In a two-dimensional magnetic nanowire, it is possible to engineer collisions between two domain walls put into motion by an externally applied field. We show that the topological defects that define the domain wall can be controlled to allow for both domain wall annihilation and preservation during the collisions as long as the wire remains thin. The preservation process can be used to release pinned domain walls from notches with small applied fields

Kunz, Andrew

English

epublications@Marquette

Marquette Universitye-Publications@MarquettePhysics Faculty Research and Publications Physics, Department of1-1-2009Field Induced Domain Wall Collisions in ThinMagnetic NanowiresAndrew KunzMarquette University, andrew.kunz@marquette.eduPublished version. Applied Physics Letters, Vol. 94, No. 13 (2009). DOI. © 2009 American Institute ofPhysics. Used with permission.Field induced domain wall collisions in thin magnetic nanowiresAndrew KunzaDepartment of Physics, Marquette University, Milwaukee, Wisconsin 53233, USAReceived 26 January 2009; accepted 12 March 2009; published online 31 March 2009In a two-dimensional magnetic nanowire, it is possible to engineer collisions between two domainwalls put into motion by an externally applied field. We show that the topological defects that definethe domain wall can be controlled to allow for both domain wall annihilation and preservationduring the collisions as long as the wire remains thin. The preservation process can be used torelease pinned domain walls from notches with small applied fields. © 2009 American Institute ofPhysics. DOI: 10.1063/1.3112577Understanding the dynamic properties of a moving mag-netic domain wall in a thin, narrow nanowire is a challengefor fundamental physics and for technological applications inmagnetic recording and sensing. In a thin, narrow wire themagnetic moments of the material lie in the plane of thewire, oriented along the long axis due to the strong shapeanisotropy.1–3 Although energetically unfavorable, a domainwall may exist in the wire separating regions of oppositemagnetization. The simplest domain wall is a transverse wallwith head to head or tail to tail alignment with the magneticmoments rotating through a total of 180°. Fast, reliable, andcontrollable motion of the domain wall is essential for theoperation of several proposed nanowire storage, logic, andsensing devices.4,5 There is a large effort to understand andcontrol the motion of a single domain wall with lithographicpatterning techniques, current pulses, and tailored fields;6–12however it will be necessary to inject and move several do-main walls concurrently for practical application.5,13Electric currents and externally applied magnetic fieldsare the two principle mechanisms for driving a domain wallalong a wire. A current is known to each domain wall in thesame direction, maintaining the overall magnetic structure inthe wire.14 However, when a magnetic field is used to movetwo domain walls, the domain walls move in opposite direc-tions and collide. In this letter it is shown that the collision iscapable of preserving the domain configuration when thestructure of the colliding domain walls is properly controlled.A magnetic domain wall can be considered a compositeobject consisting of two or more topologic defects. In a mag-netic nanowire, the possible defects are vortices and antivor-tices with winding number of n=1, and edge defects withhalf-integer winding number n= 12 .15 Possible windingnumbers and their relevant magnetic structure is representedin Fig. 1a. The simplest domain wall in a thin nanowireconsists of two elementary edge defects of opposite windingnumber for a net composite charge of zero.15 Two possiblecomposite structures are presented in Fig. 1b. It is knownthat the annihilation requires an interaction between defectswith opposite topological charge.16 Therefore, by suitablecreation of the domain structure, both domain wall annihila-tion and preservation can be realized.The tool used for visualization of the collisions in amagnetic nanowire is a micromagnetic simulation utilizingthe Landau–Lifshitz equation of motion for a magneticmoment mmt= − m  H  −Msm  m  H  , 1where  is the gyromagnetic ratio,  is the phenomenologi-cal damping parameter, Ms is the saturation magnetization,and H is the total field experienced by the moment.17 Afourth order predictor-corrector integration time step of lessthan a picosecond and phenomenological damping of =0.008 are used to complete the simulations. The materialsparameters are those typical of Permalloy with saturationmagnetization Ms=8.0105 A /m, exchange stiffness A=1.310−11 J /m, and no crystalline anisotropy. Wires withrectangular cross sections width ranging from 50 to 300 nmand thickness ranging from 2 to 10 nm were simulated. Theresults presented below are dependent on the thickness. Afield-driven domain wall moves quickest, and with the mostconsistent structure, for fields less than the critical Walkerfield where vortices and antivortices nucleate in the domainwall.9,18 For this reason, the driving fields used in the simu-lations are all under 15 Oe, which allows for easy control ofthe magnetic structure.Two 180° domain walls are inserted at different loca-tions along the length of the wire, creating three longitudinaldomains. As shown in time-lapse sequence of Figs.2a–2d, the magnetic moments in each domain wall arealigned parallel to each other along the +y-axis and separatea reversed magnetic domain in the center of the wire−x-axis from the two end domains +x-axis. Experimen-tally a domain wall can be injected into a wire with the useaElectronic mail: andrew.kunz@marquette.edu.FIG. 1. a Schematic representations of a magnetic vortex winding numbern=1, antivortex n=−1, and their half-integer equivalents. A domain wallhas a total winding number of zero and in b is shown to be composed oftwo half-vortices of opposite winding number.APPLIED PHYSICS LETTERS 94, 132502 20090003-6951/2009/9413/132502/3/$25.00 © 2009 American Institute of Physics94, 132502-1of an injection pad attached to one end of the wire.11 Themagnetic structure of the wall can be controlled by the use ofa bias field which can change the magnetic state of the padleaving the wire unaffected. The elementary topologicalcharges for each wall are given in Fig. 2a. When a 10 Oeexternal field is applied along the +x-axis the domains ori-ented along the field direction grow at the expense of thereverse domain as expected. When the domain walls meet,each edge defect annihilates with an edge defect of oppositetopological charge. The annihilation takes place through areversal of the center reversed domain into the direction ofthe domain wall magnetization and energy is dissipatedthrough the production of spin waves in the wire.The simulation is repeated exactly as above, but with themagnetization and therefore the winding numbers of theright-hand domain wall reversed as shown in the time-lapsesequence in Figs. 3a–3d. The applied field drives the do-main walls toward each other, but in this case the walls donot annihilate when they collide. To annihilate, two defectsof opposite topological charge must interact or a pair ofcharges must be created19–22 and in this case at each edge theinteracting topologic charges are the same. The time lapseshows that prior to the collision the central domain shrinksbut instead of rotating into the direction of the domain wallsas before, the rotation process is frustrated. The best path toreversal is to rotate out-of-plane but the strong shape aniso-tropy of the thin wire inhibits this process. The walls bounceoff of each other before relaxing into the final equilibriumstructure shown in Fig. 3d. The final structure is a 360°domain wall.23–29 Wires ranging in cross-section width from50 to 300 nm wire simulated and in each case when thethickness was increased beyond 8 nm the domain walls an-nihilated upon contact. Keeping the wire thin, and the driv-ing fields below the critical Walker field, helps the systemmaintain a two-dimensional magnetic structure. As the thick-ness of the wire grows, the full skyrmion charge, which isa product of the winding number and the out-of-plane mag-netization polarization of a topologic defect, becomesimportant.16,19 Due to the first term of the LL Eq. 1, eachdomain wall rotates about the applied field in a clockwisedirection when looking along the direction of the appliedfield giving rise to an opposite skyrmion charge at each ofthe interacting edge defects and leading to a dynamic path ofannihilation. However, in the thin 1005 nm2 cross-sectionwire the domain structure is robust so that a field of over 600Oe is necessary to remove the 360° wall. At the same timethe domain walls are weakly coupled such that a 30 Oe fieldcan separate them back into two individual 180° walls.The collision process can be used to release a domainwall that is pinned by a notch as shown in the time-lapseseries of Figs. 4a–4d. Domain wall pinning is critical formany proposed devices but removing the wall from the notchrequires large fields, current pulses, or laser heating. In thiscase a domain wall is held in place by a small notch whichrequires a minimum field of 80 Oe to release it. The left wallis driven along the wire by a 10 Oe field until it collides withthe pinned wall. The pinned wall is forced out of the notchFIG. 2. Time-lapse sequence of two domain walls being driven by a 10 Oefield aligned along the +x-axis in a 5 nm thick wire. In a the elementarytopologic charges are given. Opposite topologic charges annihilate.FIG. 3. Time-lapse sequence of two domain walls being driven by a 10 Oefield aligned along the +x-axis in a 5 nm thick wire. In a the elementarytopologic charges are given. The topologic charges are preserved leading tothe 360° domain wall d.FIG. 4. Time-lapse sequence of a collision between a wall driven by a 10 Oefield and a wall pinned by a small notch. The collision drives the pinnedwall from the notch, which captures the moving wall.132502-2 Andrew Kunz Appl. Phys. Lett. 94, 132502 2009during the collision. This wall will then be shifted down thewire by reversing the applied field.In summary, by preparing the domain walls with the cor-rect magnetization, it is possible to preserve the walls in afield-driven collision. The elementary winding numbers foreach of the colliding domain walls must be identical, and thenanowire must behave two-dimensionally to hold the mag-netic moments in the plane of the wire. As the wire thicknessis increased, the magnetization is capable of rotating out ofthe plane and the walls annihilate. The collisions can be usedto release pinned domain walls with weak external fields.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 author also acknowledges the support of the Helen WayKlingler College of Arts and Sciences at Marquette Univer-sity.1J.-Y. Lee, K.-S. Lee, S. Choi, K. Y. Guslienko, and S.-K. Kim, Phys. Rev.B 76, 184408 2007.2R. D. McMichael and M. J. Donahue, IEEE Trans. Magn. 33, 41671997.3O. A. Tretiakov, D. Clarke, G.-W. Chern, Y. B. Bazaliy, and O. Tcherny-shyov, Phys. Rev. Lett. 100, 127204 2008.4D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P.Cowburn, Science 309, 1688 2005.5S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320, 190 2008.6D. Petit, A.-V. Jausovec, H. T. Zeng, E. Lewis, L. O’Brien, D. Read, andR. P. Cowburn, Appl. Phys. Lett. 93, 163108 2008.7A. Vanhaverbeke, A. Bischof, and R. Allenspach, Phys. Rev. Lett. 101,107202 2008.8J.-Y. Lee, K.-S. Lee, and S.-K. Kim, Appl. Phys. Lett. 91, 122513 2007.9A. Kunz and S. C. Reiff, Appl. Phys. Lett. 93, 082503 2008.10A. Kunz and S. C. Reiff, J. Appl. Phys. 103, 07D903 2008.11S. Glathe, R. Mattheis, and D. V. Berkov, Appl. Phys. Lett. 93, 0725082008.12L. Thomas, M. Hayashi, X. Jiang, R. Moriy, C. Rettner, and S. S. P.Parkin, Nature London 443, 197 2006.13M. Hayashi, L. Thomas, R. Moriya, C. Rettner, and S. S. P. Parkin,Science 320, 209 2008.14A. Yamaguchi, T. Ono, S. Nasu, K. Miyake, K. Mibu, and T. Shinjo, Phys.Rev. Lett. 92, 077205 2004.15O. Tchernyshyov and G.-W. Chern, Phys. Rev. Lett. 95, 197204 2005.16O. A. Tretiakov and O. Tchernyshyov, Phys. Rev. B 75, 012408 2007.17LLG MICROMAGNETIC SIMULATOR http:llgmicro.home.mindspring.com/v.2.61 2007.18N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 1974.19R. Hertel and C. M. Schneider, Phys. Rev. Lett. 97, 177202 2006.20K. Y. Guslienko, K.-S. Lee, and S.-K. Kim, Phys. Rev. Lett. 100, 0272032008.21K.-S. Lee, K. Y. Guslienko, J.-Y. Lee, and S.-K. Kim, Phys. Rev. B 76,174410 2007.22R. Hertel, S. Gilga, M. Fanhle, and C. M. Schneider, Phys. Rev. Lett. 98,117201 2007.23X. Portier and A. K. Petford-Long, Appl. Phys. Lett. 76, 754 2000.24J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C.Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86, 1098 2001.25M. Klaui, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, A.Pavlovska, E. Bauer, S. Cherifi, S. Heun, and A. Locatelli, Appl. Phys.Lett. 85, 5637 2004.26F. J. Castano, C. A. Ross, C. Frandsen, A. Eilez, D. Gil, H. I. Smith, M.Redjdal, and F. B. Humphrey, Phys. Rev. B 67, 184425 2003.27G. D. Chaves-O’Flynn, K. Xiao, D. L. Stein, and A.D. Kent, J. Appl.Phys. 103, 07D917 2008.28C. B. Muratov and V. V. Osipov, J. Appl. Phys. 104, 053908 2008.29J.-G. Zhu and Y. Zheng, in Spin Dynamics in Confined Magnetic Struc-tures I, edited by B. Hillebrands and K. Ounadjela Springer, Berlin,Heidelberg, 2002.132502-3 Andrew Kunz Appl. Phys. Lett. 94, 132502 2009

Field Induced Domain Wall Collisions in Thin Magnetic Nanowires

https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1127&amp;context=physics_fac

Field Induced Domain Wall Collisions in Thin Magnetic Nanowires

Abstract

Similar works

Full text

Available Versions

epublications@Marquette