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.

Sources of magnetic fields-magnetic monopoles-have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes-classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

No abstract

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two fieldinduced quantum critical points and over a broad range of temperature. Based on an ideal spinladder Hamiltonian, comprehensive numerical modelling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the complete phase diagram. Quantum spin systems display a remarkable diversity of fascinating physical behavior. This is especially true for systems such as spin ladders, which have a gapped or a gapless ground state, respectively, for an even or an odd number of ladder legs [1]. For two-leg ladders, and in general for any even leg number, quantum phase transitions (QPTs) between gapped and gapless phases can be driven by an external magnetic field. While these QPTs are generic in quantum magnets [2], the nature of the gapless phase depends crucially on the dimensionality of the spin system. In two and higher dimensions, a quantum critical point (QCP) separates the low-field, quantum disordered (QD) phase, with gapped triplet excitations, from a gapless phase with long-range antiferromagnetic (AF) order, which can be well described as a Bose-Einstein Condensate (BEC) of magnons [2,3,4].By contrast, for one-dimensional (1D) systems such as ladders, both long-ranged magnetic order and BEC are precluded due to phase fluctuations. In addition, spin excitations are best viewed as interacting fermions, whereas a bosonic representation pertains in higher dimensions. The physics of the gapless phase in 1D is thus quite different. It is a (spin) Luttinger liquid (LL) [5], and is a key component of the rich phase diagram presented in Fig. 1 [3 , 6, 7, 8, 9]. In the LL, the spectrum is gapless with algebraically decaying spin correlations. Because there is no finite order parameter, the LL regime is reached from the high-temperature, classical regime through a crossover rather than a phase transition. Nevertheless, clear manifestations of LL behavior are expected not only in the correlation functions but also in thermodynamic quantities such as the magnetization and specific heat. and Bs (spin system fully polarized). The contour plot shows the magnetic specific heat as Cm(T, B)/T . Local maxima from the reduction of the triplet gap by the Zeeman effect are indicated by crosses. Circles denote the LL crossover based on measurements of the magnetocaloric effect [ Fig. 4], black lines are fits to extract the critical fields, and the dashed blue line indicates the onset of long-ranged order below 100 mK [21,22]. Inset: lattice structure of (Hpip)2CuBr4 in projection along the b-axis, with Cu atoms blue and Br white.However, materials in which to explore such effects are rather rare. Investigations of the spin excitations and arXiv:0808.2715v2 [cond-mat.str-el]

We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua.

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.

Field-controlled magnetic order in the quantum spin-ladder system (Hpip)2CuBr4

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO4(OH)2, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k=(0,0.186,1/2) was found below T(N)=2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638μ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833μ(B)) points along the b axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.