Artificial defects such as notches and antinotches are often attached to magnetic nanowires to serve as trapping (pinning) sites for domain walls. The magnetic field necessary to release (depin) the trapped domain wall from the notch depends on the type, geometric shape, and dimensions of the defect but is typically quite large. Conversely we show here that for some notches and antinotches there exists a much smaller driving field for which a moving domain wall will travel past the defect without becoming trapped. This dynamic pinning field also depends on the type, geometric shape and defect dimensions. Micromagnetic simulation is used to investigate both the static and dynamic pinning fields and their relation to the topologic structure of the domain wall

Kunz, Andrew

Priem, Jonathan D.

English

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Marquette Universitye-Publications@MarquettePhysics Faculty Research and Publications Physics, Department of6-1-2010Dynamic Notch Pinning Fields for Domain Wallsin Ferromagnetic NanowiresAndrew KunzMarquette University, andrew.kunz@marquette.eduJonathan D. PriemMarquette UniversityPublished version. IEEE Transactions on Magnetics, Vol. 46, No. 6 ( June 2010), DOI. © 2010Institute of Electrical and Electronics Engineers. Used with permission.IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010 1559Dynamic Notch Pinning Fields for DomainWalls in Ferromagnetic NanowiresAndrew Kunz and Jonathan D. PriemPhysics Department, Marquette University, Milwaukee, WI 53233 USAArtificial defects such as notches and antinotches are often attached to magnetic nanowires to serve as trapping (pinning) sites fordomain walls. The magnetic field necessary to release (depin) the trapped domain wall from the notch depends on the type, geometricshape, and dimensions of the defect but is typically quite large. Conversely we show here that for some notches and antinotches thereexists a much smaller driving field for which a moving domain wall will travel past the defect without becoming trapped. This dynamicpinning field also depends on the type, geometric shape and defect dimensions. Micromagnetic simulation is used to investigate both thestatic and dynamic pinning fields and their relation to the topologic structure of the domain wall.Index Terms—Magnetic devices, magnetic domains, magnetization reversal.I. INTRODUCTIONT HE DYNAMIC properties of magnetic domain wallsmoving in ferromagnetic nanowires are being investi-gated due to their potential for applications in logic, sensing,and memory devices [1], [2]. In these devices it is importantto know and control the location of the domain wall alongthe wire. There is a significant amount of research underwayto describe the magnetic field necessary to remove domainwalls from artificial defects such as notches cut into the wire,and antinotches attached to the wire as these defects can beused to hold domain walls at specific known locations [3]–[6].The notches typically serve as strong pinning sites as largemagnetic fields are necessary to release the domain wall fromthe notch. This depinning field is typically much larger than theWalker breakdown field which results in low average domainwall speeds [7]. It has been shown that current pulses of thecorrect length and collisions of domain walls can also be usedto release the domain walls from the notches with much smallerfields [8], [9]. The usefulness of domain wall collisions for thedepinning process in a device depends in part on the ability ofa domain wall to move past a notch without being captured,otherwise a domain wall must exist at every notch. In this paperwe report on a dynamic notch pinning potential which dependson the strength of the driving field, and therefore the speed ofthe domain wall as it approaches a defect. Fast moving domainwalls are able to pass a notch that is able to capture and holdslower moving walls. The large depinning field ensures that thewall will remain in the notch when reasonable strength fieldsare applied leading to a new technique for writing informationstored in a domain wall configuration.II. SIMULATION DETAILSWe simulate the motion and potential trapping of a domainwall with standard three-dimensional micromagnetic simula-Manuscript received October 29, 2009; revised December 10, 2009; acceptedJanuary 12, 2010. Current version published May 19, 2010. Corresponding au-thor: A. Kunz (e-mail: andrew.kunz@marquette.edu).Digital Object Identifier 10.1109/TMAG.2010.2041044tion. The simulations follow the standard Landau-Lifshitz equa-tion of motion for the magnetic moments in the wire(1)where is the gyromagnetic ratio, is the saturation mag-netization and is the total magnetic field acting on a mag-netic moment [10]. The materials parameters are for permalloy.We simulate wires with a minimum length of 3 microns and anm rectangular cross-section. The wire is discretizedinto identical cubes and integrated with a 4th order predictor cor-rector technique with a simulated integration time step of lessthan a picosecond and a damping parameter of .To put the walls in motion, magnetic fields are applied tofree domain walls along the long axis of the wire. We keep themoving wall field strength below the so-called Walker break-down field to maintain the domain walls of a known shape andbecause this is the field range for which the walls move thequickest. We place notches and antinotches along the wire toserve as potential trapping sites for the domain wall.III. RESULTS AND DISCUSSIONIn narrow, thin ferromagnetic nanowires the magnetic mo-ments lie in the plane of the film and are oriented along the longaxis direction. A transverse domain wall separates oppositelyoriented head-to-head, or tail-to-tail domain walls [11]. In Fig. 1we show the final state for two triangular notch/anti-notch con-figurations each with two different domain wall magnetizations(up or down in the figure), separating tail-to-tail domains. Ineach case a domain wall entered from the left side of the figureand was driven to the right by a 15 Oe field placed to the leftand parallel to the long axis of the wire. The final location ofthe domain wall depends on the domain wall orientation, notchlocation and notch type. The pinning potential of the defect canbe summarized best with a simple topologic model [12]. Wehave labeled the sign of the topologic half charge on each endof the domain wall (a complete domain wall has a net topologiccharge of 0). We see that positive charges are strongly pinnedat antinotches, whereas negative charges are pinned strongly atnotches.If the wall reaches the right most defect it must pass the otherpotential trapping sites. The dynamic wall behavior in the region0018-9464/$26.00 © 2010 IEEE1560 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010Fig. 1. Images a) and b) show the final simulated magnetic structure for atail-to-tail domain wall driven from left to right in the figure for a given antinotchand notch configuration. The topologic charge structure of the domain wall isplaced on the figure. Images c) and d) show the same for a different notch con-figuration. Notches trap negative topologic charges and antinotches trap positivecharge.Fig. 2. Dynamic pinning fields as a function of notch depth (or antinotchheight) for a negative topologic charge. For small defect sizes the domain wallscan be driven past notches without being trapped, a 12 nm notch depth and 36nm antinotch heights are required to trap a moving domain wall. The dashedlines are guides for the eye to help follow the trends.of a potential pinning site really depends on whether or not thewall will be captured. When the wall passes a site, it does so withits magnetic structure almost unaffected with at most a smalloscillation. However when a wall is captured the free end of thewall continues along, showing domain wall growth before thewall is snapped back toward the pinning site.We explored the ability of a moving domain wall to move pasta defect as a function of the type of notch and the dimensionsof the notch for the given domain wall configuration. In Fig. 2we summarize the driving field necessary to move a domain wallpast a notch or antinotch, placed on the top edge of the nanowire,as a function of the depth of the notch. A head to head domainwall with magnetic moments pointing down is driven from leftto right along the wire. The orientation of magnetic momentsplaces the negative topologic charge on the top of the wire andthe positive topologic charge on the bottom of the wire such asthat shown in Fig. 1(b) and (c). The notch is a more effectivepinning site in this configuration but the antinotch is still a weaktrapping site. In short there is a different strength of interactionfor notches and antinotches with positive and negative defects.In Fig. 3 we show the results of our simulations which give thefield necessary to remove the now pinned wall from the notch orantinotch. The different field values between Fig. 2 and Fig. 3Fig. 3. Static pinning fields as a function of notch depth (or antinotch height)for a negative topologic charge. For domain walls trapped in notches (see Fig. 2)large fields are necessary to remove the walls. The lines are guides for the eyeto help follow the trends.demonstrates that there is a significant difference in the staticpinning field which holds the wall in place and the dynamicpinning field which we define as the minimum field necessaryto move a domain wall past a defect. The overall relationshipremains the same in that the notch is a strong trap for a negativedefect both in catching and releasing a wall. This behavior ofFigs. 2, 3 is confirmed by placing the notch and antinotch onthe bottom of the wire. The results are essentially reversed withthe antinotch trapping the positive wall charge more effectively.The difference in the interaction strength means that forshallow defects there is a field at which the domain walls canbe driven fast enough to blow past a notch without becomingtrapped. In Fig. 2 we show that a 12 nm notch depth (and a36 nm antinotch height) is necessary to begin to trap the wallalthough the speed at which the wall approaches the notchallows the trapping to occur or not occur. We have confirmedthis behavior by applying transverse in-plane fields to thedomain wall driving field. A transverse field can be used tosignificantly speed up, or slow down, domain walls driven byidentical driving fields [13]. In this case the driving field wasused to increase the speed of a domain wall which allowedit to pass a notch where it was trapped without the drivingfield. Energetically this means the moving domain wall carriessufficient kinetic energy to climb the potential barrier for fullmagnetization reversal that the defect creates. As the depth ofthe defects increase, a domain wall is no longer able to pass thenotch. The maximum driving field of 16 Oe corresponds to theWalker field above which the transverse domain walls undergocomplicating transformations.We see a similar, although reversed behavior when the depthof the notch is kept constant and the width of the notch is varied.In this case as the width increases, the pinning behavior de-creases. This is expected because as the width increases the wireedge becomes effectively smooth.The ability of a moving domain wall to either be captured orpass a notch in a wire allows for a simple technique to write do-main walls in a known configuration. In Fig. 4 we show a fewsimulated images (Fig. 4(a)–(c)) which lead to the final mag-netic states for a series of domain walls (Fig. 4(d)–(f)) injected atlow fields from the pad on the left end of the wire [14]. There areKUNZ AND PRIEM: DYNAMIC NOTCH PINNING FIELDS FOR DOMAIN WALLS IN FERROMAGNETIC NANOWIRES 1561Fig. 4. Static and dynamic pinning allows for precise control of a domainwall. Walls can be injected (a), driven past notches (b) and placed where youwant them as other walls are injected into the wire (c). Figs. (d)–(f) showthree different final domain wall configurations which could be considered bitsequences.eight notches placed on the upper edge of the wire; the domainwalls are written from right to left. As shown in Fig. 4(a) theright most domain wall passed by each of the first six notches be-fore being captured at the seventh notch. An additional in-planetransverse magnetic field was used to keep the domain wallspeed high until it passed the sixth notch [13]. Once the notchpassed the sixth notch the transverse field was turned off but thedriving field was left on to drive the wall into the final notchas shown in Fig. 4(b). The next wall was injected, Fig. 4(c),and driven into its final location with a combined driving andtransverse field until it passed the notch before the pinning site,without affecting the position of the first wall. Each domain wallwas written in the same way leaving the final configuration asshown in Fig. 4(d). Fig. 4(e), (f) are two different final binary bitsequences. Each configuration was written in a simulation timeof less than 25 ns.In conclusion there are two important fields to know whenmoving and capturing domain walls with artificial defects. Adynamic pinning field determines the minimum field necessaryto pass a moving domain wall past a defect without being cap-tured and the static pinning field is the minimum field neededto remove a captured domain wall from the defect. The specificvalue of the field depends on the topologic structure of the do-main wall and the dimensions and type of defect but the staticpinning field is always much stronger than the dynamic pinningfield. By varying the wall speed domain walls can be movedwith magnetic fields in one direction and placed reliably at spe-cific locations in a wire.ACKNOWLEDGMENTThis work was supported by the National Science Foundationunder Grant DMR-0706194.REFERENCES[1] S. S. P. Parkin, M. Hayashi, and L. Thomas, “Magnetic domain-wallracetrack memory,” Science, vol. 320, pp. 190–194, 2008.[2] D. A. Allwood, “Magnetic domain-wall logic,” Science, vol. 309, pp.1688–1692, 2005.[3] S.-H. Huang and C.-H. Lai, “Domain wall depinning by controlling itsconfiguration at notch,” Appl. Phys. Lett., vol. 95, p. 032505, 2009.[4] L. K. Bogart, “Dependence of domain wall pinning potential land-scapes on domain wall chirality and pinning site geometry in planarnanowires,” Phys. Rev. B, vol. 79, p. 054414, 2009.[5] D. Petit, “Mechanism for domain wall pinning and potential land-scape modification by artificially patterned traps in ferromagneticnanowires,” Phys. Rev. B, vol. 79, p. 214405, 2009.[6] D. Petit, “Domain wall pinning and potential landscapes created byconstrictions and protrusions in ferromagnetic nanowires,” J. Appl.Phys., vol. 103, p. 114307, 2008.[7] N. L. Schryer and L. R. Walker, “The motion of 180 domain wallsin uniform dc magnetic fields,” J. Appl. Phys., vol. 45, pp. 5406–5421,1974.[8] M. Hayashi, “Dependence of current and field driven depinning of do-main walls on their structure and chirality in permalloy nanowires,”Phys. Rev. Lett., vol. 97, p. 207205, 2006.[9] A. Kunz, “Field Induced domain wall collisions in thin magneticnanowires,” Appl. Phys. Lett., vol. 94, p. 132502, 2009.[10] Micromagnetic Simulator ver. 2.61 [Online]. Available: http://ll-gmicro.home.mindspring.com[11] R. D. McMichael and M. J. Donahue, “Head to head domain wall struc-ture in thin magnetic strips,” IEEE Trans. Magn., vol. 33, no. 5, pp.4167–4169, Oct. 1997.[12] O. Tchernyshyov and G.-W. Chern, “Fractional vortices and compositedomain walls in flat nanomagnets,” Phys. Rev. Lett., vol. 95, p. 197404,2005.[13] A. Kunz and S. C. Reiff, “Enhancing domain wall speeds in nanowireswith transverse magnetic fields,” J. Appl. Phys., vol. 103, p. 07D903,2008.[14] A. Kunz and S. C. Reiff, “Dependence of domain wall structure for lowfield injection into magnetic nanowires,” Appl. Phys. Lett., vol. 94, p.192504, 2009.

Dynamic Notch Pinning Fields for Domain Walls in Ferromagnetic Nanowires

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Dynamic Notch Pinning Fields for Domain Walls in Ferromagnetic Nanowires

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