Tianheng Han

Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet.

The experimental realization of quantum spin liquids is a long-sought goal in physics, as they represent new states of matter. Quantum spin liquids cannot be described by the broken symmetries associated with conventional ground states. In fact, the interacting magnetic moments in these systems do not order, but are highly entangled with one another over long ranges. Spin liquids have a prominent role in theories describing high-transition-temperature superconductors, and the topological properties of these states may have applications in quantum information. A key feature of spin liquids is that they support exotic spin excitations carrying fractional quantum numbers. However, detailed measurements of these ‘fractionalized excitations’ have been lacking. Here we report neutron scattering measurements on single-crystal samples of the spin-1/2 kagome-lattice antiferromagnet ZnCu3(OD)6Cl2 (also called herbertsmithite), which provide striking evidence for this characteristic feature of spin liquids. At low temperatures, we find that the spin excitations form a continuum, in contrast to the conventional spin waves expected in ordered antiferromagnets. The observation of such a continuum is noteworthy because, so far, this signature of fractional spin excitations has been observed only in one-dimensional systems. The results also serve as a hallmark of the quantum spin-liquid state in herbertsmithite.

Spin-induced optical conductivity in the spin-liquid candidate herbertsmithite.

We report a direct measurement of the low-frequency optical conductivity of large-area single-crystal herbertsmithite, a promising spin-liquid candidate material, by means of terahertz time-domain spectroscopy. In the spectral range below 1.4 THz, we observe a contribution to the real part of the in-plane conductivity σ(ab)(ω) from the spin degree of freedom. This spin-induced conductivity exhibits a power-law dependence on frequency σ(ab)(ω) ~ ω(β) with β ≈ 1.4. Our observation is consistent with the theoretically predicted low-frequency conductivity arising from an emergent gauge field of a gapless U(1) Dirac spin liquid.

Refining the Spin Hamiltonian in the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu3(OH)6Cl2 Using Single Crystals

We report thermodynamic measurements of the S=1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where χ(z)/χ(p)>1 at high temperatures and χ(z)/χ(p)<1 at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal an anisotropy. By comparing with theoretical calculations, the presence of a small easy-axis exchange anisotropy can be deduced as the primary perturbation to the dominant Heisenberg nearest neighbor interaction. These results have great bearing on the interpretation of theoretical calculations based on the kagome Heisenberg antiferromagnet model to the experiments on ZnCu3(OH)6Cl2.

Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite

Low energy inelastic neutron scattering on single crystals of the kagome spin-liquid compound ZnCu3(OD)6Cl2 (herbertsmithite) reveals in this paper antiferromagnetic correlations between impurity spins for energy transfers h(with stroke)ω < 0.8 meV (~ J/20). The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wave vectors (100) and (00 3/2), which is consistent with antiferromagnetic correlations between pairs of nearest-neighbor Cu impurities on adjacent triangular (Zn) interlayers. The corresponding impurity lattice resembles a simple cubic lattice in the dilute limit below the percolation threshold. Such an impurity model can describe prior neutron, NMR, and specific heat data. The low energy neutron data are consistent with the presence of a small spin gap (Δ ~ 0.7 meV) in the kagome layers, similar to that recently observed by NMR. Finally, the ability to distinguish the scattering due to Cu impurities from that of the planar kagome Cu spins provides an important avenue for probing intrinsic spin-liquid physics.

Interplay of thermal and quantum spin fluctuations in the kagome lattice compound herbertsmithite

We present a Raman spectroscopic investigation of the Herbertsmithite ZnCu3(OH)6Cl2, the first realization of a Heisenberg s=1/2 antiferromagnet on a perfect kagome lattice. The magnetic excitation spectrum of this compound is dominated by two components, a high temperature quasi elastic signal and a low temperature, broad maximum. The latter has a linear low energy slope and extends to high energy. We have investigated the temperature dependence and symmetry properties of both signals. Our data agree with previous calculations and point to a spin liquid ground state.

Local spin susceptibility of the S=1/2 kagome lattice in ZnCu3(OD)6Cl2

We report single-crystal 2-D NMR investigation of the nearly ideal spin S=1/2 kagome lattice ZnCu3(OD)6Cl2. We successfully identify 2-D NMR signals originating from the nearest-neighbors of Cu2+ defects occupying Zn sites. From the 2-D Knight shift measurements, we demonstrate that weakly interacting Cu2+ spins at these defects cause the large Curie-Weiss enhancement toward T=0 commonly observed in the bulk susceptibility data. We estimate the intrinsic spin susceptibility of the kagome planes by subtracting defect contributions, and explore several scenarios.

Infrared phonons as a probe of spin-liquid states in herbertsmithite ZnCu3(OH)6Cl2

We report on temperature dependence of the infrared reflectivity spectra of a single crystalline herbertsmithite in two polarizations-parallel and perpendicular to the kagome plane of Cu atoms. We observe anomalous broadening of the low frequency phonons possibly caused by fluctuations in the exotic dynamical magnetic order of the spin liquid.

Synthesis and characterization of single crystals of the spin- 1 2 kagome-lattice antiferromagnets Zn x Cu 4 − x (OH) 6 Cl 2

The Zn-paratacamite family, Zn

Synthesis and Characterization of Single Crystal Samples of Spin-

_{x}

1/2

Cu