Session V40: Superconducting Vortices: Pinning & Lattice Effects

Complex vortex pinning landscape in YBCO: temperature- and orientation-dependent $J_{c}$ studies

Studying the temperature and field-orientation dependence of critical current density $J_{c}$ gives insight into vortex pinning. The orientation dependence of $J_{c}$ in YBa$_{2}$Cu$_{3}$O$_{\sim 7}$, containing both correlated disorder and localized `isotropic' defects, was determined at temperatures $T$ = 77 K to 5 K in magnetic fields up to $\mu _{0}H$ = 6 T. The inductive measurements ensured very low dissipation levels, with electric fields $E \quad \sim $ 10$^{-10}$ V/cm in the highly textured YBCO thin layers. The study revealed systematic changes in the orientation dependent $J_{c}$. At high temperatures, $J_{c}$ exhibited a \textit{peak} for \textbf{H} $\vert \vert $ $c$-axis; with decreasing $T$, the $J_{c}$ became almost independent of angle and at still lower temperatures, it exhibited a \textit{minimum} for \textbf{H} $\vert \vert $ $c$-axis. These findings are interpreted in terms of a competition between different types of pinning sites in a complicated pinning landscape. Research at ORNL sponsored by Div. Materials Sciences and Engineering, USDOE.   

Comparative study of flux creep in superconductors over a broad spectrum of pinning properties

Thermal fluctuations are responsible for the phenomenon of flux creep in type-II superconductors, which allows some level of vortex motion even when the current density is below the critical current density ($J_c$). Creep studies in the high temperature oxide superconductors (HTS) have been a topic of continuous attention since the discovery of these materials. The topic is of both fundamental interest, as HTS vortex matter exhibits a rich variety of dynamic regimes, and practical relevance, as creep reduces the``effective'' $J_c$ in wires that are used for power applications. To gain a more general understanding of creep phenomena we have performed comparative studies of the time relaxation of the ``persistent'' superconducting current, $J(t)$, in a variety of type-II superconductors. The $J(t)$ was determined from magnetization (via the critical state model) using a SQUID magnetometer. The materials studied include thin films and single crystals of HTS, pnictides, MgB$_2$ and conventional low T$_c$ superconductors. This allows the spanning of several orders of magnitude in $J_c$, in the fraction $J_c$/$J_0$, where $J_0$ is the depairing current density, and in the Ginzburg number ($G_i$), which measures the importance of thermal fluctuations. I will discuss the evidence for glassy or non-glassy relaxation in the various systems.   

Enhanced superconducting vortex pinning with disordered nanomagnetic arrays

We studied the effect of disorder on superconducting vortex pinning produced by arrays of artificial pinning sites. The magnetoresistance of samples with pinning configurations varying from a triangular array to an almost random distribution of pinning sites provides a controlled system for such studies. Interestingly even small degrees of order are sufficient to produce enhanced pinning at well defined magnetic fields. These effects increase with increasing order and evolve towards the expected magnetoresistance matching minima for a triangular array. Surprisingly, with increasing disorder the position of the first matching minimum decreases. Furthermore, additional matching minima with complex structures appear at higher fields.   

Vortex pinning by BaSnO$_{3}$--based correlated disorder in thick YBa$_{2}$Cu$_{3}$O$_{\sim 7}$ films: angular dependence of $J_{c}$ via contact-free methods

Pinning of vortices by second phase BaSnO$_{3}$ ``columnar defects'' has been studied in thick, $c$-axis oriented films of YBa$_{2}$Cu$_{3}$O$_{\sim 7}$, deposited epitaxially on (100) LaAlO$_{3}$. The dependence of the critical current density $J_{c}$ on orientation of the magnetic field was determined for temperatures $T$ = 77-5 K in applied magnetic fields $\mu _{0}H$ = 0-6 T. The contact-free inductive methods insured measurements at very low dissipation levels, with electric field $E \quad \sim $ 10$^{-10}$ V/cm. Results of this study will be compared and contrasted with findings for YBCO materials with a more complex pinning landscape from multiple defect types. Research at ORNL sponsored by Div. Materials Sciences and Engineering, USDOE. Work by CVV supported by AFOSR and Air Force Research Lab.   

The Significance of Edge-Barrier Pinning in Superconducting Bridges

Edge-barrier pinning in thin superconducting films provides additional pinning over that of the bulk pinning. When using bridges greater than 1 $\mu $m to determine the critical current density (J$_{c})$ of films, this additional pinning is typically ignored. However, theoretical and experimental data presented here indicate that this pinning enhancement is non-negligible with bridge widths of less than 100 $\mu $m and on par with the bulk pinning at a few microns. In the present study, bridges in YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ (YBCO) thin films were repeatedly narrowed to avoid issues of sample to sample variation. Bridge widths starting at 500 $\mu $m and 50 $\mu $m were patterned by photolithography with subsequent narrowing performed by photolithography and focused ion beam milling, respectively. Transport J$_{c}$ was determined after each bridge size. Theoretical analysis follows that of J.R Clem [e.g. Elistratov et al, Phys. Rev. B 66, 220506 (2002)]. Theoretical implications of the narrow bridge effect on J$_{c}$(H) and J$_{c}$(T) plots are not simple scalar changes. Based on these results presented here, two key points are: 1) J$_{c}$ data comparison among institutions using different bridge sizes can provide improper conclusions (similarly as not accounting for film thickness), and 2) the J$_{c}$(T) and J$_{c}$(H) curve shapes are skewed differently for different widths. The implication of these effects will be discussed.   

Vortex pinning in superconducting/ferromagnetic bilayer with tunable domain width

We have used magnetoresistance to determine the activation energy of flux pinning in superconducting/ferromagnetic bilayer, consisting of superconducting Nb and ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy, separated by a Si buffer layer. Using a novel demagnetization procedure we can acquire randomly oriented stripe domain pattern with a well-defined average domain width $L$. We show that depending on the value of $L$, the temperature, and the magnetic field, the activation energy for flux pinning may be either enhanced or suppressed by the interaction between the vortices and the magnetic moment of the domains. Despite the randomness of the domain structure, the activation energy shows maxima at some magnetic fields, indicating commensurability effects. Our results are consistent with the formation of $L$-dependent arrangements of vortices, such as the triangular vortex lattice for small $L$, and the single-vortex or double-vortex chain structures at larger $L$. Our work provides a comprehensive picture of the flux pinning in the superconducting/ferromagnetic bilayer.   

Pinning of Flux Lines by Planar Defects

The technologically most interesting property of type-II superconductors is their ability to carry a bulk current with as little dissipation as possible. The Lorentz force acts on flux lines and hence gives rise to dissipation. Pinning centers play an important role in preventing the flux line motion and sustaining superconductivity. We study the influence of grain boundaries on order and transport in type-II superconductors and find that they lead to a novel glassy phase, planar glass [1,2]. In this talk we will characterize the planar glass and discuss its stability with respect to point impurities and columnar defects. \newline [1] A. Petkovic and T. Nattermann, Phys. Rev. Lett. \textbf{101}, 267005 (2008), \newline [2] A. Petkovic, T. Emig and T. Nattermann, Phys. Rev. B \textbf{79}, 224512 (2009).   

Oscillatory vortex dynamics in weak-pinning channels with periodic constrictions

The dynamics of vortex flow in confined geometries can be explored with weak-pinning channels of superconducting a-NbGe surrounded by strong-pinning NbN channel edges. Periodic constrictions of the channel walls lead to strong oscillations of the critical current, which we observe through transport measurements of the vortex dynamics. We explore the role of the shape and periodicity of the confining potential, as well as intervortex interactions, by fabricating a variety of samples that me measure over a range of temperatures. For small magnetic fields, the measured critical currents are completely reversible with magnetic field, indicating that all of the vortices are confined to the weak-pinning channels. Beyond a certain threshold field, typically after at least several periods of the critical current oscillations, the critical current begins to exhibit magnetic hysteresis, characteristic of vortex entry into the strong-pinning NbN banks.   

Effects of charge density waves on flux dynamics in weak-pinning single crystals of NbSe$_{2}$ : free flux flow, flux-core size effects, and unexpected doubling of$ J_{c}(H)$ `peak effect'

The interaction of two different ordering schemes -- charge density waves (CDWs) and superconductivity -- is studied in high-quality samples of NbSe$_{2}$, particularly in the motion of magnetic flux quanta. More specifically, the study is on the effect of ``switching off'' the CDW phase -- effected by doping with Ta -- on the magnetic-field $H $dependence of: (i) the Lorentz-force-driven free flux flow (FFF) resistivity \textit{$\rho $}$_{f}$ associated with the ordered motion of vortices, and (ii) critical current density $J_{c}$. FFF is achieved for the first time in this material. The field dependence of \textit{$\rho $}$_{f}$ deviates from traditional Bardeen-Stephen flux flow and is more consistent with effects of flux \textit{core size }as predicted by Kogan and Zelezhina. However, the suppression of CDW's seems to have no significant effect on these properties. On the other hand, $J_{c}(H)$ shows a surprising \textit{double} peak for the CDW-suppressed sample --contrary to previous studies in which the $J_{c}$ peak was shown to \textit{disappear. }Possible mechanisms are discussed.   

Matching effect in a superconducting MoGe antidot array

MoGe antidot arrays - films containing periodic arrays of nanoscale holes with $\sim $100 nm spacing have been fabricated using anodized aluminum oxide as substrates. Pronounced matching effect (magnetoresistance oscillations) was observed at temperatures near the zero-field critical temperature. By comparing the magnetic field dependences of the resistance and critical temperature in various magnetic field directions, we find that the matching effect in our MoGe antidot arrays originates from hole-induced suppression of the critical temperature.   

Matching Effect and Dynamic Phases of Vortex Matter in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ Nanoribbon With a Periodic Array of Holes

Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ nanoribbons with a periodic square array of nanoscale holes were fabricated through focused ion beam milling. Systematic resistive measurements over an extended temperature range enabled us to investigate phenomena associated with the matching effect in a vortex matter with periodic pinning. We found a novel feature of the vortex matching effect, namely that it is enhanced near the melting field due to the presence of soft solids and a mixture of solid-liquid phases. We also observed driving current dependent appearance of the matching effect and striking features in the voltage-current behavior associated with various driven regimes of the vortex matter related to vortex dynamic phase transitions.   

Hysteresis in the RF-Induced Flux Lattice Annealing (RIFLA) of the superconducting state in Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-y}$

We report hysteresis in flux lattice (FL) annealing by an rf magnetic field for the cuprate superconductor Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-y}$. A strained FL is formed by placing the sample in the coil (inductance $L)$ of a tuned NMR probe circuit and rotating the coil and sample in a fixed \textbf{\textit{B}} at low temperature. A series of rf pulses in the coil generates an alternating magnetic field that anneals the FL. It decreases the sample's rf skin depth, which reduces $L$ and increases the resonant frequency ($f)$ of the probe. Rotation in small steps about an axis parallel to the CuO planes and perpendicular to \textbf{\textit{B}} with annealing after each step generates a peak in $f$ whose shape is the same for rotation in both directions (no rotation hysteresis) and is a maximum for \textbf{\textit{B}} parallel to the CuO planes. When rotation is done in both directions without annealing, the substantial hysteresis reported here occurs. This work was supported at UCLA by NSF Grants DMR-0334869 and DMR-0804625, and at U. Maryland by NSF Grant DMR- 0653535.   

Metastable Vortex Lattice Phases in MgB$_{2}$

We present results of recent small-angle neutron scattering (SANS) measurements in MgB$_{2}$ which reveal an unprecedented degree of vortex lattice (VL) metastability. Three different VL phases are observed, all of which have a triangular symmetry. At low fields the VL is aligned with the crystalline $a$-axis. At intermediate fields the VL rotates away from the $a$-axis, leading to two degenerate domain orientations. Once the rotation reaches 30\r{ } a single domain, high field VL is reformed, now aligned along the a*-axis. These three VL orientations are consistent with our earlier reports [R. Cubitt \textit{et al}., PRL \textbf{91}, 047002 (2003)]. Metastable configurations are obtained when crossing the equilibrium VL transition lines by cooling or heating in a constant field. At any given field and temperature the equilibrium VL can be obtained either by inducing vortex motion by a small amplitude field oscillation or by a zero field cooling (ZFC) procedure. The equilibrium VL phase diagram differ significantly from our earlier published report and from theoretical predictions [M.E. Zhitomirsky \textit{et al}., PRB \textbf{69}, 054508 (2004)]. The implications of these results and how they affect our understanding of two-gap superconductivity in MgB$_{2}$ will be discussed.