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.
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 $N_{corr}$.
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 diel
ectric 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.
The dc-magnetization of the unique S=1/2 kagome antiferromagnet Herbertsmithite has been measured down to 0.1K. No sign of spin freezing is observed in agreement with former muSR and ac-susceptibility results. The low temperature magnetic response is
dominated by a defect contribution which exhibits a new energy scale $simeq 1$ K, likely reflecting the coupling of the defects. The defect component is saturated at low temperature by H>8T applied magnetic fields which enables us to estimate an upper bound for the non saturated intrinsic kagome susceptibility at T=1.7K.
