Scaling behavior of the generalized susceptibility in La2-xSrxCuO4+y

Local quantum phase transition in YFe2Al10

A phase transition occurs when correlated regions of a new phase grow to span the system and the fluctuations within the correlated regions become long lived. Here, we present neutron scattering measurements showing that this conventional picture must be replaced in YFe₂Al₁₀, a compound that forms naturally very close to a [Formula: see text] quantum phase transition. Fully quantum mechanical fluctuations of localized moments are found to diverge at low energies and temperatures; however, the fluctuating moments are entirely without spatial correlations. Zero temperature order in YFe₂Al₁₀ is achieved by an entirely local type of quantum phase transition that may originate with the creation of the moments themselves.

Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates

The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in (2+1)D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum [Formula: see text], measured from the ordering vector, and of the frequency ω and the temperature T which scale as [Formula: see text] at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy [Formula: see text] for all momenta, a resistivity [Formula: see text], a [Formula: see text] contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements. This reveals, in agreement with the theory, that the frequency dependence of the attractive irreducible particle-particle vertex in the d-wave channel is the same as the irreducible particle-hole vertex in the full symmetry of the lattice.

Quantum Criticality in Quasi-Two-Dimensional Itinerant Antiferromagnets

Quasi-two-dimensional itinerant fermions in the antiferromagnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with temperature and a contribution to specific heat or thermopower proportional to TlnT. It is shown, here, that a generic model of itinerant anti-ferromagnet can be canonically transformed so that its critical fluctuations around the AFM-vector Q can be obtained from the fluctuations in the long wavelength limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently, and in a large regime of parameters, they are determined, not by renormalized spin fluctuations, but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a spatial correlation length which is proportional to the logarithm of the temporal correlation length, i.e., for some purposes, the effective dynamic exponent z=∞. The time dependence gives ω/T scaling at criticality. The observed resistivity and entropy then follow. Several predictions to test the theory are also given.

Neutron scattering and μSR investigations of the low temperature state of LuCuGaO₄

LuCuGaO₄ has magnetic Cu(2+) and diamagnetic Ga(3+) ions distributed on a triangular bilayer and is suggested to undergo a spin glass transition at Tg ∼ 0.4 K. Using μSR (muon spin rotation) and neutron scattering measurements, we show that at low temperature the spins form a short range correlated state with spin fluctuations detectable over a wide range of timescales: at 0.05 K magnetic fluctuations can be detected in both the μSR time window and also extending beyond 7 meV in the inelastic neutron scattering response, indicating magnetic fluctuations spanning timescales between ∼10(-5) and ∼10(-10) s. The dynamical susceptibility scales according to the form χ″(ω)T(α), with α = 1, throughout the measured temperature range (0.05-50 K). These effects are associated with quantum fluctuations and some degree of structural disorder in ostensibly quite different materials, including certain heavy fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond glasses. We therefore suggest that LuCuGaO₄ is an interesting model compound for the further examination of disorder and quantum magnetism.

Dynamic scaling in the susceptibility of the spin-1/2 kagome lattice antiferromagnet herbertsmithite

The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu(3)(OH)(6)Cl(2), is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity chiT(alpha) with alpha approximately 0.66 can be expressed as a universal function of H/T or omega/T. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum critical point.

Scale-free antiferromagnetic fluctuations in the s = 1/2 kagome antiferromagnet herbertsmithite

Neutron spectroscopy and diffuse neutron scattering on herbertsmithite [ZnCu(3)(OH)(6)Cl(2)], a near-ideal realization of the s=1/2 kagome antiferromagnet, reveal the hallmark property of a quantum spin liquid: instantaneous short-ranged antiferromagnetic correlations in the absence of a time-averaged ordered moment. These dynamic antiferromagnetic correlations are weakly dependent of neutron-energy transfer and temperature, and persist up to 25 meV and 120 K. At low energy transfers a shift of the magnetic scattering to low Q is observed with increasing temperature, providing evidence of gapless spinons. It is argued that these observations provide important evidence in favor of resonating-valence-bond theories of (doped) Mott insulators.

Emergence of coherent magnetic excitations in the high temperature underdoped La2-xSrxCuO4 superconductor at low temperatures

We use inelastic neutron scattering to measure the magnetic excitations in underdoped La2-xSrxCuO4 (x=0.085, T_{c}=22 K) for large energy (5<E<200 meV) and temperature (5<T<300 K) ranges. At low T, the response is highly structured in E and q, with peaks in the local susceptibility at 15 and 50 meV and a four-peaked structure in q for E approximately 185 meV. Raising T from 30 K greater, similarT_{c} to 300 K causes the structure in chi;{''}(q,omega) present for E<70 meV to disappear. It is replaced with a strongly damped response. We attribute this change to the disappearance of the pseudogap with increasing temperature.

Quantum criticality and universal scaling of a quantum antiferromagnet

Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL), which is of relevance to many quasi-one-dimensional materials. The magnetic material KCuF3 realizes an array of weakly coupled spin chains (or LLs) and thus lies close to but not exactly at the LL quantum critical point. By using inelastic neutron scattering we have collected a complete data set of the magnetic correlations of KCuF3 as a function of momentum, energy and temperature. The LL description is found to be valid over an extensive range of these parameters, and departures from this behaviour at high and low energies and temperatures are identified and explained.

Scaling of the magnetic response in doped antiferromagnets

A theory of the anomalous omega/T scaling of the dynamic magnetic response in cuprates at low doping is presented. It is based on the memory function representation of the dynamical spin susceptibility in a doped antiferromagnet where the damping of the collective mode is constant and large, whereas the equal-time spin correlations saturate at low T. Exact diagonalization results within the t-J model are shown to support assumptions. Consequences, for both the scaling function and the normalization amplitude, are well in agreement with neutron scattering results.

Novel dynamic ccaling regime in hole-doped La2CuO4

Only 3% hole doping by Li is sufficient to suppress the long-range three-dimensional (3D) antiferromagnetic order in La2CuO4. The spin dynamics of such a 2D spin liquid state at T<<J was investigated with measurements of the dynamic magnetic structure factor S(omega,q), using cold neutron spectroscopy, for single crystalline La2Cu0.94Li0.06O4. S(omega,q) peaks sharply at (pi,pi) and crosses over around 50 K from omega/T scaling to a novel low temperature regime characterized by a constant-energy scale. The possible connection to a crossover from the quantum critical to the quantum disordered regime of the 2D antiferromagnetic spin liquid is discussed.

Scaling near the quantum-critical point in the SO(5) theory of the high-T(c) superconductivity

We study the quantum-critical point scenario within the unified theory of superconductivity and antiferromagnetism based on the SO(5) symmetry. Closed-form expression for the quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear sigma-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also presented.

Time reparametrization group and the long time behavior in quantum glassy systems

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( R(p)G) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor

Polarized and unpolarized neutron scattering was used to measure the wave vector- and frequency-dependent magnetic fluctuations in the normal state (from the superconducting transition temperature, Tc = 35 kelvin, up to 350 kelvin) of single crystals of La1.86Sr0.14CuO4. The peaks that dominate the fluctuations have amplitudes that decrease as T-2 and widths that increase in proportion to the thermal energy, kBT (where kB is Boltzmann's constant), and energy transfer added in quadrature. The nearly singular fluctuations are consistent with a nearby quantum critical point.

Spin Susceptibility Scaling in High-Temperature Superconductors

The spin response of a nested Fermi surface represented by a tight binding energy band is found to exhibit scaling in frequency divided by temperature within a restricted regime close to half-filling of the band. Computations of the spin susceptibility reveal a surprising momentum variation at various temperatures and frequencies. Neutron scattering data on the high-temperature superconductor YBa(2)Cu(3)O(6+x) are analyzed for scaling near a momentum vector that spans nested regions of the orbit. Changes in the Fermi energy remove the scaling properties and reduce the susceptibility to the conventional Fermi liquid behavior of ordinary metals. These results imply that pairing mechanisms of superconductivity need to cope with competing spin density wave and charge density wave instabilities.