Micromagnetic simulation is used to model the injection of a domain wall into a magnetic nanowire with field strengths less than the so-called Walker field. This ensures fast, reliable motion of the wall. When the wire is located at the edge of a small injecting disk, a bias field used to control the orientation of the domain wall can reduce the pinning potential of the structure. The low field injection is explained by a simple model, which relies on the topological nature of a domain wall. The technique can quickly inject multiple domain walls with a known magnetic structure

Kunz, Andrew

Reiff, Sarah C.

English

epublications@Marquette

Marquette Universitye-Publications@MarquettePhysics Faculty Research and Publications Physics, Department of1-1-2009Dependence of Domain Wall Structure for LowField Injection into Magnetic NanowiresAndrew KunzMarquette University, andrew.kunz@marquette.eduSarah C. ReiffMarquette UniversityPublished version. Applied Physics Letters, Vol. 94, No. 19 (2009). DOI. © 2009 American Institute ofPhysics. Used with permission.Dependence of domain wall structure for low field injection intomagnetic nanowiresAndrew Kunza and Sarah C. ReiffDepartment of Physics, Marquette University, Milwaukee, Wisconsin 53233, USAReceived 18 February 2009; accepted 28 April 2009; published online 14 May 2009Micromagnetic simulation is used to model the injection of a domain wall into a magnetic nanowirewith field strengths less than the so-called Walker field. This ensures fast, reliable motion of the wallN. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 1974. When the wire is located at theedge of a small injecting disk, a bias field used to control the orientation of the domain wall canreduce the pinning potential of the structure. The low field injection is explained by a simple model,which relies on the topological nature of a domain wall. The technique can quickly inject multipledomain walls with a known magnetic structure. © 2009 American Institute of Physics.DOI: 10.1063/1.3139066The motion of a domain wall through a long, narrownanowire has been studied extensively due to its importancein several proposed devices in logic, sensing, andrecording.1,2 Physically it is important to understand how tomove the domain wall quickly and reliably, which in partdepends on the magnetic structure of the domain wall.3–6 In athin, narrow nanowire, the presence of a domain wall is en-ergetically unfavorable so it is necessary to inject the domainwall into the wire. It is known that a domain wall moves thequickest, with a constant structure when driven by magneticfields weaker than the so-called Walker field, which is typi-cally about 15 Oe in a nanowire.3,7 Here we report micro-magnetic simulation results describing a technique to quicklyinject a domain wall with a controllable magnetic structureinto a nanowire with external magnetic field strengths lessthan the Walker field. The injection technique demonstratesthe influence of the topological nature of a domain wall.Controlling the topology of the domain wall makes it pos-sible to reliably inject and densely pack multiple domainwalls into a wire, which is necessary for viable magneticnanowire devices.The domain wall injection was simulated by integratingthe three-dimensional time dependent Landau–Lifshitz equa-tion of motion for a magnetic moment in an applied field.8The materials parameters used are for a permalloylike mate-rial Ms=8105 A /m, A=1.310−11 J /m with a damp-ing constant of 0.008 and a cubic discretization cell sizeranging from 2 to 5 nm on edge. For the simulation resultspresented here, the nanowire has a rectangular cross-sectional area of 1005 nm2 and the injection pad is a5-nm-thick disk with a 500 nm diameter. The diameter of thepad was kept small so that it would remain single domain asvortices and domain walls inside the pad influence the injec-tion properties.9 In each case, a saturating field was appliedat 170° from the +x-axis and then slowly relaxed so that theinitial magnetic state was primarily in the −x direction. Forconsistency, each simulated structure was started from thesame initial magnetic state. A magnetic field was appliedalong the long axis of the wire +x-axis to inject a head-to-head domain wall along with a bias field applied along they-axis to control the direction of the magnetic moments inthe domain wall. The external fields were applied at timezero, and a wall was considered to be injected if it was in thewire after 2 ns. The typical injection time was under a nano-second and we never found a case where it was likely thatwaiting longer would result in an injection.In a thin, narrow nanowire, the strong shape anisotropydetermines that the magnetic moments lie in the plane of thewire and are oriented along the long axis. The simplest tran-sition between domains is a transverse wall that separatestwo head-to-head or tail-to-tail domains.10 In a long, straightwire, domain walls can be nucleated at the ends of the wireby a large magnetic field. As shown in Fig. 1, the nucleationfield is found to be over 200 Oe for a 1005 nm2 wire. Thisnucleation field depends on the dimensions of the wire andthe bias field but even as the dimensions are increased thenucleation field is much greater than the Walker field, about15 Oe in a 1005 nm2 wire.3,7 It is possible to use aninjection pad, which is essentially a large magnetic regionattached at one end of the wire, to inject domain walls with alower field from one end of the wire. The pad is typicallylocated with the wire in the middle.11–13 The inclusion of a500 nm diameter disk decreases the injection field to around100 Oe. Previous work with the wire offset from the centerof the pad shows injection fields of this magnitude.9 In Fig.1, the injection field is found to be independent of the biasfield used to inject domain walls of a known chirality, whenthe wire is located at the center of the disk. Moving the wireto the top or bottom edge of the disk leads to a sharp reduc-aElectronic mail: andrew.kunz@marquette.edu.FIG. 1. Injection fields x-direction as a function of bias field y-directionfor three injection geometries into a 1005 nm2 wire. The injection field isdecreased for small positive bias fields when the wire is moved to the topedge of the injection pad.APPLIED PHYSICS LETTERS 94, 192504 20090003-6951/2009/9419/192504/3/$25.00 © 2009 American Institute of Physics94, 192504-1tion in the injection field for reasonable bias fields. As shownin Fig. 1 when the wire is located at the top of the disk, biasfields greater than 50 Oe in the +y-direction lower the injec-tion field to as little as 5 Oe. This field is less than the criticalWalker field resulting in the fastest, most reliable domainwall motion.3,7 Interestingly, the injection field is not sym-metric for negative bias fields; there is a strong dependenceon the direction of the bias field when the wire is located atan edge. This implies that the injection structures geometrypreferentially selects a domain wall orientation. This behav-ior is confirmed by moving the wire to the bottom edge ofthe disk. In this case the behavior is reversed; the injectionfield is small for negative bias fields and large for positivebias fields. The topological structure of a domain wall can beused to explain the selectivity.Moving the wire from the center of the injection disk tothe top reduces the number of corner pinning sites from twoto one, however Fig. 1 shows that the injection field is es-sentially the same without a bias field and for negative biasfields for the two disk structures. This behavior implies thata reduction in the number of corner pinning sites is not re-sponsible for the lower injection field but that the pinningmechanism itself is important. Domain wall pinning is a richtopic of current interest due to its importance in reliablymoving walls through wires.11,13 Domain walls can bepinned by both notches and antinotches.14–16 We rely on atopologic model of a domain wall to explain the injectionmechanism. A domain wall can be considered a topologicalobject consisting of two or more defects.17 In a two-dimensional 2D structure, like a thin wire, the typical de-fects can be described by a winding number, with a vortexhaving a winding number of n= +1 and an anti-vortex of n=−1 as shown in Fig. 2a. When defects are found along theedge of a wire, the winding numbers are half-integer struc-tures of which several orientations are presented in Fig. 2a.A domain wall is a composite object of zero net windingnumber, and we present domain wall orientations for asimple transverse wall in Fig. 2b.A simulated time lapse sequence of the injection of adomain wall into a wire is presented in Fig. 3a. Note thatalong the top edge of the system the winding number ispositive but along the bottom edge it is negative. The domainwall injects in about 700 ps. In Fig. 3b and 3c, cartoonrepresentations of the four possible transverse domain orien-tations are presented. It is of particular importance to notethat when the winding number of the defect along the edgeof the system with no pinning sites is positive, the wall easilyinjects, otherwise it is pinned. It is always the positive defectthat is pinned. This behavior of the positive defect beingpinned is consistent with the behavior noticed in antinotcheswhere negative defects are pinned by notches.14,16When the wire is located at, or slightly offset from, thecenter of the pad a positive defect must always pass a pin-ning site to enter the wire, independent of the domain wallchirality.9 By moving the wire to the top of the injection pad,a bias field can be used to arrange the location of the positivedefect. This eliminates the domain wall pinning site and thewall easily injects. The dependence on the strength of thebias field is due to the ease of rotating the magnetization ofthe nanopad. While the bias field rotates the magnetization ofthe pad and leaves the magnetic state of the wire unaffected,larger bias fields do a more effective job of aligning themagnetization of the pad as shown in Fig. 3a. The bias fieldessentially places the domain wall at the injection site andthe wall is easily pushed into the wire by the injecting field.A 50 Oe field is sufficient to cause the magnetization of thesmall disk to essentially saturate; smaller bias fields are notstrong enough to position the wall directly at the end of thewire, thus a larger injection field is needed.It is possible to inject domain walls with small magneticfields using a “L” shaped bend in a long wire, and this tech-nique is useful for studying single domain walls but L geom-etry only allows for a single domain wall to be in thewire.6,16 For nanowire devices to be viable, it will be neces-sary to inject multiple walls and to control their magneticstructure.1 The disk structure we present is capable of realiz-ing this behavior. Once the domain wall is injected into thewire, the fields quickly drive the wall along the length of thewire. Because the injection field is less than the criticalWalker field, the domain wall maintains its orientation at alltimes. It is now possible to inject a second domain wall intoFIG. 2. a Cartoon representations of the magnetic structure for 2D topo-logic defects with their winding numbers n. Edge defects have half-integerwinding numbers. In b, two composite representations for a transversedomain wall. The net winding number is zero.FIG. 3. a Simulated time lapse sequence for the typical injection of adomain wall into the wire with a bias field in the +y direction. The injectionpad saturates and the wall is pushed into the wire by the small injection fieldwhen positive defects are along the top edge a and b. The domainorientations in c have large injection fields because the +defects are pinnedat the injection site.192504-2 A. Kunz and S. C. Reiff Appl. Phys. Lett. 94, 192504 2009the wire by reversing both the bias field and the injectionfield. The field reversal keeps the winding number of the topdefect positive as shown in the cartoon of Fig. 3b anda second domain wall quickly is injected. This process canbe repeated to inject multiple domain walls into the wire.The simulated injection of three domain walls into a 505 nm2 wire is presented in Fig. 4. The equilibrium domainstructure demonstrates the potential to pack many domainwalls in a small length of wire. Control of the topologicaldefects allows the domain walls to remain in the wire whenthe walls collide.17–19In conclusion, a nanodisk is used as a domain wall in-jector for a magnetic nanowire. When the wire is located atthe edge of the nanodisk, the domain walls inject quicklywith small fields and a known domain wall orientation. Abias field is used to control the domain wall magnetizationbut the geometry selects which chirality of domain wall toinject. A simple model using the topological nature of a do-main wall was presented to show that controlling the positivedefect is necessary to easily inject a domain wall. Control ofthe injected domain walls leads to a simple method to injectand densely pack multiple walls into a wire.This work was financially supported by a Cottrell Col-lege Science Award from Research Corporation and by theNational Science Foundation Grant No. DMR-0706194.The authors also acknowledges the course release time sup-ported by the Helen Way Klingler College of Arts and Sci-ences at Marquette University.1S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320, 190 2008.2D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P.Cowburn, Science 309, 1688 2005.3A. Kunz and S. C. Reiff, J. Appl. Phys. 103, 07D903 2008.4J.-Y. Lee, K.-S. Lee, S. Choi, K. Y. Guslienko, and S.-K. Kim, Phys. Rev.B 76, 184408 2007.5A. Vanhaverbeke, A. Bischof, and R. Allenspach, Phys. Rev. Lett. 101,107202 2008.6E. R. Lewis, D. Petit, A.-V. Jausovec, L. O’Brien, D. E. Read, H. T. Zeng,and R. P. Cowburn, Phys. Rev. Lett. 102, 057209 2009.7N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 1974.8LLG Micromagnetic Simulator http://llgmicro.home.mindspring.com.9D. McGrouther, S. McVitie, J. N. Chapman, and A. Gentils, Appl. Phys.Lett. 91, 022506 2007.10R. D. McMichael and M. J. Donahue, IEEE Trans. Magn. 33, 41671997.11C. C. Faulkner, D. A. Allwood, and R. P. Cowburn, J. Appl. Phys. 103,073914 2008.12K. Weerts, P. Neutens, L. Lagae, and G. Borghs, J. Appl. Phys. 103,094307 2008.13D. Atkinson, D. S. Eastwood, and L. K. Bogart, Appl. Phys. Lett. 92,022510 2008.14M. Hayashi, L. Thomas, C. Rettner, R. Moriya, X. Jiang, and S. S. P.Parkin, Phys. Rev. Lett. 97, 207205 2006.15L. K. Bogart, D. Atkinson, K. O’Shea, D. McGrouther, and S. McVitie,Phys. Rev. B 79, 054414 2009.16D. Petit, A.-V. Jausovec, D. Read, and R. P. Cowburn, J. Appl. Phys. 103,114307 2008.17O. Tchernyshyov and G.-W. Chern, Phys. Rev. Lett. 95, 197204 2005.18A. Kunz, Appl. Phys. Lett. 94, 132502 2009.19J.-G. Zhu and Y. Zheng, in Spin Dynamics in Confined Magnetic Struc-tures I, edited by B. Hillebrands and K. Ounadjela Springer, Berlin,2002.FIG. 4. Simulated image showing three domain walls injected into a505 nm wire. Due to the orientation of the positive defects and the nega-tive defects, the domain walls do not annihilate when they collide.192504-3 A. Kunz and S. C. Reiff Appl. Phys. Lett. 94, 192504 2009

Dependence of Domain Wall Structure for Low Field Injection into Magnetic Nanowires

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Dependence of Domain Wall Structure for Low Field Injection into Magnetic Nanowires

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