Vortex Distributions near Surface Steps

Flux dynamics in type-II superconductors is an important problem in condensed matter physics. Studies of vortex pinning and motion could lead to improved critical currents for technological applications, as well as address fundamental issues such as the nature of the complex vortex phase diagram. Much work has been performed in this area, often with measurements such as bulk magnetization and transport. However, to examine local flux behavior around isolated defects, such as surface steps, it is useful to image the vortices directly. One technique which is well suited for such work is the Scanning SQUID Microscope (SSM).

Our research group has a SSM which operates down to 2.5K with a Nb tri-layer dc SQUID and pickup loop, which we fabricate in our cleanroom. The pickup loop is scanned approximately 2mm above the surface and has a diameter of between 5mm and 10mm. The operation of the SSM is described on our SSM info page. For low vortex densities, the SSM can easily resolve individual vortices, as shown in upper right and lower images above, of vortex distributions in patterned Nb thin-films. When the intervortex spacing becomes on the order of the pickup loop radius, the vortex images merge together, but we can still measure variations in the local flux density as shown in the upper left image of a NbSe₂ crystal. In addition to imaging flux distributions, the SSM can be used as a local probe of flux dynamics. This can be accomplished by fixing the location of the pickup loop, e.g. near a defect, then monitoring the SQUID signal as a function of time.

We have been studying vortex behavior in several different systems: surface steps in NbSe₂ crystals, patterned steps in Nb thin-films, and patterned strips of Nb and weak-pinning amorphous MoGe thin films. Many of the uneditied images can be found on the SSM data page, although these are not notated with any of the parameters, such as field strength, temperature, transport current, etc.

The following contains a summary of the various experiments with edited and notated images and graphs.

We have studied the distribution of flux in the vicinity of surface steps in NbSe₂. The steps are formed when the crystals are cleaved, as different numbers of crystal layers peel off in different regions. Preliminary Scanning SQUID Microscope (SSM) images around these steps indicate highly nonuniform distributions of vortices upon field cooling the samples then removing the applied field. This work was motivated by the Bitter decoration work of Pardo et al (see references below), where similar flux distributions were measured, also in NbSe₂. The observed increase in flux density at the low side of the surface steps may be explained by an energy barrier for vortex motion due to the increase of the line energy for a vortex moving from a thin region (low side of step) to a thicker region (high side). This argument would suggest that vortices should be impeded in moving from a thin to thick region of a superconductor, but should move freely from a thick to thin region. Such a process has evoked the name, "vortex diode". Unfortunately, the surfaces of the NbSe₂ crystals we have looked at have been quite complex, and it is often difficult to determine the flux creep direction and correlate that with the surface step dimensions from our SSM images.

F. Pardo, F. de la Cruz, P.L. Gammel, E. Bucher, C. Ogelsby, D.J. Bishop, "Real Space Images of the Vortex Lattice Structure in a Type II Superconductor during Creep over a Barrier", PRL 79, 7 ('97), 1369.

B.L.T. Plourde, D.J. Van Harlingen, "Scanning SQUID Microscopy of Flux Distributions and Motion near Surface Features in NbSe₂"NATO ASI Proceedings, 356, 281 (1999).

Recently, we have fabricated various patterns of steps of controlled height in Nb thin films (1000Å-2000Å). With these samples, we know the size of the sample, as well as the exact size, location and orientation of the surface steps. The Nb films are first patterned into 2mm squares by Reactive Ion Etching (RIE). Steps are created by patterning a mask of etch windows onto the Nb squares using photolithography. The exposed Nb in the windows is partially etched to various depths (dependent on etch time) using RIE again. The layout of the square and the etch windows is given in the following diagram.

We have studied samples with this pattern made from both Nb and a-MoGe films in our SSM. Images are obtained by cooling the samples in various fields and imaging the flux distribution both with the field on and in zero field. The etched surface steps have a significant effect on the distribution of vortices in the square. Away from the steps, the vortices are uniformly spaced, with the separation governed by the cooling fields. Near the steps, the vortices are more densely packed at the low sides of the steps while the regions near the high side of the steps have fewer vortices. This effect has been observed in BSCCO crystals in Bitter decoration measurements by Vinnikov, et al.. We have imaged the vortex distribution around trenches etched in weak pinning a-MoGe films for different step heights and cooling field strengths. We then extract the vortex locations and produce averaged vortex density distributions across the width of the trench. These averaged traces show the peak in vortex density at the low side of the surface steps and the corresponding vortex-free region on the high side of the step. The width of these vortex-free regions is independent of the step height over the range of steps we have studied (25nm - 125nm, with the total thickness = 200nm). This width decreases with larger cooling fields, varying as B^-1/2.

Upon removing the cooling field, these vortex distributions around the Nb trenches do not change much, unlike the NbSe₂ measurements. This is most likely due to the much stronger pinning in our Nb films than in the NbSe₂ crystals. We have recently patterned these same geometries in weak-pinning MoGe films, where we expect the vortex patterns to change significantly with changes in the applied field. We have imaged field-cooled distributions of vortices in the MoGe samples, but we have not yet studied the vortex dynamics under field changes in these samples.

Field-cooled distributions around trenches in Nb (pdf)	Images (7/8/99) of 3 different 2mm wide Nb squares. Concentric octagonal trenches (100mm wide) of various depths (300Å , 500Å, 750Å) have been etched into the squares. Upon field-cooling, the vortices preferentially pin along the low side of the steps of the trench. The regions around the high side of the steps contain relatively few vortices.
Vortex lattice in MoGe square with no steps (pdf)	Image (11/22/99) of vortices in 2mm wide, 2000Å thick MoGe square. Because of the weak-pinning and long penetration length, the vortices are ordered into a lattice even at small fields (39mOe).
Field-cooled distributions around trenches in MoGe (pdf)	Images (10/20/99) of 2mm wide MoGe squares with different depth trenches.

Hongjie Dai, Jie Liu, Charles M. Lieber, "Surface Pinning and Grain Boundary Formation in Magnetic Flux-Line Lattices of BSCCO High-Tc Superconductors", PRL 72, 5 ('94), 784.

L.Ya. Vinnikov, T.L. Barkov, B. Irmer, K. Kragler, G. Saemann-Ischenko, "Vortex arrays in the BSCCO single crystals in the vicinity of steps on the sample surface", Physica C 308 ('98), 99.

We have also begun imaging and measuring the transport properties of thin SC strips, fabricated with a single longitudinal step of controlled height, as shown in this diagram. This should allow us to investigate the effect of the line tension energy barrier for a single surface step. If this barrier dominates the behavior, then the critical current which we measure through the strip should be different for opposite polarities of transport currents, as one direction would push vortices up the step (thin to thick) while the opposite polarity would push vortices down the step. Of course, in practice the situation is more complicated, as geometrical barriers at the edges due to the thin film strip geometry play a significant role.

Using the same fabrication described previously for the square thin-film samples, we pattern the SC thin-film into strips of various widths with leads for injecting currents and measuring voltages. One layout of strips has been optimized for experiments in the SSM and is shown in this diagram. We have studied 60mm and 150mm wide Nb strips in the SSM. Field-cooled images of the strips are similar to the images of the large Nb squares in the previous section. The presence of the step along the strip significantly alters the field-cooled flux pattern, with only a single row of vortices forming along the low side of the step for the smallest cooling fields. For larger cooling fields, the density in the initial row increases, and vortices fill in the rest of the strip, forming secondary rows parallel to the low-field row along the step. If we apply a small transport current to these field-cooled flux patterns, most of the vortices remain frozen in place, due to the strong pinning of the Nb films.

Because of the large value of H_c1 in Nb, flux entry is difficult to observe with the SSM, as the large fields hinder the resolution of individual vortices. We have observed flux entry due to the self-field of the transport current, with no applied external field, but this only occurs for large currents, where sample heating is significant. Thus instead of the expected Bean-like profile for flux entry into a strong-pinning film, we observe a highly nonuniform distribution of flux in the strip, which depends on the speed with which the current was increased, indicating some sort of thermomagnetic instability. Further investigations of the flux entry in Nb strips are planned, as well as studies of flux entry into other strong pinning films which have a smaller value of H_c1 than Nb.

The following pages give some of the preliminary results from the measurements on Nb strips:

Recently, we have fabricated the 150mm wide strip pattern in amorphous MoGe films from Rut Besseling in the research group of Peter Kes in Leiden, NL. These films have very weak pinning and H_c1 is much lower than that of Nb, so vortices enter the strips at much lower fields and relatively small transport currents shift the vortex distribution. Upon zero-field cooling then increasing the external field, vortices enter the strip when the field at the edge of the strip exceeds H_c1. For a strip with uniform thickness, these vortices are swept to the center of the strip by the screening currents, forming a dome-shaped distribution, with vortex-free regions near the edges. This behavior was predicted by Clem and Benkraouda. For a strip with a single longitudinal step, the same procedure produces an ordered single row of vortices along the low side of the step, forming a denser ridge of vortices for larger fields. Transport currents applied along the strip then shift the vortex distribution due to the Lorentz force. With a strip without a surface step, the vortex dome is shifted to either side depending on the polarity of the applied current. The motion of the vortex distribution in the strip with a step is highly asymmetric. Transport currents with the Lorentz force directed towards the step cause the vortex density at the low side of the step to increase, with relatively little flux on the thicker half of the strip. The opposite polarity of current, so that the Lorentz force is away from the step, pushes the flux away from the step and toward the edge on the thin side of the strip almost immediately.

vortex domes (pdf)	***New. Formation of vortex dome for 150mm MoGe strip with and without surface step.
shift of domes, no step (pdf)	***New. Shift of vortex dome in 150mm MoGe strip without surface step.
shift of domes, with step (pdf)	***New. Shift of vortex dome for 150mm MoGe strip with 400A surface step. Shifting is highly asymmetric with the transport current due to the step.

We are performing transport measurements on strips with and without steps outside the SSM to study the field dependence of the critical current. Preliminary measurements indicate an asymmetry with field for strips with a step, which could be related to the presence of extra screening currents flowing along the step surface.

In future runs, we will use the voltage leads on the strips in the SSM to measure the critical current of the strips and to correlate the I_c(H) curves with the corresponding images of the flux distribution. We also plan on utilizing the ability of the SQUID to resolve single vortices to measure the threshold Lorentz force for pushing flux over the step barrier. This will allow us to directly study the interaction of a single vortex with a defect (the surface step).

A preprint of our paper on these strip measurements for the M²S Conference Proceedings is available on our preprint website.

We have noticed a strange interaction effect between the scanning and the vortices. This effect is only manifested in the a-MoGe samples, where it is possible to push vortices around with the tip of the SSM. For stronger pinning Nb samples, we can scan a given region multiple times with the distribution of vortices unchanged. The interaction is definitely localized at the contact point between the tip and the sample surface - vortices under the pickup loop (between 25mm and 100mm from the tip) are not disturbed. If we scan a region with an orientation such that the pickup loop images the vortices before they are passed over by the tip, we obtain a clean, unperturbed image of the vortex distributions. However, if we scan the same region again (without recooling through T_c), the vortices will be shifted around and generally pushed out to the edges of the scan range. Most of the a-MoGe images presented in our previous measurements were taken with this orientation of scanning, immediately after establishing the vortex state. We have not yet been able to identify the interaction mechanism - more experiments are planned. Some of the images of swept vortex regions are summarized on these pages:

The research group of Franco Nori at the University of Michigan has done extensive computer simulations of vortex dynamics, with particular emphasis on the collective effects of driven vortices interacting with various pinning distributions. An excellent summary of this research can be found on their website.

Maamar Benkraouda, John R. Clem, "Critical current from surface barriers in type-II superconducting strips", PRB 58 (1998), 15103.

Maamar Benkraouda, John R. Clem, "Magnetic hysteresis from the geometrical barrier in type-II superconducting strips", PRB 53 (1996), 5716.

Ernst Helmut Brandt, Mikhail Indenbom, "Type-II superconductor strip with current in a perendicular magnetic field", PRB 48 (1993), 12893.

H. Castro, B. Dutoit, A. Jacquier, M. Baharami, and L. Rinderer, "Experimental study of the geometrical barrier in type-I superconducting strips", PRB 59 (1999), 596.

M. E. Gaevski, A.V. Bobyl, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, M. Baziljevich, H. Bratsberg, S.F. Karmanenko, "Magneto-optical study of magnetic-flux penetration into a current-carrying high-temperature-superconductor strip", PRB 59 (1999), 9655.

J. Groth, C. Reichhardt, C. J. Olson, S. Field, Franco Nori, "Vortex Plastic Dynamics in Twinned Superconductors ", PRL 77, 3625 (1996).

C.J. Olson, C. Reichhardt, and Franco Nori, "Non-equilibrium Dynamic Phase Diagram for Vortex Lattices ", PRL 81, 3757 (1998).

C. Reichhardt, C. J. Olson, J. Groth, Stuart Field, and Franco Nori, "Microscopic Derivation of the Kim and Bean State in Pinned Superconductors ", PRB 52 10441 (1995).

C. Reichhardt, C. J. Olson, J. Groth, Stuart Field, and Franco Nori, "Flux Behavior in the Bose Glass Regime near the Mott Transition", PRB 53, R8898 (1996)

E. Zeldov, John R. Clem, M. McElfresh and M. Darwin, "Magnetization and transport currents in thin superconducting films", PRB 49 (1994), 9802.

Images of field-cooled 150mm Nb strip (pdf)	Recent (7/28/99) images of a 150mm wide Nb strip, both in the step region and in the uniform thickness region beyond the step.
Images of field-cooled 60mm Nb strip (pdf)	Recent (6/25/99) images of a 60mm wide Nb strip. The images are taken around the end of the step, i.e. the left 1/3 of the images are outside of the step region, while the step goes across the right 2/3, with the low side of the step near the top of the image.
Flux entry in 150mm Nb strip (pdf)	Images of a 150mm wide Nb strip with a 550A step. The strips were zero-field cooled, then the transport current was gradually applied, eventually resulting in nonuniform flux entry due to the self-field. Black and white patches correspond to flux bundles (of + and - vortices) with vortex spacings much smaller than the resolution of our SSM.