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]

Nonlinear dielectric susceptibilities in supercooled liquids: a toy model

The dielectric response of supercooled liquids is phenomenologically modeled by a set of Asymmetric Double Wells (ADW), where each ADW contains a dynamical heterogeneity of $N_{corr}$ molecules. We find that the linear macroscopic susceptibility $\chi_1$ does not depend on $N_{corr}$ contrary to all higher order susceptibilities $\chi_{2k+1}$. We show that $\chi_{2k+1}$ is proportional to the $k^{th}$ moment of $N_{corr}$, which could pave the way for new experiments on glass transition. In particular, as predicted by Bouchaud and Biroli on general grounds [Phys. Rev. B, {\bf 72}, 064204 (2005)], we find that $\chi_3$ is proportional to the average value of $N_{corr}$. We fully calculate $\chi_3$ and, with plausible values of few parameters our model accounts for the salient features of the experimental behavior of $\chi_3$ of supercooled glycerol.Comment: 13 pages, 5 figure

Evidence of growing spatial correlations during the aging of glassy glycerol

We have measured, as a function of the age $t_a$, the aging of the nonlinear dielectric susceptibility $\chi_3$ of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time $\tau_{\alpha}(t_a)$, this scaling breaks down for $\chi_3$, suggesting an increase of the amplitude of $\chi_3$. This is a strong indication that the number $N_{corr}$ of molecules involved in relaxation events increases with $t_a$. For $T=0.96 \times T_g$, we find that $N_{corr}$ increases by $\sim 10$ when $t_a$ varies from $1\mathrm{ks}$ to $100\mathrm{ks}$. This sheds new light on the relation between length scales and time scales in glasses.Comment: Accepted in Physical Review Letter

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

Direct experimental evidence of a growing length scale accompanying the glass transition

Understanding glass formation is a challenge because the existence of a true glass state, distinct from liquid and solid, remains elusive: Glasses are liquids that have become too viscous to flow. An old idea, as yet unproven experimentally, is that the dynamics becomes sluggish as the glass transition approaches because increasingly larger regions of the material have to move simultaneously to allow flow. We introduce new multipoint dynamical susceptibilities to estimate quantitatively the size of these regions and provide direct experimental evidence that the glass formation of molecular liquids and colloidal suspensions is accompanied by growing dynamic correlation length scales.Comment: 5 pages, 2 figure

Control parameter for the glass transition of glycerol evidenced by the static-field-induced nonlinear response

International audienceBy studying a nonlinear susceptibility on supercooled glycerol, we show that applying a static field E st increases the glass transition temperature T g by an amount quadratic in E st. This has important consequences: (i) it reinforces the relation between the two paths put forward in the last years to unveil the dynamical correlation volume close to T g ; (ii) it clarifies the interpretation of nonlinear measurements; (iii) it yields a new control parameter of the glass transition, which paves the way for experiments deepening our understanding of glasses

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

Dielectric constant of glasses: first observation of a two-dimensional behavior

The 1kHz real part $\chi'$ of the dielectric constant of a structural glass was measured at low temperature $T$ down to 14 mK. Reducing the sample thickness $h$ to 10 nm suppresses the usual minimum of $\chi'$ for measuring fields $E<.5$ MV/m. This contradicts the Two Level System (TLS) model but is well accounted for by including TLS-TLS interactions where excitations delocalize between TLS's through a $E$-induced mechanism recently designed: for small $h$'s this interaction is reduced, which explains the two-dimensional behavior of $\chi'(T)$. Hence, interactions play a key role in standard thick samples.Comment: latex finesse3.tex, 5 files, 4 figures, 4 pages [SPEC-S02/050], submitted to Phys. Rev. Let

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