Criticality of Tuning in Athermal Phase Transitions

Abstract

We experimentally address the importance of tuning in athermal phase transitions, which are triggered only by a slowly varying external field acting as tuning parameter. Using higher order statistics of fluctuations, a singular critical instability is detected for the first time in spite of an apparent universal self-similar kinetics over a broad range of driving force. The results as well as the experimental technique are likely to be of significance to many slowly driven non-equilibrium systems from geophysics to material science which display avalanche dynamics.In equilibrium statistical physics, continuous phase transitions are critical and are characterized by a diverging correlation length ξ at the critical point. On the other hand, first order transitions are non-critical where the probability of phase transformation is governed by the free energy barrier through the Boltzmann factor [1]. In contrast, athermal first order phase transitions are not influenced by thermal fluctuations and proceed through a set of metastable states of free energy local minima, and hence as the external field (temperature, magnetic field, stress etc.) is varied, display bursty and discrete avalanches [2]. Theoretical models such as random field ising model and the renormalization group analysis [3,4] map these non-equilibrium first order phase transitions to equilibrium critical phenomenon, although the divergence of the correlation length at the critical field has never been clearly demonstrated. Experiments are inconclusive whether these systems self organize to the critical state over a broad range of external field [5,6,7,8,9], or if there exists a unique critical point that is smudged by a wide critical zone as postulated by the concept of "plain-old criticality" [4,10,11]. The bottleneck arises since most experimental claims of critical behavior are based on observation of a scale-free kinetics which causes power law decay in size distribution or the power spectrum of the avalanches [6,9], but none of these are direct probes to ξ itself.In systems with many degrees of freedom [12,13], the non-gaussian component (NGC) in time dependent fluctuations (or noise) in physical observables act as an indicator of long-range correlation between individual fluctuators [14,15]. This has been studied in the context of Barkhausen noise from magnetization avalanches, which probes the role of long-range magnetic interactions in the domain wall depinning when subjected to external magnetic field [16]. Here, we focus on the avalanches in the electrical resistivity, ρ(t), during temperature-driven * electronic mail:chandni@physics.iisc.ernet.in martensite transformation (MT), which is a prototype of athermal phase transition [2]. We demonstrate that the NGC in avalanche induced noise is an extremely sensitive kinetic detector of criticality in continuously driven non-equilibrium systems. We show, for the first time, the existence of a singular 'global instability' [3,10] or divergence of ξ as a function of temperature in MT indicating, (i)...

Simple kinetic sensor to structural transitions

“…The effect of drive rates has been probed in our earlier work as well 18 and Fig.8(a) shows very similar results. To understand the second spectral characteristics (i.e.…”

“…Similar correlation of non-Gaussian electrical noise and first order structural phase change was observed in NiTi thin film as well 18 , outlining an excellent kinetic detector of structural phase transition. The NGC in resistivity noise has been attributed to emergence of a long range correlation in many systems with electronic 24 , structural 18 or magnetic 25 phase transitions. The magnitude of σ (2) is directly associated to a correlation length ξ which, in case of martensitic alloys, characterizes the range of elastic correlation in the system.…”

“…However, our experiments here indicate that the thermal fluctuations do play a minor role in NiTi. It is also important to note that the power spectral density of noise changes very little for various drive rates 18,19 , indicating the second spectral properties to be far more sensitive to small deviations from athermal behavior and adiabatic limit than the noise itself. …”

Correlated Conductance Fluctuations Close to the Berezinskii-Kosterlitz-Thouless Transition in Ultrathin NbN Films

“…Experiments on a wide variety of systems like doped silicon [13], metal nanowires [14], shape memory alloys [15,16], disordered magnetic alloys [17] etc. have shown that time dependent fluctuations (noise) in physical observables exhibit a strong non-Gaussian behavior due to the presence of long-range correlations originating from coulomb forces, internal strain fields or magnetic interactions.…”

“…The second spectrum is a sensitive technique to estimate the presence of non-Gaussian component (NGC) in the resistance fluctuations [15,31,32]. The experimental scheme employed to measure the second spectrum is shown in Fig.…”