Critical Vortex Velocity Research Articles

Influence of thickness and domain structure on the vortex instability of superconducting/ferromagnetic bilayers

We report on the vortex instability in superconducting/ferromagnetic (FM) bilayers. Samples consisting of a 23 nm thick Mo2N superconducting layer with a capping layer of Co, Fe20Ni80, or FePt ferromagnets were grown by sputtering at room temperature on silicon (100). Our study reveals that the critical vortex velocity in these superconducting bilayers is significantly influenced by the thickness of the FM layers rather than the specific magnetic domain structure. When comparing samples with FM layers of 10 nm and 50 nm thickness, we observe a notable increase in vortex velocities at low magnetic fields, with speeds rising from approximately 3.5 km s−1 to around 6 km s−1 as the thickness increases. This trend extends to moderate and high magnetic fields. Furthermore, we establish a direct correlation between vortex velocities and the thermal conductance of the FM layers. These findings provide valuable insights for the interplay of magnetic and thermal properties within these hybrid systems, with potential implications for the design of future devices and applications.

Vortex dynamics in amorphous MoSi superconducting thin films

Vortex dynamics in superconductors have received a great deal of attention from both fundamental and applied researchers over the past few decades. Because of their critical role in the energy relaxation process of type-II superconductors, vortex dynamics have been deemed a key factor for the emerging superconducting devices, but the effect of irradiation on vortex dynamics remains unclear. With the support of electrical transport measurements under external magnetic fields and irradiation, the photon effect on vortex dynamics in amorphous MoSi (a-MoSi) superconducting thin films is investigated in this work. The magnetic-field-dependent critical vortex velocity v* derived from the Larkin–Ovchinnikov (LO) model is not significantly affected by irradiation. However, vortex depinning is found to be enhanced by photon-induced reduction in the potential barrier, which mitigates the adverse effect of film inhomogeneity on superconductivity in the a-MoSi thin films. A thorough understanding of the vortex dynamics in a-MoSi thin films under the effect of external stimuli is of paramount importance for both further fundamental research in this area and the optimization of future superconducting devices.

Quasiparticle scattering time in NbN superconducting thin films

A deep understanding of the quasiparticle inelastic scattering rate in superconducting materials is beneficial for the further development of ultrasensitive and rapid superconducting detectors. From the flux flow instability in current–voltage characteristics of NbN superconducting films, we have derived the critical vortex velocity (ʋ*) and quasiparticle inelastic scattering time (τE) of the 10- and 15-nm-thick NbN films at different magnetic fields and temperatures within the framework of the Larkin–Ovchinnikov model. The critical vortex velocity drove the transition from the power law ʋ* ∝ B−1/2 dependent to field-independent behavior where the nonequilibrium quasiparticles are uniformly distributed. The inelastic scattering time of quasiparticles obeys T−n temperature dependence, where the exponents are 2.5 and 2.3 for the 10 and 15-nm-thick NbN films, respectively. As the thickness of the film decreases from 15 to 10 nm, a reduction of τE from 88 to 12 ps is observed at 8 K. Moreover, the small value of τE for ultra-thin films can be associated with the low-average value of the superconducting gap, which is precisely what the detector needs.

Critical phenomenon of vortex motion in superconductors: Vortex instability and flux pinning

We have studied vortex dynamics in superconducting materials at very high vortex velocities as a function of the applied magnetic field. High velocity vortex dynamics can become critical, so that an instability occurs, leading the system to quench abruptly to the normal state. The presence of pinning mechanisms in all superconductors not only is able to foster high critical currents but it can strongly influence vortex flow, thus determining a different behavior of the critical vortex velocity v*. The magnetic field dependence of v* is extremely sensitive to the type of material pinning, and this is crucial for an applicative point of view, since vortex motion approaching v* means a dissipative flux flow state which will probably end with a flux flow instability. If it is possible to predict these critical parameters, than it will be easier to control those critical phenomena. Although a fully theoretical model of flux flow instability in the presence of pinning is still lacking, a phenomenological approach has been recently proposed for the hot-electron vortex flow instability. Here we present a successful example of perfect correspondence between experiment and theoretical approach in the case of Mo3Ge thin films with and without geometrical pinning barriers.

Speed limit to the Abrikosov lattice in mesoscopic superconductors

We study the instability of the superconducting state in a mesoscopic geometry for the low pinning material Mo$_3$Ge characterized by a large Ginzburg-Landau parameter. We observe that in the current driven switching to the normal state from a nonlinear region of the Abrikosov flux flow, the mean critical vortex velocity reaches a limiting maximum velocity as a function of the applied magnetic field. Based on time dependent Ginzburg-Landau simulations we argue that the observed behavior is due to the high velocity vortex dynamics confined on a mesoscopic scale. We build up a general phase diagram which includes all possible dynamic configurations of Abrikosov lattice in a mesoscopic superconductor.

Influence of artificial pinning on vortex lattice instability in superconducting films

In superconducting films under an applied dc current, we analyze experimentally and theoretically the influence of engineered pinning on the vortex velocity at which the flux-flow dissipation undergoes an abrupt transition from low to high resistance. We argue, based on a nonuniform distribution of vortex velocity in the sample, that in strongly disordered systems the mean critical vortex velocity for flux-flow instability (i) has a nonmonotonic dependence on magnetic field and (ii) decreases as the pinning strength is increased. These findings challenge the generally accepted microscopic model of Larkin and Ovchinnikov (1979 J. Low. Temp. Phys.34 409) and all subsequent refinements of this model which ignore the presence of pinning centers.

Regimes of flux transport at microwave frequencies in nanostructured high-Tcfilms

We report on combined dc and microwave electronic measurements of magnetic flux transport in micron and submicron-patterned high-${T}_{c}$ films. In a given temperature regime below the superconducting transition temperature ${T}_{c}$, the current-driven flux transport is restricted to flux motion guided by the submicron patterns. Via frequency-dependent measurements of the forward transmission coefficient ${S}_{21}$ it is demonstrated that the mechanism of the guided flux transport depends on the microwave frequency and the geometrical size of the superconducting structures. At low frequencies, flux is transported via Abrikosov vortices leading to additional microwave losses. Above a geometrically defined frequency, a different mechanism seems to be responsible for flux transport that does not contribute to the microwave losses and most likely represents a phase-slip type mechanism. The limiting vortex velocity obtained from the frequency dependence of the microwave properties agrees with the Larking-Ovchinnikov critical vortex velocity that is determined via dc pulse measurements. In spite of the change of mechanism, guidance of flux persists in these nanopatterns up to high frequencies of several GHz.

Flux transport in nanostructured high-Tc films at microwave frequencies

The understanding of flux transport in micro- and nanostructured superconducting systems that are exposed to an electromagnetic field at microwave frequencies is of interest for basic aspects of vortex matter and for potential application of superconductivity in fluxonic devices. We report on the combination of dc and microwave electronic measurements on submicron-patterned high-Tc films. The frequency dependence of the forward transmission coefficient S21 indicates that the mechanism of flux transport depends on the velocity of vortices. At low frequencies, flux transport via Abrikosov vortices is present leading to additional microwave losses. Above a geometrically defined frequency, a different, loss-free mechanism seems to be responsible for flux transport. This mechanism most likely represents a phase-slip type of mechanism. The limiting vortex velocity obtained from the frequencies dependence of the microwave properties agrees with the Larkin–Ovchinnikov critical vortex velocity determined via dc pulse measurements. In spite of the change of mechanism, guidance of flux persists in these nano-patterns up to high frequencies.

Non-linear Flux Flow Resistance of Type-II Superconducting Films

We analyze the flux-flow (FF) regime in type-II superconducting films exhibiting quite strong pinning. By driving the vortex lattice (VL) up to high dissipative states, the moving VL undergoes an instability, leading to an abrupt change from the FF to the normal state, which is displayed in the current-voltage characteristics as a voltage jump at a critical vortex velocity v ∗. The temperature and magnetic field dependence of v ∗ is investigated in different materials, and an unpredicted low field behavior of v ∗(B) is found. Moreover, for velocities lower than v ∗, a non-linear FF resistance is observed, with a “peak” in the current dependence of the dynamic resistance. This is a remarkable feature of a dynamic transition from disordered to ordered VL occurring in the FF state. We suggest that both unusual effects observed in v ∗(B) and R FF(I) can be accounted for intrinsic pinning.

Magnetic field and temperature dependence of the critical vortex velocity in type-IIsuperconducting films

We study the vortex dynamics in the instability regime induced by high dissipative stateswell above the critical current in Nb superconducting strips. The magnetic field andtemperature behavior of the critical vortex velocity corresponding to the observed dynamicinstability is ascribed to intrinsic non-equilibrium phenomena. The Larkin–Ovchinnikov(LO) theory of electronic instability in high velocity vortex motion has been applied tointerpret the temperature dependence of the critical vortex velocity. The magnetic fielddependence of the vortex critical velocity shows new features in the low-field regime notpredicted by LO.

X-ray imaging of the dynamic magnetic vortex core deformation

The creation and annihilation of magnetic vortex–antivortex pairs has been predicted to have a role in magnetic switching in permalloy nanostructures, but has never previously been observed. High-speed X-ray microscopy now enables the evolution and dynamics of this process to be studied in detail. Magnetic thin-film square- or disc-shaped nanostructures with adequate dimensions exhibit a magnetic vortex state: the magnetization vectors lie in the film plane and curl around the structure centre. At the very centre of the vortex, a small, stable core exists where the magnetization points either up or down1,2. The discovery of an easy core reversal mechanism3 did not only open the possibility of using such systems as magnetic memories, but also initiated the fundamental investigation of the core switching mechanism itself4,5,6,7,8,9,10,11,12,13,14,15. Theoretical modelling predicted that the reversal is mediated by the creation and annihilation of a vortex–antivortex pair3,4,16, but experimental support has been lacking until now. We used high-resolution time-resolved magnetic X-ray microscopy to experimentally reveal the first step of the reversal process: the dynamic deformation of the vortex core. In addition, we have measured a critical vortex velocity above which reversal must occur5,17. Both observations support the previously proposed reversal mechanism.

Flux flow velocity instability in wide superconducting films

To understand energy losses related to vortex high velocity we study the critical voltage in the current-voltage (I-V) characteristics above which in the flux flow regime a sudden voltage jump appears. Different mechanisms have been proposed to account for the existence of a critical vortex velocity corresponding to the observed instability, such as heating effects or intrinsic non equilibrium phenomena. Nevertheless experimental studies of flux flow instabilities in wide superconducting films have been less investigated. We report on critical voltage measurements in Nb wide superconducting strips. We perform I-V measurements as function of magnetic field by using different bias modes (sweeping, compensated long and short pulsing). The magnetic field dependence of the critical voltage shows different features in the three operation modes. We quantitatively estimate self-heating effects taking into account cryogenic stabilization criteria and thermal diffusion calculations, and we demonstrate that the observed dynamics instabilities are not triggered by Joule self-heating. The Larkin–Ovchinnikov (LO) theory of non linear effects in the vortex motion has been then applied to interpret the critical velocity results. The magnetic field dependence of the vortex critical velocity shows some discrepancies with the LO predicted behaviour.

Energy relaxation at a hot-electron vortex instability

At high dissipation levels, vortex motion in a superconducting film has been observed to become unstable at a certain critical vortex velocity ${v}^{*}$. At substrate temperatures substantially below ${T}_{C}$, the observed behavior can be accounted for by a model in which the electrons reach an elevated temperature relative to the phonons and the substrate. Here we examine the underlying assumptions concerning energy flow and relaxation times in this model. A calculation of the rate of energy transfer from the electron gas to the lattice finds that at the instability, the electronic temperature reaches a very high value close to the critical temperature. Our calculated energy relaxation times are consistent with those deduced from the experiments. We also estimate the phonon mean free path and assess its effect on the flow of energy in the film.

Flux-Flow Resistivity Anisotropy in the Instability Regime of thea−bPlane of Epitaxial SuperconductingYBa2Cu3O7−δThin Films

Measurements of the nonlinear flux-flow resistivity rho and the critical vortex velocity vphi* at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov (Z. Eksp. Teor. Fiz 68, 1915 (1975) [Sov. Phys. JETP 41, 960 (1976)]) are reported along the node and antinode directions of the d-wave order parameter in the a-b plane of epitaxial YBa2Cu3O7-delta films. In this pinning-free regime, rho and vphi* are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of rho is almost independent of temperature and field. We attribute the observed results to the anisotropic quasiparticle distribution on the Fermi surface of YBa2Cu3O7-delta.

Charge carrier dynamics and the critical vortex velocity in high-T c superconductors

Charge carrier dynamics and the critical vortex velocity in high-T c superconductors

Charge carrier dynamics and the critical vortex velocity in high-Tc superconductors

A model is presented to explain the recently observed voltage jumps in Bi 2 Sr 2 CaCu 2 O 8+δ superconducting thin films. The present approach provides additional evidence of the validity of the flux-flow instability model. The field and temperature dependences of the critical vortex velocity were attributed to the physics of the vortex core in clean superconductors (high-T c superconductors) which is very different from the physics of the vortex core in dirty superconductors. The quasiparticle diffusion coefficient D qp was calculated based on the assumption that the quasiparticle motion is considered as a transport phenomenon on random walks. In addition, the effects of scattering of normal excitations by quasiparticles localized in the vortex core moving together with the vortex on the inelastic scattering time of quasiparticles τ in was also calculated. The predictions of the model and the experimental observations are in excellent agreement.

Vortex Dynamics and Instabilities in Layered and Homogeneous Ta/Ge Superconductors

We present measurements of a dynamically induced instability in the vortex state of an amorphous multilayer and a single alloy layer of Ta/Ge. The critical vortex velocity shows quantitative agreement with the predictions of Larkin and Ovchinnikov calculated using parameters determined independently from the normal state resistivity data. Both samples show a weak field dependence in the critical velocity implying a velocity dependent pinning force in the vortex solid state and a broadening of the transition resulting from the velocity distribution in the liquid state.

Anisotropy of a vortex instability observed at high current densities in YBa2Cu3O7δ superconducting films

Experimental data are provided for YBaCuO films that an instability of the vortex system, which manifests itself by a voltage jump at a critical current I*, exhibits strong anisotropy if the magnetic field is tilted from parallel to perpendicular to the c-axis. The angular dependence of I* can be well described by a model emphasizing the component of the magnetic field parallel to the c-axis. If the current range is restricted to values close to I*, the current-voltage characteristics below the instability show a satisfactory agreement with the prediction of the theory of ‘Self-Organized Criticality’ (SOC). In terms of this theory it is possible to relate the critical vortex velocity v* to the temperature and field dependent characteristic size of the underlying vortex avalanches. If, however, standard Larkin-Ovchinnikov theory is applied to describe the instability, this critical velocity is related to the scattering rate of quasiparticles. Analyzed in this way and assuming an isotropic diffusion constant of the quasiparticles, an anisotropic scattering rate and its temperature dependence can be extracted.

Influence of He Ion bombardment at medium energies on the vortex instability at high current densities observed in YBaCuO films

Isothermal current-voltage (I - V) characteristics of c-axes oriented YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} films taken in different external magnetic fields {mu}{sub 0}H, exhibit voltage jumps at a well defined current density J{sup *}(T, H) pointing to a specific instability of the vortex system. Interpreted as Larkin- Ovchinnikov (LO)-instability, this behavior allows to extract the inelastic scattering time {tau}{sub in} of quasiparticles. In the present work, the LO-analysis is applied to study the effect of additional defects on {tau}{sub in}. For this purpose, YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} films were irradiated at 77K with increasing fluences {phi} of 350 keV He{sup +} ions. The I - V characteristics were determined in the temperature range 45K < T < 80K and in magnetic fields up to 5 Tesla. While J{sup *} as well as the superconducting transition temperature T{sub c} are significantly decreased by the ion bombardment, the critical vortex velocity as deduced from LO-theory is much less affected. If the temperature dependence of the extracted scattering times {tau}{sub in} is rescaled by plotting versus the reduced temperature t = T/T{sub c}({phi}), the results for all ion fluences fall on one common curve within the error bars. This leads to the conclusion thatmore » a universal quasiparticle density n{sub N}(t) dominates the scattering rate 1/{tau}{sub in}.« less