Direct observation of domain wall structures in curved permalloy wires containing an anti-notch
C.W. Sandweg, N. Wiese, D. McGrouther, S.J. Hermsdoerfer, H. Schultheiss, B. Leven, S. McVitie, B. Hillebrands, J.N. Chapman
aa r X i v : . [ c ond - m a t . m t r l - s c i ] F e b Direct observation of domain wall structures incurved permalloy wires containing an anti-notch
C.W. Sandweg, N. Wiese, D. McGrouther, S.J. Hermsdoerfer, H.Schultheiss, B. Leven, S. McVitie, B. Hillebrands, and J.N. Chapman Fachbereich Physik and Forschungsschwerpunkt MINAS, Technische Universit¨at Kaiserslautern,Erwin-Schr¨odinger-Straße 56, D-67663 Kaiserslautern, Germany Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom (Dated: October 24, 2018)The formation and field response of head-to-head domain walls in curved permalloy wires, fabri-cated to contain a single anti-notch, have been investigated using Lorentz microscopy. High spatialresolution maps of the vector induction distribution in domain walls close to the anti-notch havebeen derived and compared with micromagnetic simulations. In wires of 10 nm thickness the wallsare typically of a modified asymmetric transverse wall type. Their response to applied fields tan-gential to the wire at the anti-notch location was studied. The way the wall structure changesdepends on whether the field moves the wall away from or further into the notch. Higher fields areneeded and much more distorted wall structures are observed in the latter case, indicating that theanti-notch acts as an energy barrier for the domain wall.
PACS numbers: 75.60.Ch 75.70.-i
I. INTRODUCTION
The motion of domain walls (DWs) in small ferromag-netic elements has recently attracted much experimentaland theoretical interest due to their application potentialin magnetic logic [1] and data storage [2] as well as fortheir fundamental physical properties [3]. DWs interactdirectly with electric currents and magnetic fields andtheir manipulation is of specific interest for the develop-ment of ’domain wall’ electronics. Towards this end, acurrent-driven DW pendulum, working equivalently to agravitational pendulum, has been implemented recently,providing information on the effective mass of a DW [4].However, it is also important to know the structure of theDW as a number of different possibilities have been iden-tified in magnetic wires some 100s of nanometres in widthand made from a soft magnetic material such as permal-loy (Ni Fe ). In particular, transverse domain walls(TDWs), asymmetric transverse domain walls (aTDWs)and vortex domain walls (VDWs) have been the subjectof experimental and theoretical studies [5, 6]. Moreover,for wires with geometries close to the phase boundariesfor different wall types, transformation during the courseof an experiment is not unusual [7]. Hence direct ob-servation to follow variation in the structure of a DW isfrequently necessary.Characterization of magnetic domains and the struc-ture of the walls between them can be performed us-ing various techniques including magneto-optical Kerrmicroscopy, magnetic force microscopy, X-ray magneticcircular dichroism and Lorentz microscopy [8]. In thispaper, we report on Lorentz microscopy investigationsof DW formation and manipulation in curved permalloywires containing anti-notches or protuberances. Exper-imental results are compared with results obtained us-ing micromagnetic simulation. The reason for fabricatingnotches or anti-notches in magnetic wires is primarily to FIG. 1: (a) SEM image of the fabricated permalloy wires, (b)low-magnification bright field TEM image showing an anti-notch. provide locations where DWs can be pinned. For vari-ous applications it is important to know precisely whereDWs are located and also to know how the geometry ofthe notch affects the pinning potential. The latter quan-tity depends not only on the notch itself but also on theDW structure. For this reason we have also investigatedthe DW structure as a function of applied field until it ispulled free of the anti-notch, leaving the magnetizationon both sides aligned in a similar sense.
II. SAMPLE PREPARATION
The samples were produced using a combination ofelectron beam lithography and high vacuum evaporation.The required wire pattern was written in 120 nm thickPMMA (950K 4%) spun onto Si N ’window’ substratesof the kind used extensively in transmission electron mi-croscopy (TEM) [9]. Such substrates contain one or more100 µ m square regions of unsupported Si N , ∼
50 nmthick, and, as such, are essentially transparent to elec-
FIG. 2: (color online) Remanent states of the curved wirewith radius r = 5 µ m after saturation in a field parallel to the y -axis. (a) and (b), DPC images of the x - and y -componentsof magnetic induction, and (c), color induction map deducedfrom (a) and (b). trons. It is here that the wires to be studied were fabri-cated. After deposition of 10 nm of permalloy, lift-off ofthe PMMA in acetone left the desired pattern of wires.Figure 1 shows a scanning electron microscopy im-age of the sample. It comprises semi-circular wires withradii varying in steps of 5 µ m from 5 µ m to 50 µ m, thewire width being 500 nm. Such geometries are attrac-tive since DWs can easily be created and subsequentlymoved by external magnetic fields [4]. Wall creation isaccomplished by letting the magnetization distributionrelax following the application of a large field parallel tothe symmetry axis ( y -direction). Movement of the DWalong the wire then requires application of an orthogonalfield ( x -direction). A low magnification bright field TEMimage, fig. 1(b), shows that the wire is very well definedand also provides detail of the anti-notch located midwayalong the wire. The anti-notch was semicircular in shapewith a radius of 250 nm.To determine the detailed form of the DWs generated,the differential phase contrast (DPC) mode of Lorentzmicroscopy was used [10]. The TEM was a modifiedPhilips CM20 equipped with (non-immersion) Lorentzlenses, thereby allowing magnetic imaging in a field-freeenvironment with the standard objective lens switchedoff [11]. In the experiments conducted here, the objec-tive lens was weakly excited to provide a magnetic fieldsuitable for moving the DW around. Control of the field FIG. 3: (color online) Micromagnetic simulation of the mag-netization distribution in the vicinity of the anti-notch forcomparison with fig. 2. A simplified schematic is shown be-low. to which the wires were subjected was achieved by tilt-ing the TEM holder, thereby subjecting the specimento a component of field in the plane of the wires. Inthe DPC imaging mode, pairs of images sensitive to or-thogonal components of induction perpendicular to theelectron trajectory are formed. The images are derivedfrom the currents falling on opposite sectors of a quadrantdetector and, as all the information is recorded simulta-neously, are in perfect registration. Analysis of the imagepairs then yields a quantitative vector map of averagedinduction, vividly showing the detailed magnetic struc-ture of the DWs under investigation. The resolution ofthe resulting map is determined principally by the probediameter which in this instance was ≈
25 nm.For comparison purposes, micromagnetic simulationswere undertaken using OOMMF [12]. Parameters usedwere standard for permalloy (M s = 860 emu/cm , A =1.3x10 − erg/cm and K = 0) whilst the cell size was 5nm x 5 nm x 10 nm. The cell dimensions in the planeof the film were comparable with the material exchangelength whilst that in the third dimension was set equalto the film thickness. III. RESULTS
Figures 2(a) and (b) show respectively the B x and B y components of induction of a DW at a notch whilst fig.2(c) shows the calculated vector induction distributiondisplayed as a color map. The field used to create theDW was ≈ y -directionwas always subject to a small error. However, applica-tion of a small propagation field in the x -direction, H prop , was all that was required to move the wall to the locationshown in the figures. The wire used for fig. 2 was theone with the smallest radius of curvature. Figure 3 showsthe equivalent micromagnetic simulation. It is clear thatthere is good agreement between experiment and simu-lation in terms of the general form assumed by the DW,which is of the head-to-head kind. The apex of the wallappears to be pinned close to the right hand side of theanti-notch (at A) whilst below the anti-notch a complexinduction distribution exists. Thus in reality the DWshould be thought of more as a DW packet [13], extend-ing as it does over dimensions rather greater than theanti-notch diameter at the lower edge of the wire. Theoverall geometry is essentially that of an aTDW whichcan be represented schematically by two DWs of unequallength as shown in the inset of fig. 3. Here, the princi-pal difference from a standard aTDW is due to the influ-ence of the non-uniform magnetisation distribution in theanti-notch, in which there is inevitably some circulationof flux. Despite this, as can be seen most clearly fromthe arrows in fig. 3, the circulation is never complete andno vortex can be discerned, as would be the case for avortex domain wall (VDW).To test the stability of the DW around the anti-notchposition a small field was applied in the negative x -direction. Application of a field in this direction shouldpush the DW further into, and subsequently through, theanti-notch. The results are shown in fig. 4. At a fieldof 7 Oe a modest extension ( ∼
25 %) of the DW widthalong the bottom edge of the wire can be seen. Underfurther field increase, the wall marked AB in the orig-inal DW packet became more pronounced and the endB moved progressively away from the anti-notch whilstthe wall marked AC became increasingly indistinct asthe wall angle decreased. At 13 Oe, B was displacedby almost 1 µ m from its original position and by 15 Oethe DW was completely depinned leaving the wire essen-tially uniformly magnetized other than in the immediatevicinity of the anti-notch. Here there was still significantvariation in the induction orientation, the magnetizationclose to the edge of the anti-notch trying to follow itscontour, thereby reducing magnetostatic energy at theexpense of a modest increase in exchange energy.Not dissimilar results were obtained when a DW wasformed, in the same way as before, in the wire with thelargest radius of curvature. Figure 5(a) shows the induc-tion color map derived from a pair of DPC images whenthe y -axis field was reduced to zero. Once again a head-to-head DW resulted although in this instance the apexwas on the opposite side of the anti-notch at location D.This is likely to be the result of a very small change infield direction and, as such, is not important here. Againa field in the negative x -direction was applied to the wirebut now it should be noted that the effect of the fieldwas to cause the wall to move away from, rather thaninto, the anti-notch. The results are shown in the re-mainder of fig. 5. For fields up to 4 Oe there was nodiscernible change in the DW structure. However, by afield of 6 Oe, both the DW location and overall widthhad changed. The wall apex moved ∼
500 nm from Dwhilst the width along the lower edge increased by ∼ FIG. 4: Color vector maps of the magnetic induction in acurved wire with radius r = 5 µ m under application of in-creasing magnetic fields in the negative y -direction. in figs. 4 and 5 was typical, the experiments were re-peated many times with observations being made on thewires with radii 5, 40, 45 and 50 µ m. Qualitativelythis turned out to be the case. Moreover, in all casesit was found that the field required to pull an aTDWaway from the anti-notch (depinning field, H depin ) wassignificantly lower than that required to push the aTDWthrough it (transmission field, H trans ). For the three FIG. 5: Color vector maps of the magnetic induction in acurved wire with radius r = 50 µ m under application of in-creasing magnetic fields in the negative y -direction. wires with the largest radii the mean fields were foundto be H depin = (4 . ± .
0) Oe and H trans = (8 . ± . prop = (1 . ± .
4) Oe. The valueof the transmission field is considerably smaller than thefields seen in fig. 4 and further observations confirmedthat there was a clear increase in this field with decreas-ing wire radius. A final observation relates to what hap-pened to the DWs at fields just above those required topull them away from the anti-notch, typically fields in the4 to 7 Oe range. Here there was considerable variation inthe distance that the DW moved, presumably due to theexistence of local DW pinning sites. A good example ofsuch local pinning was apparent in fig. 5 where the DWremained at the same location some 500 nm away fromthe anti-notch until a field of 10 Oe was applied. Study ofstructural TEM images revealed no obvious defect aboutthe pinning site and certainly local pinning did not occurat the same distance from the anti-notch for other wires. Further work is ongoing to study such variations in be-havior of nominally identical wires fabricated in a singlebatch.
IV. DISCUSSION AND CONCLUSION
The formation and field response of head-to-head DWsin curved permalloy wires fabricated with a single anti-notch have been investigated using Lorentz-microscopy.Specifically, high spatial resolution color maps of the vec-tor induction distribution in the vicinity of the anti-notchhave been derived from pairs of DPC images. At rema-nence, the DW is in the form of an aTDW with mod-est magnetization circulation occurring in the anti-notchitself. Experimental results and micromagnetic simula-tions are in good agreement. Moreover, for wires withthe radii of curvature studied here, the remanent DWstructure was essentially independent of this parameter.Detailed information on the way the DW responds toapplied fields tangential to the wire at the anti-notch lo-cation was obtained by analyzing pairs of DPC imagesrecorded under different fields. As recording times aretypically 15 s Lorentz TEM is a very efficient techniquefor such in situ experimentation. Here we considered twocases, one where the effect of the field was to move thewall away from the anti-notch and the other where thewall had to be pushed through the anti-notch before astate of ’uniform’ magnetization was realized. In the for-mer case, fields ≈ ◦ wall in charac-ter. As the specific wall energy increases with wall angle[8] significant Zeeman energy is presumably required toeffect this change. Thus the field strength required tomove a DW from the vicinity of an anti-notch dependsvery strongly on the side of the anti-notch where the apexof the wall is located and the direction of the applied field.The dependence of pinning and depinning fields on thenotch geometry has been described previously with re-spect to the energy landscape a DW packet experiencesin the vicinity of an artificial pinning site [14]. Also theinfluence of triangular notches on TDWs was recentlystudied in detail by electron holography [15, 16]. Here,due to the reduced size of the DW package inside thenotch, the total energy of the transverse wall can be sig-nificantly reduced so that the notch acts as a potentialwell. In contrast, in the case of the anti-notch presentedabove, the aTDW is pinned in front of the artificial pin-ning site, which indicates that the anti-notch representsan energy barrier which the DW has to overcome beforeit can continue to propagate. Furthermore, our exper-iments show that the depinning and transmission fieldsfrom the notch are larger than the propagation field nec-essary to move the DW along the wire towards the notchat the beginning of the field sequence. Therefore, theanti-notch acts like an energy barrier with small poten-tial wells at both sides. It should be noted that the chosengeometry acts as a weak pinning potential in comparisonto other shapes, as reflected by the comparably low fieldsfor depinning and transmission [14, 15].In summary, the complex behavior of DWs in magneticwires with an anti-notch has been studied directly andin great detail using high resolution Lorentz microscopy.From the investigation the overall shape of the pinningpotential has been determined. V. ACKNOWLEDGMENT
The authors acknowledge the Nano+Bio Center ofthe Kaiserslautern University of Technology for techni-cal support and Andreas Beck for sample preparation.Financial support by the European Commission withinthe EU-RTNs SPINSWITCH (MRTN-CT-2006-035327)and MULTIMAT (MRTN-CT-2004-505226) and by theDFG within the SPP1133 is gratefully acknowledged.The views expressed are solely those of the authors, andthe other Contractors and/or the European Communitycannot be held liable for any use that may be made ofthe information contained herein.
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