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.

TbMnO3 is an orthorhombic insulator where incommensurate spin order for temperature T(N)<41 K is accompanied by ferroelectric order for T<28 K. To understand this, we establish the magnetic structure above and below the ferroelectric transition using neutron diffraction. In the paraelectric phase, the spin structure is incommensurate and longitudinally modulated. In the ferroelectric phase, however, there is a transverse incommensurate spiral. We show that the spiral breaks spatial inversion symmetry and can account for magnetoelectricity in TbMnO3.

As liquids crystallize into solids on cooling, spins in magnets generally form periodic order. However, three decades ago, it was theoretically proposed that spins on a triangular lattice form a liquidlike disordered state at low temperatures. Whether or not a spin liquid is stabilized by geometrical frustration has remained an active point of inquiry ever since. Our thermodynamic and neutron measurements on NiGa2S4, a rare example of a two-dimensional triangular lattice antiferromagnet, demonstrate that geometrical frustration stabilizes a low-temperature spin-disordered state with coherence beyond the two-spin correlation length. Spin liquid formation may be an origin of such behavior.

We show that long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition in Ni3V2O8. The temperature and magnetic-field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry using Landau theory for continuous phase transitions, which shows that the spin structure alone can break spatial inversion symmetry leading to ferroelectric order. This phenomenological theory explains our experimental observation that the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.

Spin liquids are quantum phases of matter that exhibit a variety of novel features associated with their topological character. These include various forms of fractionalization -elementary excitations that behave as fractions of an electron. While there is not yet entirely convincing experimental evidence that any particular material has a spin liquid ground state, in the past few years, increasing evidence has accumulated for a number of materials suggesting that they have characteristics strongly reminiscent of those expected for a quantum spin liquid. and Shivaji Sondhi for their comments.

Frustrated systems are ubiquitous, and they are interesting because their behaviour is difficult to predict; frustration can lead to macroscopic degeneracies and qualitatively new states of matter. Magnetic systems offer good examples in the form of spin lattices, where all interactions between spins cannot be simultaneously satisfied. Here we report how unusual composite spin degrees of freedom can emerge from frustrated magnetic interactions in the cubic spinel ZnCr(2)O(4). Upon cooling, groups of six spins self-organize into weakly interacting antiferromagnetic loops, whose directors -- the unique direction along which the spins are aligned, parallel or antiparallel -- govern all low-temperature dynamics. The experimental evidence comes from a measurement of the magnetic form factor by inelastic neutron scattering; the data show that neutrons scatter from hexagonal spin clusters rather than individual spins. The hexagon directors are, to a first approximation, decoupled from each other, and hence their reorientations embody the long-sought local zero energy modes for the pyrochlore lattice.

Inelastic magnetic neutron scattering reveals a localized spin resonance at 4.5 meV in the ordered phase of the geometrically frustrated cubic antiferromagnet ZnCr2O4. The resonance develops abruptly from quantum critical fluctuations upon cooling through a first order transition to a co-planar antiferromagnet at T(c) = 12. 5(5) K. We argue that this transition is a three dimensional analog of the spin-Peierls transition.

Neutron scattering is used to probe antiferromagnetic spin fluctuations in the d-wave heavy fermion superconductor CeCoIn5 (T_(c)=2.3 K). Superconductivity develops from a state with slow (variant Planck's over 2piGamma=0.3+/-0.15 meV) commensurate [Q_(0)=(1/2,1/2,1/2)] antiferromagnetic spin fluctuations and nearly isotropic spin correlations. The characteristic wave vector in CeCoIn5 is the same as CeIn3 but differs from the incommensurate wave vector measured in antiferromagnetically ordered CeRhIn5. A sharp spin resonance (variant Planck's over 2piGamma<0.07 meV) at variant Planck's over 2piomega=0.60+/-0.03 meV develops in the superconducting state removing spectral weight from low-energy transfers. The presence of a resonance peak is indicative of strong coupling between f-electron magnetism and superconductivity and consistent with a d-wave gap order parameter satisfying Delta(q+Q0)=-Delta(q).