The Herbertsmithite Hamiltonian: μSR measurements on single crystals

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 ZnCu(3)(OD)(6)Cl(2) (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.

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.

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.