Critical behavior near the reversible-irreversible transition in periodically driven vortices under random local shear

Abstract

When many-particle (vortex) assemblies with disordered distribution are subjected to a periodic shear with a small amplitude , the particles gradually self-organize to avoid next collisions and transform into an organized configuration. We can detect it from the time-dependent voltage (average velocity) that increases towards a steady-state value. For small , the particles settle into a reversible state where all the particles return to their initial position after each shear cycle, while they reach an irreversible state for above a threshold . Here, we investigate the general phenomenon of a reversible-irreversible transition (RIT) using periodically driven vortices in a strip-shaped amorphous film with random pinning that causes local shear, as a function of . By measuring , we observe a critical behavior of RIT, not only on the irreversible side, but also on the reversible side of the transition, which is the first under random local shear. The relaxation time to reach either the reversible or irreversible state shows a power-law divergence at . The critical exponent is determined with higher accuracy and is, within errors, in agreement with the value expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. As is decreased down to the intervortex spacing in the reversible regime, deviates downward from the power-law relation, reflecting the suppression of intervortex collisions. We also suggest the possibility of a narrow smectic-flow regime, which is predicted to intervene between fully reversible and irreversible flow.

Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

“…The observed independence of the critical exponents from the driving parameters is somewhat surprising, considering that the critical regions observed here are very large, clearly going beyond the linear approximation. The similar large critical region has been reported in the nonequilibrium RIT in various systems 17 , 22 , 25 , including the vortex system 24 , where the parameter-independent critical exponents with 1.3–1.4 have been found for the shear-driven and density-driven transitions 26 .…”

“…Thus, the dimensionality of the vortex system is basically 2D, as treated by 2D simulations 1 , 13 , 18 . This is supported by the experimental fact that the thickness of the film is comparable to or smaller than the magnetic penetration depth and the possible bending distortions of vortex lines that may cause the deviation from the 2D particles picture can be ignored 24 , 26 .…”

“…In these experiments, however, the critical behavior of the depinning transition has been observed only on the moving (fluctuating diffusing [active]) side of the transition 9 , 12 , 20 , 39 , although that of RIT has been reported on both sides of the transition 20 , 24 , 26 . This is because it is difficult to obtain a reliable data of V ( t ) in the pinned (non-fluctuating quiescent [absorbing]) phase, where V ( t ) relaxes to = 0.…”

Reversible to Irreversible Transitions for Cyclically Driven Disks on Periodic Obstacle Arrays

“…When quenched disorder is present, however, plastic deformations can occur that permit particles to move relative to one another from cycle to cycle 21 . In vortex systems, studies of R-IR transitions in simulation 22 and experiments [23][24][25][26] , show that diverging time scales appear near critical drive amplitudes 25 and critical densities 26 with critical exponents similar to those observed in the dilute colloidal systems. Stoop et al 29 applied backward and forward pulse driving to hard sphere colloids moving over random obstacle arrays and obtained a variety of different dynamical phases as a function of obstacle density.…”

“…In another class of systems of collectively interacting particles that is cyclically driven over quenched disorder 21 , such as vortices in type-II superconductors [22][23][24][25][26] , magnetic skyrmions 27,28 , and colloidal particles 29 , the drive is applied uniformly to all the particles, and in the absence of quenched disorder, the assembly moves back and forth uniformly in a reversible manner. When quenched disorder is present, however, plastic deformations can occur that permit particles to move relative to one another from cycle to cycle 21 .…”