The magnetic excitations of the square-lattice spin-1/2 antiferromagnet and high-Tc parent La2CuO4 are determined using high-resolution inelastic neutron scattering. Sharp spin waves with absolute intensities in agreement with theory including quantum corrections are found throughout the Brillouin zone. The observed dispersion relation shows evidence for substantial interactions beyond the nearest-neighbor Heisenberg term, which can be understood in terms of a cyclic or ring exchange due to the strong hybridization path around the Cu4O4 square plaquettes.While there is consensus about the basic phenomenology -electron pairs with non-zero angular momentum, unconventional metallic behavior in the normal state, tendencies towards inhomogeneous charge and spin density order -of the high temperature copper oxide superconductors, there is no agreement about the microscopic mechanism. After over a decade of intense activity, there is not even consensus as to the simplest "effective Hamiltonian", which is a short-hand description of the motions and interactions of the valence electrons, needed to account for cuprate superconductivity. Because much speculation is centered on magnetic mechanisms for the superconductivity, it is important to identify the interactions among the spins derived from the unfilled Cu 2+ d-shells. The present experiments show that there are significant (on the scale of the pairing energies for highTc superconductivity) interactions coupling spins at distances beyond the 3.8Å separation of nearest-neighbor Cu 2+ ions. Cyclic or ring exchange due to a strong hybridization path around the Cu 4 O 4 squares (see Fig. 1A), from which the cuprates are built, provides a natural explanation for the measured dispersion relation. CuO 2 planes are thus the second example of an important Fermi system ( 3 He is the other [1]) where significant cyclic exchange terms have been deduced.Magnetic interactions are revealed through the wavevector dependence or dispersion of the magnetic excitations. In magnetically ordered materials, the dominant excitations are spin waves which are coherent (from site to site as well as in time) precessions of the spins about their mean values. The lower frame of Fig. 1B shows the dispersion relation calculated using conventional linear spin-wave theory in the classical large-S limit, where the only magnetic interaction is a strong nearest-neighbor superexchange coupling J [2]. We identify wavevectors by their coordinates (h, k) in the twodimensional (2D) reciprocal space of the square lattice.Spin waves emerge from the wavevector (1/2,1/2) characterizing the simple antiferromagnetic (AF) unit cell doubling in La 2 CuO 4 [3], and disperse to reach a maximum energy 2J that is a constant along the AF zone boundary marked by dashed squares in Fig. 1B. Longer-range interactions manifest themselves most simply at the zone boundary. The upper frame of Fig. 1B shows the dispersion calculated with modest interactions between next nearest-neighbors. Virtually the only visible effect of the a...

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zig-zag magnetic order. The onset of long-range magnetic order below TN = 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange. [6,7], in which edge-sharing IrO 6 octahedra form a honeycomb lattice [see Fig. 1b)], have been predicted to display novel magnetic states for composite spin-orbital moments coupled via frustrated exchanges. The exchange between neighboring Ir moments (called S i,j , S=1/2) is proposed to be [2]where J K > 0 is an Ising ferromagnetic (FM) term arising from superexchange via the Ir-O-Ir bond, and J 1 > 0 is the antiferromagnetic (AFM) Heisenberg exchange via direct Ir-Ir 5d overlap. Due to the strong spin-orbital admixture the Kitaev term J K couples only the components in the direction γ, normal to the plane of the Ir-O-Ir bond [8,9]. Because of the orthogonal geometry, different spin components along the cubic axes (γ = x, y, z) of the IrO 6 octahedron are coupled for the three bonds emerging out of each site in the honeycomb lattice. This leads to the strongly-frustrated Kitaev-Heisenberg (KH) model [2], which has conventional Néel order [see Fig. 3a)] for large J 1 , a stripy collinear AFM phase [see Fig. 3c)] for 0.4 α 0.8, where α = J K / (J K + 2J 1 ) (exact ground state at α = 1/2), and a quantum spin liquid with Majorana fermion excitations [10] at large J K (α 0.8). Measurements of the spin excitations are very important to determine the overall energy scale and the relevant magnetic interactions, however because Ir is a strong neutron absorber inelastic neutron scattering (INS) experiments are very challenging. Using an optimized setup we here report the first observation of dispersive spin wave excitations of Ir moments via INS. We show that the dispersion can be quantitatively accounted for by including substantial further-neighbor in-plane exchanges, which in turn stabilize zig-zag order. To inform future ab initio studies of microscopic models of the interactions we combine single-crystal xray diffraction with density functional calculations to determine precisely the oxygen positions, which are key in mediating the exchange and controlling the spin-orbital admixture via crystal field effects. We propose a revised crystal structure with much more symmetric IrO 6 octahedra, but with substantial departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange [9], and with frequent structural stacking faults. This differs from the currentlyadopted model, used by several band-structure calculations [14,15], with asymme...

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb 2 O 6 through its critical point using strong transverse magnetic fields. The spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean as predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviours.

There are two main theoretical descriptions of antiferromagnets. The first arises from atomic physics, which predicts that atoms with unpaired electrons develop magnetic moments. In a solid, the coupling between moments on nearby ions then yields antiferromagnetic order at low temperatures. The second description, based on the physics of electron fluids or 'Fermi liquids' states that Coulomb interactions can drive the fluid to adopt a more stable configuration by developing a spin density wave. It is at present unknown which view is appropriate at a 'quantum critical point' where the antiferromagnetic transition temperature vanishes. Here we report neutron scattering and bulk magnetometry measurements of the metal CeCu(6-x)Au(x), which allow us to discriminate between the two models. We find evidence for an atomically local contribution to the magnetic correlations which develops at the critical gold concentration (x(c) = 0.1), corresponding to a magnetic ordering temperature of zero. This contribution implies that a Fermi-liquid-destroying spin-localizing transition, unanticipated from the spin density wave description, coincides with the antiferromagnetic quantum critical point.