The electrodynamic response of heavy-electron materials with magnetic phase transitions

We have investigated the electrodynamic response of the heavy-electron compounds U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂. Particular emphasis has been devoted to the optical evidence of the antiferromagnetic phase transitions at T_N = 9.7 K, 14 K, 15 K and 17 K for U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂, respectively. In the excitation spectrum of UCu₅ and URu₂Si₂, we found an absorption in the far-infrared, which develops below T_N and is ascribed to the excitation across a spin-density-wave type gap, suggesting that the antiferromagnetic phase transition might be itinerant in nature, and invokes a Fermi surface instability. Since this gap-like feature is absent in U₂Zn₁₇ and UPd₂Al₃, we argue that these latter compounds belong to a characteristically different class of antiferromagnets, representative of the heavy-electron compounds with an ordering of essentially localized magnetic moments. The antiferromagnetic ordering then leads to a suppression of the spin-flip mechanism below T_N. At low temperatures, we observe for all compounds the formation of a narrow Drude-like resonance in the optical conductivity, which is ascribed to the electrodynamic response of the heavy-quasiparticles, and is indicative of the progressive development of the manybody coherent Kondo state, coexisting with both types of magnetic ordering. In this review, we also present the evolution of the optical properties due to Ni- and Redoping in UCu₅ and URu₂Si₂, respectively. The optical evidence of the itinerant antiferromagnetic ordering is suppressed in both compounds upon doping and particularly for the URu₂Si₂ compound this is consistent with a crossover to a ferromagnetic ground state upon Re-doping.     

Universal scaling relations in strongly anisotropic materials

We consider the critical temperature in strongly anisotropic antiferromagnetic materials, with weak coupling between stacked planes, in order to determine the interplane coupling constant from experimentally measured susceptibilities. We present theoretical arguments for a universal relation between interplane coupling and susceptibility shown numerically by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)10.1103/PhysRevLett.94.217201]. We predict a more general scaling function if the system is close to a quantum critical point, a similar relation for other susceptibilities than considered in Yasuda et al., and the validity of these relations for more general phase transitions.     

Universal behavior in non-stationary Mean Field Games

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their behavior is still far from being fully understood. When the system is confined, a notion of “ergodic state” has been introduced that characterizes most of the dynamics for long optimization times. Here we consider a class of models without such an ergodic state, and show the existence of a scaling solution that plays a similar role. Its universality and scaling behavior can be inferred from a mapping to an electrostatic problem.     

Universal dynamics behavior in superionic conducting glasses

The inelastic neutron scattering experiment on superionic glass system AgI-AgPO₃ have been performed in the energy and momentum transfer range from ? 5 to 15 meV and 0 to 8 Å^? 1, respectively by using a time of flight MARI instrument at Rutherford Appleton Laboratory, ISIS, UK. The E-dependence of the inelastic data show an excess intensity at low energy around 3 meV, the so-called Boson peak, which increased with the dopant salt. The Q-dependence of the elastic scattering reveals a prepeak at anomalously low Q value around 0.8 Å^? 1, which is not observed in the undoped AgPO₃ glass. The Q-dependence in the energy region from 1 to 3 meV shows clearly an excess intensity at Q ~ 2.2 Å ^? 1compared with the undoped AgPO₃. All these features correlate with the increasing mobility of Ag⁺ ions due to the expansion of the network structure caused by salt doping, which leads to the increase of ionic conductivity. Similar results have also been observed in the corresponding superionic glass system AgI-Ag₂S-AgPO₃ that was observed by both MARI and NEAT instrument at HMI, Berlin. The results show a universal dynamic behavior in silver phosphate glasses.     

Universal features of terahertz absorption in disordered materials

Using an analytical theory, experimental terahertz time-domain spectroscopy data, and numerical evidence, we demonstrate that the frequency dependence of the absorption coupling coefficient between far-infrared photons and atomic vibrations in disordered materials has the universal functional form, C(omega)=A+Bomega(2), where the material-specific constants A and B are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.     

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (??SR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H _c2 ^P (T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn₅.     

Universal behavior in a generalized model of contagion

Models of contagion arise broadly in both the biological and the social sciences, with applications ranging from the transmission of infectious diseases to the spread of cultural fads. In this Letter, we introduce a general model of contagion which, by explicitly incorporating memory of past exposures to, for example, an infectious agent, rumor, or new product, includes the main features of existing contagion models and interpolates between them. We obtain exact solutions for a simple version of the model, finding that under general conditions only three classes of collective dynamics exist. Furthermore, we find that, for a given length of memory, the class into which a particular system falls is determined by only two parameters. Our model suggests novel measures for assessing the susceptibility of a population to large contagion events, and also a possible strategy for inhibiting or facilitating them.     

A comparative study of the magnetic heavy-electron materials U2Zn17 and UCu5 by μ+SR

A systematic μ⁺SR study of the magnetic heavy-electron systems U₂Zn₁₇ and UCu₅ in the paramagnetic and in the magnetically ordered state is presented. In both systems the antiferromagnetic nature of the low-temperature phase could be at least partially confirmed, but the muon reveals significant differences with regard to the phase transition itself. UCu₅ behaves like a model-antiferromagnet showing a drastic increase of the relaxation rate both below and above T_N, two spontaneous frequencies in the ordered phase, and a Knight shift above T_N which scales with the bulk susceptibility. In contrast U₂Zn₁₇ shows a loss of μ⁺ asymmetry by 20% below T_N, which is independent of the external field but can be quenched in sufficiently strong longitudinal fields. No scaling of the Knight shift and the susceptibility was observed and no critical increase of the relaxation rate λ. Most astonishing is the strong and nonlinear field dependence of λ above and below T_N in both compounds. The absence of longitudinal relaxation demonstrates the static origin of λ.     

Universal critical behavior of noisy coupled oscillators

We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a generic relation between correlation and response functions appears. At the same time, the fluctuation-dissipation relation is strongly violated.     

Universal critical behavior of curvature-dependent interfacial tension

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality class. The large value of C(2)?32 implies that conventional nucleation theory becomes inaccurate even for a significantly large droplet radius.     

Universal behavior of nonequilibrium fluctuations in free diffusion processes

We show that giant nonequilibrium fluctuations are present during the free diffusive remixing occurring in ordinary liquid mixtures and in macromolecular solutions. The static structure factor of the fluctuations is measured by using a quantitative shadowgraph technique. We show that structure factors at different times and from different samples can be rescaled onto a single master curve without any adjustable parameter, thus giving strong evidence that nonequilibrium fluctuations are a universal feature of free diffusion processes.     

Universal optimal transmission of light through disordered materials

We experimentally demonstrate increased diffuse transmission of light through strongly scattering materials. Wave front shaping is used to selectively couple light to the open transport eigenchannels, specific solutions of Maxwell's equations which the sample transmits fully, resulting in an increase of up to 44% in the total angle-integrated transmission compared to the case where plane waves are incident. The results for each of several hundreds of experimental runs are in excellent quantitative agreement with random matrix theory. From our measurements we conclude that with perfectly shaped wave fronts the transmission of a disordered sample tends to a universal value of 2/3, regardless of the thickness.