Onset of the nonlinear dielectric response of glasses in the two-level system model

We have calculated the real part $\chi'$ of the nonlinear dielectric susceptibility of amorphous insulators in the kHz range, by using the two-level system model and a nonperturbative numerical quantum approach. At low temperature $T$, it is first shown that the standard two-level model should lead to a \textit{decrease} of $\chi'$ when the measuring field $E$ is raised, since raising $E$ increases the population of the upper level and induces Rabi oscillations canceling the ones induced from the ground level. This predicted $E$-induced decrease of $\chi'$ is at \textit{odds} with experiments. However, a \textit{good agreement} with low-frequency experimental nonlinear data is achieved if, in our fully quantum simulations, interactions between defects are taken into account by a new relaxation rate whose efficiency increases as $\sqrt{E}$, as was proposed recently by Burin \textit{et al.} (Phys. Rev. Lett. {\bf 86}, 5616 (2001)). In this approach, the behavior of $\chi'$ at low $T$ is mainly explained by the efficiency of this new relaxation channel. This new relaxation rate could be further tested since it is shown that it should lead: \textit{i)} to a completely new nonlinear behavior for samples whose thickness is $\simeq 10$ nm; \textit{ii)} to a decrease of nonequilibrium effects when $E$ is increased.Comment: latex Sept02.tex, 5 files, 4 figures, 17 pages, submitted to Eur. Phys. J. B. Text change

Conductance statistics in small insulating GaAs:Si wires at low temperature. II. Experimental study

We have observed reproducible conductance fluctuations at low temperature in a small GaAs:Si wire driven across the Anderson transition by the application of a gate voltage. We analyse quantitatively the log-normal conductance statistics in terms of truncated quantum fluctuations. Quantum fluctuations due to small changes of the electron energy (controlled by the gate voltage) cannot develop fully due to identified geometrical fluctuations of the resistor network describing the hopping through the sample. The evolution of the fluctuations versus electron energy and magnetic field shows that the fluctuations are non-ergodic, except in the critical insulating region of the Anderson transition, where the localization length is larger than the distance between Si impurities. The mean magnetoconductance is in good accordance with simulations based on the Forward-Directed-Paths analysis, i.e. it saturates to ${\rm ln} (\sigma (H>1)/\sigma (0))\simeq 1,$ as $\sigma (0)$ decreases over orders of magnitude in the strongly localized regime.Comment: Email contact: [email protected]

A method for measuring the nonlinear response in dielectric spectroscopy through third harmonics detection

We present a high sensitivity method allowing the measurement of the non linear dielectric susceptibility of an insulating material at finite frequency. It has been developped for the study of dynamic heterogeneities in supercooled liquids using dielectric spectroscopy at frequencies 0.05 Hz < f < 30000 Hz . It relies on the measurement of the third harmonics component of the current flowing out of a capacitor. We first show that standard laboratory electronics (amplifiers and voltage sources) nonlinearities lead to limits on the third harmonics measurements that preclude reaching the level needed by our physical goal, a ratio of the third harmonics to the fundamental signal about 7 orders of magnitude lower than 1. We show that reaching such a sensitivity needs a method able to get rid of the nonlinear contributions both of the measuring device (lock-in amplifier) and of the excitation voltage source. A bridge using two sources fulfills only the first of these two requirements, but allows to measure the nonlinearities of the sources. Our final method is based on a bridge with two plane capacitors characterized by different dielectric layer thicknesses. It gets rid of the source and amplifier nonlinearities because in spite of a strong frequency dependence of the capacitors impedance, it is equilibrated at any frequency. We present the first measurements of the physical nonlinear response using our method. Two extensions of the method are suggested.Comment: 25 pages, 8 figure

Study of the heating effect contribution to the nonlinear dielectric response of a supercooled liquid

We present a detailed study of the heating effects in dielectric measurements carried out on a liquid. Such effects come from the dissipation of the electric power in the liquid and give a contribution to the nonlinear third harmonics susceptibility chi_3 which depends on the frequency and temperature. This study is used to evaluate a possible `spurious' contribution to the recently measured nonlinear susceptibility of an archetypical glassforming liquid (Glycerol). Those measurements have been shown to give a direct evaluation of the number of dynamically correlated molecules temperature dependence close to the glass transition temperature T_g~190K (Crauste-Thibierge et al., Phys. Rev. Lett 104,165703(2010)). We show that the heating contribution is totally negligible (i) below 204K at any frequency; (ii) for any temperature at the frequency where the third harmonics response chi_3 is maximum. Besides, this heating contribution does not scale as a function of f/f_{\alpha}, with f_{\alpha}(T) the relaxation frequency of the liquid. In the high frequency range, when f/f_{\alpha} >= 1, we find that the heating contribution is damped because the dipoles cannot follow instantaneously the temperature modulation due to the heating phenomenon. An estimate of the magnitude of this damping is given.Comment: 25 pages, 10 figures, Accepted for publication in Journal of Chemical Physic

Evidence of growing spatial correlations at the glass transition from nonlinear response experiments

The ac nonlinear dielectric response $\chi_3(\omega,T)$ of glycerol was measured close to its glass transition temperature $T_g$ to investigate the prediction that supercooled liquids respond in an increasingly non-linear way as the dynamics slows down (as spin-glasses do). We find that $\chi_3(\omega,T)$ indeed displays several non trivial features. It is peaked as a function of the frequency $\omega$ and obeys scaling as a function of $\omega \tau(T)$, with $\tau(T)$ the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules $N_{corr}(T)$, increases as the system becomes glassy, and $\chi_3$ decays as a power-law of $\omega$ over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the $T$ dependence of $N_{corr}$.Comment: 22 pages, 6 figures. With respect to v1, a few new sentences were added in the introduction and conclusion, references were updated, some typos corrected

Ground state of the Kagome-like S=1/2 antiferromagnet, Volborthite Cu3V2O7(OH)2.2H2O

Volborthite compound is one of the very few realizations of S=1/2 quantum spins on a highly frustrated kagome-like lattice. Low-T SQUID measurements reveal a broad magnetic transition below 2K which is further confirmed by a peak in the 51V nuclear spin relaxation rate (1/T1) at 1.4K$\pm$0.2K. Through 51V NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% correspond to a well defined short range order, possibly of the $\sqrt{3} \times \sqrt{3}$ type. While the freezing involve all the Cu$^{2+}$ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.Comment: 4 pages, 4 figures, to appear in PR

Superconducting diamagnetic fluctuations in ropes of carbon nanotubes

We report low-temperature magnetisation measurements on a large number of purified ropes of single wall carbon nanotubes. In spite of a large superparamagnetic contribution due to the small ferromagnetic catalytical particles still present in the sample, at low temperature ($T < 0.5K$) and low magnetic field ($H < 80 Oe$), a diamagnetic signal is detectable. This low temperature diamagnetism can be interpreted as the Meissner effect in ropes of carbon nanotubes which have previously been shown to exhibit superconductivity from transport measurements.Comment: 10 pages 3 figure

Slow Relaxation Process in Ising like Heisenberg Kagome Antiferromagnets due to Macroscopic Degeneracy in the Ordered State

We study relaxation phenomena in the ferromagnetically ordered state of the Ising-like Heisenberg kagome antiferromagnets. We introduce the "weathervane loop" in order to characterize macroscopic degenerate ordered states and study the microscopic mechanism of the slow relaxation from a view point of the dynamics of the weathervane loop configuration. This mechanism may give a possible origin of the slow relaxation reported in recent experiments.Comment: 6pages, 4figures, HFM2006 proceeding

Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers

Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third- and fifth-order susceptibilities provide a definite answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorphous order. Moreover, when lowering temperature, we find that the growing transient domains are compact - that is their fractal dimension d_f = 3. The glass transition may thus represent a class of critical phenomena different from canonical second-order phase transitions for which d_f < 3.Comment: 9 pages, 3 figure