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...

One view of the cuprate high-transition temperature (high-T c ) superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasiparticles, which stand in one-to-one correspondence with the electrons in ordinary metals -although the theory has to be pushed to its limit [1]. An alternative view is that the electrons organize into collective textures (e.g. charge and spin stripes) which cannot be mapped onto the electrons in ordinary metals. The phase diagram, a complex function of various parameters (temperature, doping and magnetic field), should then be approached using quantum field theories of objects such as textures and strings, rather than point-like electrons [2,3,4,5,6]. In an external magnetic field, magnetic flux penetrates type-II superconductors via vortices, each carrying one flux quantum [7]. The vortices form lattices of resistive material embedded in the non-resistive superconductor and can reveal the nature of the ground state -e.g. a conventional metal or an ordered, striped phase -which would have appeared had superconductivity not intervened. Knowledge of this ground state clearly provides the most appropriate starting point for a pairing theory. Here we report that for one high-T c superconductor, the applied field which imposes the vortex lattice, also induces antiferromagnetic order. Ordinary quasiparticle pictures cannot account for the nearly fieldindependent antiferromagnetic transition temperature revealed by our measurements.La 2-x Sr x CuO 4 , is the simplest high-T c superconductor. The undoped compound is an insulating antiferromagnet, where the spin moments on adjacent Cu 2+ ions are antiparallel [8]. Introduction of charge carriers via Sr doping reduces the ordered moment until it vanishes at x<0.13. In addition, for x>0.05 the commensurate antiferromagnetism is replaced by incommensurate order [2,3,9,10], where the repeat distance for the pattern of ordered moments is substantially larger than the spacing between neighbouring copper ions. La 2-x Sr x CuO 4 becomes a 2 superconductor for Sr dopings of 0.06

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