Peak Effect Regime Research Articles

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

We study the critical dynamics of vortices associated with dynamic disordering near the depinning transitions driven by dc force (dc current I) and vortex density (magnetic field B). Independent of the driving parameters, I and B, we observe the critical behavior of the depinning transitions, not only on the moving side, but also on the pinned side of the transition, which is the first convincing verification of the theoretical prediction. Relaxation times, tau (I) and tau (B), to reach either the moving or pinned state, plotted against I and B, respectively, exhibit a power-law divergence at the depinning thresholds. The critical exponents of both transitions are, within errors, identical to each other, which are in agreement with the values expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. With an increase in B under constant I, the depinning transition at low B is replaced by the repinning transition at high B in the peak-effect regime. We find a trend that the critical exponents in the peak-effect regime are slightly smaller than those in the low-B regime and the theoretical one, which is attributed to the slight difference in the depinning mechanism in the peak-effect regime.

Anisotropic sliding dynamics, peak effect, and metastability in stripe systems

A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in different directions with respect to the orientation of the stripes. Depending on the strength and density of the substrate disorder, we find that there can be pronounced anisotropy in the transport produced by different dynamical flow phases. We also find a disorder-induced "peak effect" similar to that observed for superconducting vortex systems, which is marked by a transition from elastic depinning to a state where the stripe structure fragments or partially disorders at depinning. Under the sudden application of a driving force, we observe pronounced metastability effects similar to those found near the order-disorder transition associated with the peak effect regime for three-dimensional superconducting vortices. The characteristic transient time required for the system to reach a steady state diverges in the region where the flow changes from elastic to disordered. We also find that anisotropy of the flow persists in the presence of thermal disorder when thermally induced particle hopping along the stripes dominates. The thermal effects can wash out the effects of the quenched disorder, leading to a thermally induced stripe state. We map out the dynamical phase diagram for this system, and discuss how our results could be explored in electron liquid crystal systems, type-1.5 superconductors, and pattern-forming colloidal assemblies.

Driven disordered polymorphic solids: Phases and phase transitions, dynamical coexistence and peak effect anomalies

We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-law orientational correlations we obtain in our moving hexatic phase arise from circularly averaging an orientational correlation function with qualitatively different behaviour in the longitudinal (drive) and transverse directions. The intermediate coexistence regime exhibits several novel properties, including substantial enhancement in the current noise, an unusual power-law spectrum of current fluctuations and striking metastability effects. This noise arises from the fluctuations of the interface separating locally square and triangular ordered regions. We demonstrate the breakdown of effective ``shaking temperature'' treatments in the coexistence regime by showing that such shaking temperatures are non-monotonic functions of the drive in this regime. Finally we discuss the relevance of these simulations to the anomalous behaviour seen in the peak effect regime of vortex lines in the disordered mixed phase of type-II superconductors. We propose that this anomalous behavior is directly linked to the behavior exhibited in our simulations in the dynamical coexistence regime, thus suggesting a possible solution to the problem of the origin of peak effect anomalies.

Order-disorder transition of vortex matter ina-MoxGe1−xfilms probed by noise

We measure voltage noise spectra ${S}_{V}(f)$ generated by current-driven vortices at various fields $B$ including the peak-effect regime for amorphous ${\text{Mo}}_{x}{\text{Ge}}_{1\ensuremath{-}x}$ films with Corbino-disk and striplike contact geometries. Field dependences of the critical current ${I}_{c}$ and ${S}_{V}(f)$ are nearly independent of contact geometries, indicating that edge effects are not important on static or dynamic vortex properties. This is in contrast to the result reported for ${\text{NbSe}}_{2}$ crystals with much larger thickness. ${S}_{V}(f)$ at low frequency $f$ exhibits a sharp peak just below the peak field ${B}_{p}$ of ${I}_{c}$, where the characteristic time of vortex motion increases significantly. The results suggest the existence of the order-disorder transition and vortex instabilities due to coexisting vortex phases at around ${B}_{p}$.

Vortex states in the peak effect regime of [formula omitted] films probed by noise

We present measurements of voltage noise spectra generated by current driven vortices taken at different fields B including the peak-effect regime for a thick a - Mo x Ge 1 - x film with Corbino-disk and strip-like contact geometries. The field dependences of the critical current, I c ( B ) , for both contact geometries are nearly identical to each other, indicating that the edge effects are not important. For the strip-like geometry voltage noise (at low frequency) takes large values around the peak field B p of I c ( B ) and a spectral shape changes drastically just above B p , suggesting that some structural transformation of vortex solid may take place around B p .

Suppression of broadband noise at mode locking in driven vortex matter

We measure voltage noise generated by current-driven vortices for fields corresponding to the solid phase when at equilibrium including the peak-effect regime, focusing on a change in broadband noise (BBN) as the vortex system undergoes a mode-locking (ML) resonance. For all the fields steplike structure indicative of ML is observed in the $I\text{\ensuremath{-}}V$ curves. We find that BBN at high frequencies (but well below the ac drive frequency) is suppressed inside the ML steps. The results are consistent with the view that the mode-locked state is a frozen solid pinned in the moving frame of reference.

BROADBAND NOISE ACROSS THE MODE-LOCKING FREEZING IN DRIVEN VORTEX MATTER

We report on the measurements of broadband voltage noise generated by the driven vortex matter in and just below the peak-effect regime of a thick amorphous Mo x Ge 1-x film. We focus on a change in broadband noise as the system undergoes the mode-locking (ML) resonance (ML freezing), which occurs when the ac drive superimposed on the dc drive excites the lattice-oscillation modes collectively. Independent of the field studied, the noise spectrum at low frequencies f is of Lorentzian type, while it is f-independent at high f (but well below the ac-drive frequency). We find that the magnitude of noise at high f decreases in the ML resonance.

Mode locking and noise of driven vortices near the peak-effect regime

We present the measurements of broadband voltage noise generated by the driven vortices near the peak-effect regime of a thick amorphous MoxGe1−x film. We focus on a change in voltage noise as the vortex system undergoes mode locking (ML), which is a dynamic resonance between the ac drive superimposed on the dc drive and lattice-oscillation modes excited collectively. By sweeping the dc current I at fixed ac drive, we find the step-like structure in the current–voltage (I–V) characteristics indicative of ML. At high frequencies f (but well below the ac-drive frequency) the noise spectrum is f-independent. We find a trend for the amplitude of noise (at high f) to decrease in the ML step.

Peak anomaly of dynamic critical current in NbSe2 crystals

We present flow dynamics of vortex matter in the peak effect regime of 2H-NbSe2 crystals investigated by mode locking (ML) and dc transport measurements. Dynamic critical current, characterizing dynamic friction of driven vortices, exhibits a peak behavior against magnetic field and this anomaly occurs above the peak field of the critical current. In fields between these peak behaviors, the ML resonance, characterizing the lattice flow in driven vortices, disappears. The vanishing field of the ML resonance increases with frequency and saturates at high frequency. This saturation behavior will be discussed within a dynamic ordering model and also be compared to the peak anomaly of the dynamic critical current.

Dynamic ordering of driven vortex matter in the peak effect regime of amorphous MoGe films and2H−NbSe2crystals

Dynamic ordering of driven vortex matter has been investigated in the peak effect regime of both amorphous MoGe films and $2\mathrm{H}\text{\ensuremath{-}}\mathrm{Nb}{\mathrm{Se}}_{2}$ crystals by mode locking (ML) and dc transport measurements. ML features allow us to trace how the shear rigidity of driven vortices evolves with the average velocity. Determining the onset of ML resonance in different magnetic fields and/or temperatures, we find that the dynamic ordering frequency (velocity) exhibits a striking divergence in the higher part of the peak effect regime. Interestingly, this phenomenon is accompanied by a pronounced peak of dynamic critical current. Mapping out field-temperature phase diagrams, we find that divergent points follow well the thermodynamic melting curve of the ideal vortex lattice over wide field and/or temperature ranges. These findings provide a link between the dynamic and static melting phenomena which can be distinguished from the disorder induced peak effect.

Mode locking of vortex matter in the peak effect regime of amorphous MoGe films

We have investigated flow properties of vortex matter in the peak effect regime of amorphous MoGe films by a mode locking (ML) technique. While dc current–voltage (I–V) characteristic exhibits a S-shaped anomaly, we observed striking frequency dependence in a ML feature: above a minimum frequency to observe the ML resonance, the maximized ML width increases with frequency and seems to saturate at high frequency. A comparison indicates that the I–V anomaly does not coincide with the onset of ML, but occurs in a velocity range where fractions of mode locked vortices increase rapidly with velocity.

Dynamics of transition from metastable disordered state to ordered state of vortex structure in 2H-NbSe 2 single crystals

Current driven transition from a highly pinned metastable disordered phase (DP) to a more ordered equilibrium phase (EP) of vortex structure has been investigated in the peak effect regime of weakly pinned type-II superconductor 2H-NbSe 2. Critical current density ( J c) in DP shows a maximum at the onset of the peak effect (i.e. for applied field H = H on), where J c in the EP is observed to be minimum. Time needed for the transition depends exponentially on the transport current. A model to describe the kinetics of the transition is presented. Time dependence of voltage and the current dependence of relaxation time obtained from experiments are in good agreement with the model. Energy barrier ( U 0) characterizing the relaxation process extracted from the model also shows a peak at H on. Peaks in J c in the DP and U 0 have been qualitatively understood in terms of the interplay between elastic and pinning forces.

Dynamical melting and mode locking of vortex matter in 2H-NbSe2 pure single crystals

We have investigated flow properties of vortex matter around the peak effect region in 2H-NbSe2 pure single crystals by mode locking (ML) techniques. ML is a dynamic synchronization phenomenon between ac drive superimposed on dc drive and collective lattice modes excited over the driven vortex lattice. Around the peak effect regime, we observe the vanishing of the ML resonance, which is velocity dependent: At small velocity, ML vanishes just below the peak field Hp for the peak effect, while at large velocity, it vanishes above Hp. The velocity dependence of the vanishing field agrees qualitatively with a dynamical melting picture proposed by Koshelev and Vinokur.

Peak Effect and Dynamic Melting of Vortex Matter inNbSe2Crystals

We present a mode locking (ML) phenomenon of vortex matter observed around the peak effect regime of 2H-NbSe2 pure single crystals. The ML features allow us not only to trace how the shear rigidity of driven vortices persists on approaching the second critical field, but also to demonstrate a dynamic melting transition of driven vortices at a given velocity. We observe the velocity dependent melting signatures in the peak effect regime, which reveal a crossover between the disorder-induced transition at small velocity and the thermally induced transition at large velocity. This uncovers the relationship between the peak effect and the thermal melting.

Vortex matter properties of carbon-substitutedMgB2single crystals

We have studied the vortex matter phase diagram in two carbon doped ${\mathrm{MgB}}_{2\ensuremath{-}x}{\mathrm{C}}_{x}$ ($x=0.04$ and 0.1) single crystals. We have found that, as in pristine ${\mathrm{MgB}}_{2}$, the peak effect is also present in carbon doped crystals. The regime where the peak effect is developed is more extended in comparison to the undoped crystal. The enhancement of the peak effect regime, combined with the higher ${H}_{c2}^{c}(0)$, makes doped ${\mathrm{MgB}}_{2}$ more favorable for practical applications. The absence of significant bulk pinning below the line ${H}_{\mathrm{on}}(T)$, which denotes the onset points of the peak effect, implies that the Bragg glass phase is present for $H<{H}_{\mathrm{on}}(T)$. Interestingly the end points ${H}_{\mathrm{ep}}(T)$ of the peak effect are placed well below the upper critical fields ${H}_{c2}(T)$. The unexpected absence of bulk pinning above the end-point line ${H}_{\mathrm{ep}}(T)$ of the peak effect implies the presence of a slightly pinned vortex phase in the regime ${H}_{\mathrm{ep}}(T)<H<{H}_{c2}(T)$.

Measurement of magnetic relaxation in the peak regime of V 3Si

Magnetization relaxation measurements are carried out in the peak effect regime of superconducting V 3Si crystal, using Quantum Design SQUID magnetometer. Relaxation in the increasing field scan is logarithmic in time, consistent with the theory of flux creep. The relaxation on the decreasing field scan however exhibits athermal behavior which is predominantly governed by the flux avalanches triggered by the small external field perturbation experienced by the superconductor during measurement scan in an inhomogeneous field.

Dynamic transition in driven vortices across the peak effect in superconductors

We study the zero-temperature dynamic transition from the disordered flow to an ordered flow state in driven vortices in type-II superconductors. The transition current ${I}_{p}$ is marked by a sharp kink in the $V(I)$ characteristic with a concomitant large increase in the defect concentration. On increasing magnetic field B, the ${I}_{p}(B)$ follows the behavior of the critical current ${I}_{c}(B).$ Specifically, in the peak effect regime ${I}_{p}(B)$ increases rapidly along with ${I}_{c}.$ We also discuss the effect of varying disorder strength on ${I}_{p}.$

STM imaging of flux line arrangements in the peak effect regime.

We present the results of a study of vortex arrangements in the peak-effect regime of 2H-NbSe2 by scanning tunneling microscopy. By slowly increasing the temperature in a constant magnetic field, we observed a sharp transition from collective vortex motion to positional fluctuations of individual vortices at the temperature which coincides with the onset of the peak effect in ac susceptibility. We conclude that the peak effect is a disorder driven transition, with the pinning energy winning against the elastic energy.

Irreversible magnetostriction and magnetization of superconducting 2H-NbSe2 single crystals in a peak-effect regime

Magnetostriction measurements in the mixed state of superconducting 2H-NbSe2 single crystals under in-plane magnetic fields 0–12 T have revealed a peak on the magnetostriction versus magnetic field dependences in the vicinity of the upper critical field Hc2. The peak value of the longitudinal magnetostriction is higher by more than an order of magnitude in comparison with that of the transverse magnetostriction when measured along the hexagonal axis. Analysis of the measured field dependences of the magnetostriction and magnetization of 2H-NbSe2 allows one to relate the observed peculiarities of magnetostriction with the loss of order in the lattice of Abrikosov vortices, which occurs by a first-order phase transition.

Disordered type-II superconductors: a universal phase diagram for low- Tc systems

A universal phase diagram for weakly pinned low- T c type-II superconductors is revisited and extended with new proposals. The low-temperature “Bragg glass” phase is argued to transform first into a disordered, glassy phase upon heating. This glassy phase, a continuation of the high-field equilibrium vortex glass phase, then melts at higher temperatures into a liquid. This proposal provides an explanation for the anomalies observed in the peak effect regime of 2H–NbSe 2 and several other low- T c materials which is independent of the microscopic mechanisms of superconductivity in these systems.