Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points.There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.In the classical world, matter in equilibrium freezes at absolute zero temperature. A macroscopic collection of microscopic particles adopt a stationary arrangement, forming an ordered pattern, to minimize the potential energy. Quantum mechanics, on the other hand, allows fluctuations even at zero temperature. The effective strength of such zero-point motion can be tuned through the variation of a non-thermal control parameter, such as applied pressure. When such quantum fluctuations become sufficiently strong, the system undergoes a quantum phase transition to a new ground state.As simple as this sounds, quantum phase transitions are not easy to achieve. Consider, for example, the case of ice. Anybody who has skated would appreciate the fact that the melting temperature of ice is reduced by pressure. If the melting temperature were forced to vanish at a sufficiently high pressure, a quantum phase transition would take place at this pressure. However, applying pressure larger than about 0.2 GPa to ice actually makes the melting temperature go up again.

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder 1-5 that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study 6 on theheavy-electron material Y bRh 2 Si 2 found that near a field-induced quantum critical point electrons move ever more slowly and scatter off one-another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and cross-section. These studies could not shed light on whether these properties were an artifact of the applied field 7,8 , or a more general feature of field-free QCPs. Here we report that when Germanium-doped Y bRh 2 Si 2 is tuned away from a chemically induced quantum critical point by magnetic fields there is a universal behavior in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual 1 electrons decay into collective current carrying motions of the electron fluid.Recent work 6 on the heavy electron material YbRh 2 Si 2 9 has demonstrated that a magnetic field can be used to probe the heavy electron quantum critical point. This material exhibits a small antiferromagnetic (AFM) ordering temperature T N = 70 mK (Fig. 1a) that is driven to zero by a critical magnetic field B c = 0.66 T (if the field is applied parallel to the crystallographic c-axis, perpendicular to the easy magnetic plane) 6 . For 2 Past experience 7,8 suggested that a finite field quantum critical point has properties which are qualitatively different to a zero field transition, shedding doubt on the reliability of these measurements as an indicator of the physics of a quantum phase transition at zero field. However, the zero-field properties of YbRh 2 (Si 1−x Ge x ) 2 above T ≈ 70 mK for the undoped (x = 0) and doped (x = 0.05) crystals are essentially identical (Fig. 2a), suggesting that by suppressing the critical field we are still probing the same quantum critical point.In both compounds, the ac-susceptibility follows a temperature dependence χ −1 ∝ T α from 0.3 K to ≤ T ≤ 1.5 K, with α = 0.75 14 , and the coefficient of the electronic specific heat, C el (T )/T , exhibits 9 a logarithmic divergence between 0.3 K and 10 K. However, in the low-T paramagnetic regime, i. e. , T N < T < ∼ 0.3 K, the ac-susceptibility follows a CurieWeiss law (inset of Fig. 2a) with a Weiss temperature Θ W ≈ 0.3 K, and a surprisingly large effective moment µ eff ≈ 1.4µ B /Yb 3+ , indicating the emergence of coupled, unquenched spins at the quantum critical point. The electronic specific heat coefficient, C e...

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...

We have synthesized single crystals of Na2IrO3 and studied their structure, transport, magnetic, and thermal properties using powder x-ray diffraction (PXRD), electrical resistivity, isothermal magnetization M versus magnetic field H, magnetic susceptibility χ versus temperature T , and heat capacity C versus T measurements. Na2IrO3 crystallizes in the monoclinic C2/c (No. 15) type structure which is made up of Na and NaIr2O6 layers alternately stacked along the c axis. The χ(T ) data show Curie-Weiss behavior at high T > 200 K with an effective moment µ eff = 1.82(1)µB indicating an effective spin S eff = 1/2 on the Ir 4+ moments. A large Weiss temperature θ = −116(3) K indicates substantial antiferromagnetic interactions between these S eff = 1/2, Ir 4+ moments. Sharp anomalies in χ(T ) and C(T ) data indicate that Na2IrO3 undergoes a transition into a long-range antiferromagnetically ordered state below TN = 15 K. The magnetic entropy at TN is only about 20% of what is expected for S eff = 1/2 moment ordering. The reduced entropy and the small ratio TN /θ ≈ 0.13 suggest geometrical magnetic frustration and/or low-dimensional magnetic interactions in Na2IrO3. In plane resistivity measurements show insulating behavior. This together with the local moment magnetism indicates that bulk Na2IrO3 is a Mott insulator.