Classical Spin Liquid State in the S=5/2 Heisenberg Kagome Antiferromagnet Li_{9}Fe_{3}(P_{2}O_{7})_{3}(PO_{4})_{2}.

We investigate the low temperature magnetic properties of a S=5/2 Heisenberg kagome 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_{N}=1.3 K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below T^{*}∼5 K. A moderate ^{31}P NMR line broadening reveals the development of anisotropic short-range correlations concomitantly with a gapless spin-lattice relaxation time T_{1}∼k_{B}T/ℏS, which may point to the presence of a semiclassical nematic spin-liquid state predicted for the Heisenberg kagome antiferromagnetic model or to the persistence of the zero-energy modes of the kagome lattice under large magnetic fields.

Nature of the Spin Liquid Ground State in a Breathing Kagome Compound Studied by NMR and Series Expansion.

In the vanadium oxyfluoride compound (NH_{4})_{2}[C_{7}H_{14}N][V_{7}O_{6}F_{18}] (DQVOF), the V^{4+} (3d^{1}, S=1/2) ions realize a unique, highly frustrated breathing kagome lattice composed of alternately sized, corner-sharing equilateral triangles. Here we present an ^{17}O NMR study of DQVOF, which isolates the local susceptibility of the breathing kagome network. By a fit to series expansion, we extract the ratio of the interactions within the breathing kagome plane, J_{∇}/J_{Δ}=0.55(4), and the mean antiferromagnetic interaction J[over ¯]=60(7) K. Spin lattice (T_{1}) measurements reveal an essentially gapless excitation spectrum with a maximum gap Δ/J[over ¯]=0.007(7). Our study provides new impetus for further theoretical investigations in order to establish whether the gapless spin liquid behavior displayed by DQVOF is intrinsic to its breathing kagome lattice or whether it is due to perturbations to this model, such as a residual coupling of the V^{4+} ions in the breathing kagome planes to the interlayer V^{3+} (S=1) spins.

Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite.

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 threefold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establishment of the spin-liquid ground state.

Field-Induced Instability of a Gapless Spin Liquid with a Spinon Fermi Surface.

The ground state of the quantum kagome antiferromagnet Zn-brochantite, ZnCu_{3}(OH)_{6}SO_{4}, which is one of only a few known spin-liquid (SL) realizations in two or three dimensions, has been described as a gapless SL with a spinon Fermi surface. Employing nuclear magnetic resonance in a broad magnetic-field range down to millikelvin temperatures, we show that in applied magnetic fields this enigmatic state is intrinsically unstable against a SL with a full or a partial gap. A similar instability of the gapless Fermi-surface SL was previously encountered in an organic triangular-lattice antiferromagnet, suggesting a common destabilization mechanism that most likely arises from spinon pairing. A salient property of this instability is that an infinitesimal field suffices to induce it, as predicted theoretically for some other types of gapless SLs.

Spin Liquid State in the 3D Frustrated Antiferromagnet PbCuTe_{2}O_{6}: NMR and Muon Spin Relaxation Studies.

PbCuTe_{2}O_{6} is a rare example of a spin liquid candidate featuring a three-dimensional magnetic lattice. Strong geometric frustration arises from the dominant antiferromagnetic interaction that generates a hyperkagome network of Cu^{2+} ions although additional interactions enhance the magnetic lattice connectivity. Through a combination of magnetization measurements and local probe investigations by NMR and muon spin relaxation down to 20 mK, we provide robust evidence for the absence of magnetic freezing in the ground state. The local spin susceptibility probed by the NMR shift hardly deviates from the macroscopic one down to 1 K pointing to a homogeneous magnetic system with a low defect concentration. The saturation of the NMR shift and the sublinear power law temperature (T) evolution of the 1/T_{1} NMR relaxation rate at low T point to a nonsinglet ground state favoring a gapless fermionic description of the magnetic excitations. Below 1 K a pronounced slowing down of the spin dynamics is witnessed, which may signal a reconstruction of spinon Fermi surface. Nonetheless, the compound remains in a fluctuating spin liquid state down to the lowest temperature of the present investigation.

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba_{3}ZnIr_{2}O_{9}.

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba_{3}ZnIr_{2}O_{9} is a realization of a novel spin-orbital liquid state. Our results reveal that Ba_{3}ZnIr_{2}O_{9} with Ir^{5+} (5d^{4}) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J=0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir_{2}O_{9} dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.

Frozen State and Spin Liquid Physics in Na_{4}Ir_{3}O_{8}: An NMR Study.

Na_{4}Ir_{3}O_{8} is a unique case of a hyperkagome 3D corner sharing triangular lattice that can be decorated with quantum spins. It has spurred a lot of theoretical interest as a spin liquid candidate. We present a comprehensive set of NMR data taken on both the ^{23}Na and ^{17}O sites. We show that disordered magnetic freezing of all Ir sites sets in below T_{f}~7 K, well below J=300 K, with a drastic slowing down of fluctuations to a static state revealed by our T_{1} measurements. Above typically 2T_{f}, physical properties are relevant to the spin liquid state induced by this exotic geometry. While the shift data show that the susceptibility levels off below 80 K, 1/T_{1} has little variation from 300 K to 2T_{f}. We discuss the implication of our results in the context of published experimental and theoretical work.

Gapless spin liquid ground state in the S = 1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18].

The vanadium oxyfluoride [NH(4)](2)[C(7)H(14)N][V(7)O(6)F(18)] (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of S = 1/2 kagome planes of V(4+) d(1) ions with S = 1 V(3+) d(2) ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the S = 1 spins of the interplane V(3+) ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model for S = 1/2 kagome physics, and that it displays a gapless spin liquid ground state.

Singlet ground state of the quantum antiferromagnet Ba(3)CuSb(2)O(9).

We present local probe results on the honeycomb lattice antiferromagnet Ba(3)CuSb(2)O(9). Muon spin relaxation measurements in a zero field down to 20 mK show unequivocally that there is a total absence of spin freezing in the ground state. Sb NMR measurements allow us to track the intrinsic susceptibility of the lattice, which shows a maximum at around 55 K and drops to zero in the low-temperature limit. The spin-lattice relaxation rate shows two characteristic energy scales, including a field-dependent crossover to exponential low-temperature behavior, implying gapped magnetic excitations.

Kapellasite: a kagome quantum spin liquid with competing interactions.

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, 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.

Magnetic behavior of Ba3Cu3Sc4O12.

The chain-like system Ba(3)Cu(3)Sc(4)O(12) has potentially interesting magnetic properties due to the presence of Cu(2+) and a structure-suggested low dimensionality. We present magnetization M versus magnetic field H and temperature T, T- and H-dependent heat-capacity C(p), (45)Sc nuclear magnetic resonance (NMR), muon spin rotation (µSR), neutron diffraction measurements and electronic structure calculations for Ba(3)Cu(3)Sc(4)O(12). The onset of magnetic long-range antiferromagnetic (AF) order at T(N) ∼ 16 K is consistently evidenced from the whole gamut of our data. A significant sensitivity of T(N) to the applied magnetic field H (T(N) ∼ 0 K for H = 70 kOe) is also reported. Coupled with a ferromagnetic Curie-Weiss temperature (θ(CW) ∼ 65 K) in the susceptibility (from a 100 to 300 K fit), it is indicative of competing ferromagnetic and antiferromagnetic interactions. These indications are corroborated by our density functional theory based electronic structure calculations, where we find the presence of significant ferromagnetic couplings between some copper ions whereas AF couplings were present between some others. Our experimental data, backed by our theoretical calculations, rule out the one-dimensional magnetic behavior suggested by the structure and the observed long-range order is due to the presence of non-negligible magnetic interactions between adjacent as well as next-nearest chains.

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.

Ground state of the easy-axis rare-earth kagome langasite Pr3Ga5SiO14.

We report muon spin relaxation and {69,71}Ga nuclear quadrupolar resonance local-probe investigations of the kagome compound Pr3Ga5SiO14. Small quasistatic random internal fields develop below 40 K and persist down to our base temperature of 21 mK. They originate from hyperfine-enhanced 141Pr nuclear magnetism which requires a nonmagnetic Pr3+ crystal-field (CF) ground state. In addition, we observe a broad maximum of the relaxation rate at approximately 10 K which we attribute to the population of the first excited magnetic CF level. Our results yield a Van Vleck paramagnet picture, at variance with the formerly proposed spin-liquid ground state.

Impurity-induced magnetic order in low-dimensional spin-gapped materials.

We have studied the effect of nonmagnetic Zn impurities in the coupled spin ladder Bi(Cu_{1-x}Zn_{x})_{2}PO_{6} using ;{31}P NMR, muon spin resonance (microSR), and quantum Monte Carlo simulations. Our results show that the impurities induce in their vicinity antiferromagnetic polarizations, extending over a few unit cells. At low temperature, these extended moments freeze in a process which is found universal among various other spin-gapped compounds: isolated ladders, Haldane, or spin-Peierls chains. This allows us to propose a simple common framework to explain the generic low-temperature impurity-induced freezings observed in low-dimensional spin-gapped materials.

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.

Easy-axis kagome antiferromagnet: local-probe study of Nd3Ga5SiO14.

We report a local-probe investigation of the magnetically anisotropic kagome compound Nd3Ga5SiO14. Our zero-field muon spin relaxation (muSR) results provide direct evidence of a fluctuating collective paramagnetic state down to 60 mK, supported by a wipeout of the Ga nuclear magnetic resonance (NMR) signal below 25 K. At 60 mK a dynamics crossover to a much more static state is observed by muSR in magnetic fields above 0.5 T. Accordingly, the NMR signal is recovered at low T above a threshold field, revealing a rapid temperature and field variation of the magnetic fluctuations.

(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.

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.

Unconventional dynamics in triangular Heisenberg antiferromagnet NaCrO2.

We report magnetization, specific heat, muon spin rotation, and Na NMR measurements on the S=3/2 rhombohedrally stacked Heisenberg antiferromagnet NaCrO2. This compound appears to be a good candidate for the study of isotropic triangular Heisenberg antiferromagnets with very weak interlayer coupling. While specific heat and magnetization measurements indicate the onset of a transition in the range Tc approximately 40-50 K, both muon spin rotation and NMR reveal a fluctuating crossover regime extending well below Tc, with a peak of relaxation rate T1(-1) around T approximately 25 K. This novel finding is discussed within the context of excitations in the triangular Heisenberg antiferromagnets.

Direct evidence for a dynamical ground state in the highly frustrated Tb(2)Sn(2)O(7) pyrochlore.

mSR experiments have been performed on a powder sample of the "ordered spin ice" Tb(2)Sn(2)O(7) pyrochlore. At base temperature (T=35 mK), the muon relaxation is found to be of dynamical nature, which demonstrates that strong fluctuations persist below the ferromagnetic transition (T(C)=0.87 K). Hints of long-range ordering appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T(C). We propose that dynamics results from fluctuations of clusters of correlated spins with the ordered spin ice structure.