 hyperkagome antiferromagnet Na4Ir3O8

A spinel related oxide, Na(4)Ir(3)O(8), was found to have a three dimensional network of corner shared Ir(4+) (t(2g)(5)) triangles. This gives rise to an antiferromagnetically coupled S = 1/2 spin system formed on a geometrically frustrated hyperkagome lattice. Magnetization M and magnetic specific heat C(m) data showed the absence of long range magnetic ordering at least down to 2 K. The large C(m) at low temperatures is independent of applied magnetic field up to 12 T, in striking parallel to the behavior seen in triangular and kagome antiferromagnets reported to have a spin-liquid ground state. These results strongly suggest that the ground state of Na(4)Ir(3)O(8) is a three dimensional manifestation of a spin liquid.     

La2-xSrxCu1-yZnyO4: Tc and ns/m* correlations seen with muon spin rotation

We report the muon spin rotation experiments on Zn substituted La_1-x Sr_x CuO₄, for four zinc concentrations y=0.0,0.0025,0.005,0.01, at strontium concentrations x=0.15,0.20. We find that T_ c in the optimally doped (x=0.15) and overdoped (x=0.20) 2:1:4 decreases linearly with increasing zinc concentration. Plotted against the planar zinc concentration, the T_c’s of both series seem to fall on the same line. The superconducting carrier density/effective mass ratio, n_ s/m^*, at first decreases linearly, rising above this line for higher zinc concentrations. This behavior may result from the localization of carriers in an area \xi_ab around each zinc atom. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evidence for Successive Doping-Induced Dimensionality Transitions in the Spin-Chain Compound Ca2+xY2-xCu5O10

We report the results of heat capacity, SQUID magnetometry, and x-ray diffraction studies of polycrystalline and magnetically aligned Ca 2+xY 2-xCu 5O (10), a quasi-1D compound. As holes are doped into the chains from x = 0-2, the data indicate a change from 3D long-range order to 1D chain behavior to cluster behavior. We quantitatively model the magnetic and thermal properties of heavily doped Ca 4Cu 5O (10) in terms of spin clusters. Anisotropic susceptibility data indicate a doping-independent easy axis of magnetization perpendicular to the planes containing the chains; also, a spin-flop transition is observed, providing a measure of the anisotropy field.     

From Claringbullite to a New Spin Liquid Candidate Cu_3Zn(OH)_6FCl

The search for quantum spin liquid(QSL) materials has attracted significant attention in the field of condensed matter physics in recent years, however so far only a handful of them are considered as candidates hosting QSL ground state. Owning to their geometrically frustrated structures, Kagome materials are ideal systems to realize QSL. We synthesize the kagome structured material claringbullite(Cu_4(OH)_6FCl) and then replace inter-layer Cu with Zn to form Cu_3Zn(OH)_6FCl. Comprehensive measurements reveal that doping Zn~(2+) ions transforms magnetically ordered Cu_4(OH)_6FCl into a non-magnetic QSL candidate Cu_3Zn(OH)_6FCl. Therefore,the successful syntheses of Cu_4(OH)_6FCl and Cu_3Zn(OH)_6FCl provide not only a new platform for the study of QSL but also a novel pathway of investigating the transition between QSL and magnetically ordered systems.     

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.     

Suppression of antiferromagnetic spin fluctuation in Zn-substituted YBa2Cu3O7

We have prepared Zn-substituted YBa₂Cu_3−xZn_xO₇ (YBCO, x=0.0–0.09) and performed ^63,65Cu nuclear quadrupole resonance (NQR) measurements for the plane site at 300 and 100 K as a function of Zn concentration. The substitutional effects are observed in resonant frequencies and linewidths of spectra, and relaxation times as well as in the superconducting transition temperature. The spin–lattice relaxation rate 1/T₁ is reduced for the higher Zn concentration and the reduction is more significant at 100 K. The ratio of ^63,65Cu spin–lattice relaxation rates suggests that a magnetic contribution due to the antiferromagnetic spin fluctuation becomes weak as the Zn concentration increases. These effects confirm that the antiferromagnetic spin fluctuation of Cu 3d spins is suppressed by the Zn substitution due to the absence of local moment at the zinc site.     

Origin of the enhanced copper spin echo decay rate in the pseudogap regime of the multilayer high-T(c) cuprates

We report measurements of the anisotropy of the spin echo decay for the inner layer Cu site of the triple layer cuprate Hg(0.8)Re(0.2)Ba(2)Ca(2)Cu(3)O(8) (T(c)=126 K). The angular dependence of the second moment (T(-2)(2M) identical with ) deduced from the decay curves indicates that T(-2)(2M) for H0 parallel c is enhanced in the pseudogap regime below T(pg) approximately 170 K, as seen in bilayer systems. Comparison of T(-2)(2M) between H0 parallel c and H0 perpendicular c indicates that this enhancement is caused by electron spin correlations between the inner and the outer CuO2 layers. The results provide the answer to the long-standing controversy regarding the opposite T dependences of (T1T)(-1) and T(-2)(2G) (T(2G): Gaussian component) in the pseudogap regime of multilayer systems.     

Specific-heat measurements of the gap structure of the organic superconductors kappa-(ET)2Cu[N(CN)2]Br and kappa-(ET)2Cu(NCS)2

We present high resolution heat capacity measurements of the organic superconductors kappa-(ET)(2)Cu[N(CN)(2)]Br and kappa-(ET)(2)Cu(NCS)(2) in fields up to 14 T. We use the high field data to determine the normal state specific heat and hence extract the behavior of the electronic specific heat C(el) in the superconducting state in zero and finite fields. We find that in both materials for T/T(c) less or similar 0.3, C(el)(H=0) approximately T2 indicating d-wave superconductivity. The data are well described by a strong coupling d-wave model from our base temperature (T/T(c) approximately 0.1) right up to T(c). Our data help to resolve the controversy regarding the order parameter symmetry in these materials.     

Anomalous peak in the superconducting condensate density of cuprate high- T(c) superconductors at a unique doping state

The doping dependence of the ratio of the superconducting condensate density to the effective mass, n(o)(s)/m(*)(ab), was studied in detail by muon-spin rotation for Y(0.8)Ca(0.2)Ba(2)(Cu(1-z)Zn(z))(3)O(7-delta) and Tl(0.5-y)Pb(0.5+y)Sr(2)Ca(1-x)Y(x)Cu(2)O(7). Our data show that n(o)(s)/m(*)(ab) exhibits a peak at a unique doping state in the overdoped regime. Its position coincides with the critical doping state, where the normal state pseudogap was reported to appear and to deplete the electronic density of states. This finding implies that the pseudogap primarily arises from a change in the electronic ground state rather than from thermal fluctuations.     

Q2 evolution of the neutron spin structure moments using a 3He target

We have measured the spin structure functions g(1) and g(2) of 3He in a double-spin experiment by inclusively scattering polarized electrons at energies ranging from 0.862 to 5.058 GeV off a polarized 3He target at a 15.5 degrees scattering angle. Excitation energies covered the resonance and the onset of the deep inelastic regions. We have determined for the first time the Q2 evolution of Gamma(1)(Q2)= integral (1)(0)g(1)(x,Q2)dx, Gamma(2)(Q2)= integral (1)(0)g(2)(x,Q2)dx, and d(2)(Q2)= integral (1)(0)x(2)[2g(1)(x,Q2)+3g(2)(x,Q2)]dx for the neutron in the range 0.1< or =Q2< or =0.9 GeV2 with good precision. Gamma(1)(Q2) displays a smooth variation from high to low Q2. The Burkhardt-Cottingham sum rule holds within uncertainties and d(2) is nonzero over the measured range.     

Spin gap in the zigzag spin-1/2 chain cuprate Sr(0.9)Ca(0.1)CuO(2)

We report a comparative study of (63)Cu nuclear magnetic resonance spin lattice relaxation rates T(1)(-1) on undoped SrCuO(2) and Ca-doped Sr(0.9)Ca(0.1)CuO(2) spin chain compounds. A temperature independent T(1)(-1) is observed for SrCuO(2) as expected for an S=1/2 Heisenberg chain. Surprisingly, we observe an exponential decrease of T(1)(-1) for T<90 K in the Ca-doped sample evidencing the opening of a spin gap. The data analysis within the J(1)-J(2) Heisenberg model employing density-matrix renormalization group calculations suggests an impurity driven small alternation of the J(2)-exchange coupling as a possible cause of the spin gap.     

Quantum impurities and the neutron resonance peak in YBa2Cu3O7: Ni versus Zn

The influence of magnetic (S=1) and nonmagnetic (S=0) impurities on the spin dynamics of an optimally doped high temperature superconductor is compared in YBa2(Cu0.97Ni0.03)3O7 (Tc=80 K) and YBa2(Cu0.99Zn0.01)3O7 (Tc=78 K). In the Ni-substituted system, the magnetic resonance peak (which is observed at Er approximately 40 meV in the pure system) shifts to lower energy with a preserved Er/Tc ratio while the shift is much smaller upon Zn substitution. By contrast Zn, but not Ni, restores significant spin fluctuations around 40 meV in the normal state. These observations are discussed in the light of models proposed for the magnetic resonance peak.