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

Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

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We report the observation of a magnetic-field-induced transition between magnetically disordered and ordered phases in slightly under-doped La 2−x Sr x CuO 4 with x = 0.144. Static incommensurate spin-density-wave order is induced above a critical field of about 3 T, as measured by elastic neutron scattering. Our results allow us to constrain the location of a quantum critical point on the phase diagram.

We report magnetic susceptibility, specific heat, and neutron scattering measurements as a function of applied magnetic field and temperature to characterize the S = 1/2 quasi-two-dimensional frustrated magnet piperazinium hexachlorodicuprate (PHCC). The experiments reveal four distinct phases. At low temperatures and fields the material forms a quantum paramagnet with a 1 meV singlet triplet gap and a magnon bandwidth of 1.7 meV. The singlet state involves multiple spin pairs some of which have negative ground state bond energies. Increasing the field at low temperatures induces three dimensional long range antiferromagnetic order at 7.5 Tesla through a continuous phase transition that can be described as magnon Bose-Einstein condensation. The phase transition to a fully polarized ferromagnetic state occurs at 37 Tesla. The ordered antiferromagnetic phase is surrounded by a renormalized classical regime. The crossover to this phase from the quantum paramagnet is marked by a distinct anomaly in the magnetic susceptibility which coincides with closure of the finite temperature singlet-triplet pseudo gap. The phase boundary between the quantum paramagnet and the Bose-Einstein condensate features a finite temperature minimum at T = 0.2 K, which may be associated with coupling to nuclear spin or lattice degrees of freedom close to quantum criticality.