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.

The crystalline and magnetic structures of the YCo 3 -H͑D͒ system have been investigated by means of x-ray and neutron diffraction with the objective of understanding the complex magnetic changes that are observed in this system as hydrogen is added. Synchrotron x-ray diffraction ͑XRD͒ patterns were first refined to yield the lattice parameters and coordination of Y and Co atoms in the metal and two ␤-hydride phases while XRD was used for the ␥ phase. In situ neutron powder diffraction measurements of YCo 3 D x were then made in all four phases to determine the deuterium site occupancies and magnetic structures. The site occupancies were also rationalized using the Westlake geometric model. The highest hydrogen concentration measured was YCo 3 H 4.6 . Using the Westlake model, we conclude that the saturated hydrogen content would be YCo 3 H 5 . Our results reported here and in Part I ͓Phys. Rev. B 76, 184443 ͑2007͔͒ have enabled us to rationalize the changes in the magnetic structures in terms of changes in the cobalt-cobalt distance caused by the addition of hydrogen. In particular, in the antiferromagnetic ␥ phase, we observe Co atomic displacements that enable the structure to adopt a particular antiferromagnetic structure in a manner that is reminiscent of a Peierls distortion as observed in transitions from the conducting to nonconducting hydrides on addition of hydrogen in YH 3 .

It has long been realized that cations play a critical role in the readsorption of water into the interlayer region in clay minerals. To explore possible differences in the water dynamics related to the presence of cations in clays, and to examine the dynamics of its surface water, which plays a prominent role in diffusion of water in clay barriers a comparative study was carried out to highlight differences between water dynamics in montmorillonite and halloysite. Whereas montmorillonite has interlayer cations that interact with interlayer water, and which can rehydrate after dehydration at temperature, halloysite has no interlayer cations. Water is found in both interlayers and on the surface of these clay particles. In this study we show that by combining incoherent inelastic neutron scattering (quasi-elastic and elastic fixed window) and neutron spin echo, it was possible to discriminate the dynamics of surface water (by collapsing the interlayer region by heating and rehydrating the surface layer) from interlayer water. The analysis of the elastic fixed window scans in the temperature range 5−300 K revealed an extension of water dynamics in montmorillonite to lower temperatures than in halloysite. These differences suggested mechanisms that cations (Na+ in this case) in the interlayer regions facilitate water mobility allowing interlayer water to be readmitted to montmorillonite. Finally it was shown that the occurrence of magnetic fluctuations, caused by the presence of paramagnetic Fe3+ ions in the crystalline clay lattice, gave rise to a quasi-elastic contribution that disrupted the evaluation of water diffusion computed from such measurements. Therefore previous estimates of water diffusion coefficients might have been overestimated in recent literature.