Observation of the flux-antiflux boundary propagation during magnetization reversal inBi 2 Sr 2 CaCu 2 O 8 + δ with single vortex resolutionA. Schwarz, U. H. Pi, M. Liebmann, R. Wiesendanger, Z. G. Khim, and D. H. Kim Citation: Applied Physics Letters 88, 012507 (2006); doi: 10.1063/1.2161815 View online: http://dx.doi.org/10.1063/1.2161815 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in On the roles of Bi2Sr2CuOx intergrowths in Bi2Sr2CaCu2Ox/Ag round wires: c-axis transport and magnetic fluxpinning Appl. Phys. Lett. 104, 152602 (2014); 10.1063/1.4871805 Flux-flow behaviors on a Bi 2 Sr 2 Ca Cu 2 O 8 + δ (Bi-2212) stack J. Appl. Phys. 103, 07C716 (2008); 10.1063/1.2840612 ‘Flux Waves’ in Bi2Sr2CaCu2O8+δ AIP Conf. Proc. 850, 793 (2006); 10.1063/1.2354943 Thermally assisted flux flow and individual vortex pinning in Bi 2 Sr 2 Ca 2 Cu 3 O 10 single crystals grown bythe traveling solvent floating zone technique J. Appl. Phys. 97, 10B114 (2005); 10.1063/1.1855531 Flux pinning and dissipation in textured multifilamentary ( Bi–Pb ) 2 Sr 2 Ca 2 Cu 3 O x / Ag tapes J. Appl. Phys. 89, 3861 (2001); 10.1063/1.1353560

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Observation of the flux-antiflux boundary propagation during magnetizationreversal in Bi2Sr2CaCu2O8+� with single vortex resolution

A. Schwarz,a� U. H. Pi, M. Liebmann,b� and R. WiesendangerInstitute of Applied Physics and Microstructure Research Center, University of Hamburg,Jungiusstrasse 11, 20355 Hamburg, Germany

Z. G. KhimSchool of Physics, Seoul National University, Seoul 151-742, South Korea

D. H. KimDepartment of Physics, Yeungnam University, Kyungsan 712-749, South Korea

�Received 21 June 2005; accepted 2 December 2005; published online 5 January 2006�

Snapshots of the flux distribution during magnetization reversal of a high-temperaturesuperconductor Bi2Sr2CaCu2O8+� single crystal in the presence of artificial columnar defects wererecorded using magnetic force microscopy. Thereby, the flux-antiflux boundary width and itsdisplacement by annihilation of individual vortex-antivortex pairs could be visualized. In general theflux density follows Bean’s model. However, step dislocations with a strongly anisotropic pinningbehavior lead locally to a nonmonotonous flux distribution and result in a delay of the boundarypropagation. © 2006 American Institute of Physics. �DOI: 10.1063/1.2161815�

During magnetization reversal of type II superconduct-ors, regions occupied by vortices of opposite polarity areseparated by a flux-antiflux boundary. Flux penetration intothe specimen and the general features of the reversal processare described by the longitudinal1 and transversal2 Beanmodel, respectively. Its basic statement is that the currentdensity J=��Ha, which is induced at the surface to excludethe externally applied magnetic field Ha, exerts a certain Lor-

entz force density F̄L=J� B̄ on the penetrating local average

magnetic flux density B̄. Thereby, the flux is displaced fromthe sample edges towards the center, whenever the critical

current density Jc is reached and F̄L exceeds the mean pin-

ning force density F̄pin, which originates from sample imper-fections. If the field magnitude is reduced, vortices leave thesample starting from the edges. If the field direction is re-versed, vortices of opposite polarity �antivortices� penetratefrom the edges, whereby a flux-antiflux boundary is intro-duced into the sample. Note that the Bean model neglectsflux quantization, averages over distances much larger thanthe intervortex spacing, and does not discriminate betweendifferent types of defects. Therefore, this model does notmake any statements about the fine structure of the boundaryregion, where vortices and antivortices coexist, and the in-fluence of different types of defects.

An understanding of the magnetization process and theinfluence of pinning is mandatory to develop devices basedon superconducting materials. Naturally, high-temperaturesuperconductors are of particular interest. Up to now,magneto-optical means have been employed to investigateflux distributions with respect to the Bean model in suchmaterials �see, e.g., Jooss3 for a review�, but the resolution isdiffraction limited. On the other hand, magnetic force mi-croscopy �MFM� has proven its capability to detect indi-

vidual vortices via their magnetic field in the low flux den-sity regime.4 If the magnetic fields of neighboring vorticesstrongly overlap �high flux density regime�, flux densityvariations can still be imaged, because the MFM signal isproportional to the magnetic field generated by the totalflux.5 Moreover, this technique allows to image the surfacetopography with high resolution, e.g., monoatomic stepheights are easily resolved, whereby structural defects can beexamined with respect to their pinning properties.5,6 Here wepresent a MFM study of the flux-antiflux boundary propaga-tion during magnetization reversal of a Bi2Sr2CaCu2O8+�

single crystal platelet. Since single vortex resolution is ob-tained, information beyond the Bean model becomes directlyaccessible.

All experiments have been performed with our homebuilt force microscope �Hamburg design�,7 which is operatedin ultrahigh vacuum, at a base temperature of 5.2 K and in anexternally applied magnetic field up to �0Ha=Ba=5 T. Acantilever with a ferromagnetic iron coated tip at its free endis utilized to detect the tip-sample interaction via the fre-quency modulation technique. Surface topography as well asmagnetic properties can be probed with appropriate data ac-quisition schemes. To record MFM images we chose a scanheight h of about 18 nm and a cantilever oscillation ampli-tude A=10 nm. Details of the experimental setup, proce-dures, modes of operation can be found in Ref. 7.

The Bi2Sr2CaCu2O8+� single crystal �about a�b�c=2.2 mm�0.72 mm�0.048 mm in size� was grown by afloating zone method and then irradiated with 1.3 GeV ura-nium ions to form artificial columnar defects8 parallel to thec axis. They act as strong pinning centers.5 The ion dosecorresponded to a matching flux density of Bm=2 mT. Fur-thermore, stacking fault dislocations, which exhibit an aniso-tropic pinning behavior,9 are present in the investigatedcrystal.

Tip axis, crystal c axis and magnetic field direction areoriented normal to the sample surface �z direction�. Aftermagnetizing the tip in Ba= +100 mT parallel to the tip axis,the sample was field cooled from above Tc down to T

a�Author to whom correspondence should be addressed; electronic mail:aschwarz@physnet.uni-hamburg.de

b�Present address: II. Department of Physics, RWTH Aachen, 52056 Aachen,Germany.

APPLIED PHYSICS LETTERS 88, 012507 �2006�

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=5.2 K in Ba=BFC=−3 mT. Then, Ba was ramped stepwisefrom −3 to +50 mT. To study the magnetization reversal andin particular the mechanisms of the boundary displacement,snapshots of the vortex configuration were recorded for eachBa on the same sample area. Four of them are displayed inFigure 1�a�–1�d�. For comparison, the flux density Bz�x� andits evolution with increasing Ba according to the one-dimensional Bean model is sketched in �e�.

The glass-like random vortex configuration after fieldcooling is imaged in �a�. Since MFM detects the magneticfield associated with the quantum flux �0=2 ·10−15 T m−2,each vortex appears as a dot with a radius on the order of theLondon penetration depth � �for Bi2Sr2CaCu2O8 ��200 nm�. The dark contrast indicates a repulsive tip-vortexinteraction, i.e., tip magnetization and vortex polarity are an-tiparallel. The total number of N=BFC·ascan/�0=62 vortices

corresponds reasonably well to BFC=−3 mT and the scanarea ascan=49 �m2. Four strong pinning sites are marked bycrosses, to evalute their role during magnetization reversal.For the same reason, the barely visible faint line is markedby two arrows. At the corresponding position in the topogra-phy image a step with a height of about �0.36±0.05� nm wasfound at exactly that position. Previously, we identified suchstraight steps with heights less than the surface cleavage stepheight of c /2=1.55 nm as stacking fault dislocations andreported a strongly anisotropic pinning behavior.9 After ap-plying a field opposite to the direction during field cooling,antivortices enter the sample from the edges, where the mag-netization reversal due to individual vortex-antivortex anni-hilation processes starts. At 30 mT the first antivortices enterthe scan area. In �b� the situation at 32.5 mT is shown. Theincoming antivortices �bright contrast due to the attractivetip-vortex interaction� already penetrated the scan area fromthe right. The four crosses mark the same strong pinningsites as identified in �a�. While the two on the left are stilloccupied by vortices, the one between the two parallel whitelines is empty and the right one is already occupied by anantivortex. Vortices and antivortices are well separated fromeach other by an about 1-�m-wide zone of zero vortex den-sity marked by two parallel white lines, where neither vorti-ces nor antivortices are detected. The following propagationmechanism can be inferred: In the boundary region flux clo-sure is achieved by the formation of vortex-antivortex loops.Since the antivortices are driven towards the sample centerby the Lorentz force, their radii shrink with increasing Ba.Finally, the loop collapses below a certain radius, if its elasticenergy becomes larger than its pinning energy. Thereby, avortex-antivortex pair is annihilated. The remaining emptycolumnar defect is reoccupied by another mobile incomingantivortex. Note that the loop is rather asymmetric, sinceonly the mobile antivortex part moves towards the ratherfixed strongly pinned vortex part.

The width w of the zone of zero vortex density is relatedto the range of the attractive vortex-antivortex force FV-AVand the pinning force. The attraction between vortices ofopposite polarity can be approximated using FV-AV=−L ·�0

2 / �4��0�2� ·K0��r /��. Here, r is the vortex-antivortexseparation, L is the length of the vortex line, and K0��r /�� isthe derivative of the modified Bessel function, which has theform K0�r /��= ��� /2r�1/2 ·e−r/� for r��.10 Since FV-AV de-cays exponentially, the characteristic decay length � ,w isexpected to be not much larger than a few �, which agreeswell with our observation of w�5�. Using r=w and L=c,i.e, the platelet thickness, an attractive force of 7 pN can beestimated, which should correspond approximately to thepinning strength of the mobile incomming vortices. Note fur-ther that since the typical lateral dragging force exerted bythe scanning tip on a vortex is only about 1.5 pN in ourexperimental situation,11 the influence of the measurementprocedure on the genuine vortex arrangement is negligible.

In �c� the antivortex front has reached the stacking faultdislocation �see arrows�. It now appears as a bright strip. In aprevious investigation9 we found vortices are quite mobilealong such line defects, while they are strongly trapped in theperpendicular direction. For an attractive tip-vortex interac-tion, vortices are attracted towards the tip if scanned acrossthe line defect, whereby the whole dislocation step appearsbright, even if only a few vortices are attached to the linedefect. If the tip-vortex interaction is repulsive, as in �a� and

FIG. 1. �a� MFM image of the flux glass state after field cooling in BFC=−3 mT �scan area: ascan=7 �m�7 �m�. �b� After increasing Ba to 32.5 mT,the flux-antiflux boundary is visible as zone of zero vortex density betweenthe parallel lines separated by w�1 �m. �c� At 42.5 mT the antivorticeshave reached the line defect �marked by arrows�, which now appears asbright strip. �d� The situation after complete magnetization reversal of thescan area. �e� Sketch of the experimental situation according to the one-dimensional transversal Bean model.2 Flux penetration Bz�x� �mirror sym-metric with respect to the sample center at x=0� with increasing field andpropagation of the boundary �see arrows� with respect to the scan area isshown. The dashed line corresponds to the homogeneous flux density afterfield cooling. �f� Averaged cross section taken perpendicular to the linedefect in the boxed area from �d�. Due to the stacking fault dislocations, theflux density does not change monotonically.

012507-2 Schwarz et al. Appl. Phys. Lett. 88, 012507 �2006�

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�b�, vortices are pushed to the side along the line defect andare therefore not imaged. Note further, that on the left side ofthe line defect only a few individual antivortices are visible,while their density is much larger on the right side. Thisinhomogeneous distribution occurs because the line defectcan accommodate a large amount of vortices, which thenrepel vortices of the same polarity. Clearly, the advance ofthe flux-antiflux boundary is severely hindered by the pres-ence of a continuous line defect perpendicular to the propa-gation direction than by a porous random distribution ofpoint-like defects.

Further increasing of Ba results in a complete magneti-zation reversal of the imaged area, as visible in �d�. Thevortex density is so large that only the strongly pinned vor-tices can be identified, because they repel the more mobilevortices, leaving a dark ring around them. According to thetransversal Bean model sketched in �e�, the vortex densitybetween the flux-antiflux boundary and the sample edgesshould decrease monotonically towards the sample center.Since the magnitude of the MFM signal is proportional to themagnetic field generated by the vortices, flux density varia-tions can still be detected.5 In �f� the average cross sectiontaken perpendicular to the incoming vortex front from theboxed area in �d� is displayed. Right to the line defect asteady decrease of the vortex density towards the samplecenter is observed. On the line defect itsself the density isenhanced, but reduced in the vicinity, due to the repulsionbetween vortices of the same polarity. Thereby, a nonmono-tonic flux distribution is induced near the stacking fault dis-locations. It can be concluded that randomly distributed pointdefects result in a vortex distribution as predicted by theBean model, while strong deviations are induced by ex-tended line defects, which can accomodate a large number ofvortices.

In summary, we demonstrated that MFM is a suitabletechnique to visualize the dynamics of the magnetization re-versal and particularly the propagation of the flux-antifluxboundary in type II superconductors with single vortex reso-lution. In our case the boundary consists of a 5� wide zoneof zero vortex density, which propagates by annihilation ofvortex-antivortex pairs. Line defects with a strong pinningeffect delay a transversal movement of the boundary andcause a nonmonotonic flux distribution in their vicinity aftercomplete magnetization reversal. In regions with columnardefects the resulting flux density decreases monotonously to-wards the sample center, as predicted by the Bean model.

Financial support from the DFG and from the NSI�NCRC� program of KOSEF, Korea, is gratefully acknowl-edged.

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012507-3 Schwarz et al. Appl. Phys. Lett. 88, 012507 �2006�

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