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Domain Walls in Bent Nanowires

F. Lofink1,*, A. Philippi-Kobs1,2,†, M. R. Rahbar Azad1, S. Hankemeier1, G. Hoffmann1,‡, R. Frömter1, and H. P. Oepen1,2

  • 1Institut für Nanostruktur- und Festkörperphysik, Universität Hamburg, Jungiusstraße 11, 20355 Hamburg, Germany
  • 2The Hamburg Centre of Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany

  • *Present address: Fraunhofer Institute for Silicon Technology, Fraunhoferstr. 1, 25524 Itzehoe, Germany. fabian.lofink@isit.fraunhofer.de
  • †Present address: Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany.
  • ‡Present address: Department of Physics, National Tsing Hua University, Hsinchu, Taiwan.
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Phys. Rev. Applied 8, 024008 – Published 17 August, 2017

DOI: https://doi.org/10.1103/PhysRevApplied.8.024008

Abstract

The influence of geometric parameters on the magnetic fine structure of domain walls in bent nanowires is investigated. The domain pattern in the soft-magnetic Co39Fe54Si7 alloy is studied via scanning electron microscopy with polarization analysis and modeled via micromagnetic simulations. It is demonstrated that the bending angle affects details of the microstructure as well as the preponderant domain-wall type. A phenomenological model is developed that provides the global energy minimum of individual types of domain walls as a function of the geometric parameters of the wire. The results can be directly transferred to permalloy wires, as permalloy and Co39Fe54Si7 alloy have a comparable magnetostatic exchange length.

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References (63)

  1. J.-P. Tetienne, T. Hingant, J.-V. Kim, L. Herrera Diez, J.-P. Adam, K. Garcia, J.-F. Roch, S. Rohart, A. Thiaville, D. Ravelosona, and V. Jacques, Nanoscale imaging and control of domain-wall hopping with a nitrogen-vacancy center microscope, Science 344, 1366 (2014).
  2. A. Bisig, M.-A. Mawass, M. Stärk, C. Moutafis, J. Rhensius, J. Heidler, S. Gliga, M. Weigand, T. Tyliszczak, B. Van Waeyenberge, H. Stoll, G. Schütz, and M. Kläui, Dynamic domain wall chirality rectification by rotating magnetic fields, Appl. Phys. Lett. 106, 122401 (2015).
  3. P. S. Keatley, W. Yu, L. O’Brien, D. E. Read, R. P. Cowburn, and R. J. Hicken, Time-resolved Kerr microscopy of coupled transverse domain walls in a pair of curved nanowires, J. Appl. Phys. 115, 17D507 (2014).
  4. J. Leliaert, B. Van de Wiele, A. Vansteenkiste, L. Laurson, G. Durin, L. Dupré, and B. Van Waeyenberge, Influence of material defects on current-driven vortex domain wall mobility, Phys. Rev. B 89, 064419 (2014).
  5. V. Estévez and L. Laurson, Magnetic domain-wall dynamics in wide permalloy strips, Phys. Rev. B 93, 064403 (2016).
  6. R. Allenspach and P.-O. Jubert, Magnetic domain walls in nanowires, MRS Bull. 31, 395 (2006).
  7. M. Kläui, Head-to-head domain walls in magnetic nanostructures, J. Phys. Condens. Matter 20, 313001 (2008).
  8. V. Estévez and L. Laurson, Head-to-head domain wall structures in wide permalloy strips, Phys. Rev. B 91, 054407 (2015).
  9. L. Döring, C. Hengst, F. Otto, and R. Schäfer, Interacting tails of asymmetric domain walls: Theory and experiments, Phys. Rev. B 93, 024414 (2016).
  10. P. J. Metaxas, M. Albert, S. Lequeux, V. Cros, J. Grollier, P. Bortolotti, A. Anane, and H. Fangohr, Resonant translational, breathing, and twisting modes of transverse magnetic domain walls pinned at notches, Phys. Rev. B 93, 054414 (2016).
  11. A. Pivano and V. O. Dolocan, Chaotic dynamics of magnetic domain walls in nanowires, Phys. Rev. B 93, 144410 (2016).
  12. V. Raposo, S. Moretti, M. A. Hernandez,, and E. Martinez, Domain wall dynamics along curved strips under current pulses: The influence of Joule heating, Appl. Phys. Lett. 108, 042405 (2016).
  13. S. S. P. Parkin, M. Hayashi, and L. Thomas, Magnetic domain-wall racetrack memory, Science 320, 190 (2008).
  14. M. Diegel, R. Mattheis, and E. Halder, 360° domain wall investigation for sensor applications, IEEE Trans. Magn. 40, 2655 (2004).
  15. J. Vandermeulen, B. Van de Wiele, L. Dupré, and B. Van Waeyenberge, Logic and memory concepts for all-magnetic computing based on transverse domain walls, J. Phys. D 48, 275003 (2015).
  16. R. McMichael and M. Donahue, Head to head domain wall structures in thin magnetic strips, IEEE Trans. Magn. 33, 4167 (1997).
  17. Y. Nakatani, A. Thiaville, and J. Miltat, Head-to-head domain walls in soft nano-strips: A refined phase diagram, J. Magn. Magn. Mater. 290–291, 750 (2005).
  18. H. Youk, G.-W. Chern, K. Merit, B. Oppenheimer, and O. Tchernyshyov, Composite domain walls in flat nanomagnets: The magnetostatic limit, J. Appl. Phys. 99, 08B101 (2006).
  19. A. Thiaville, Y. Nakatani, F. Piéchon, J. Miltat, and T. Ono, Transient domain wall displacement under spin-polarized current pulses, Eur. Phys. J. B 60, 15 (2007).
  20. M. Kläui, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, A. Pavlovska, E. Bauer, S. Cherifi, S. Heun, and A. Locatelli, Head-to-head domain-wall phase diagram in mesoscopic ring magnets, Appl. Phys. Lett. 85, 5637 (2004).
  21. D. Backes, C. Schieback, M. Kläui, F. Junginger, H. Ehrke, P. Nielaba, U. Ruediger, L. J. Heyderman, C. S. Chen, T. Kasama, R. E. Dunin-Borkowski, C. A. F. Vaz, and J. A. C. Bland, Transverse domain walls in nanoconstrictions, Appl. Phys. Lett. 91, 112502 (2007).
  22. C. W. Sandweg, N. Wiese, D. McGrouther, S. J. Hermsdoerfer, H. Schultheiss, B. Leven, S. McVitie, B. Hillebrands, and J. N. Chapman, Direct observation of domain wall structures in curved permalloy wires containing an antinotch, J. Appl. Phys. 103, 093906 (2008).
  23. M. Kläui, H. Ehrke, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, D. Backes, L. J. Heyderman, C. A. F. Vaz, J. A. C. Bland, G. Faini, E. Cambril, and W. Wernsdorfer, Direct observation of domain-wall pinning at nanoscale constrictions, Appl. Phys. Lett. 87, 102509 (2005).
  24. T. Taniyama, I. Nakatani, T. Namikawa, and Y. Yamazaki, Resistivity due to Domain Walls in Co Zigzag Wires, Phys. Rev. Lett. 82, 2780 (1999).
  25. S. Hankemeier, A. Kobs, R. Frömter, and H. P. Oepen, Controlling the properties of vortex domain walls via magnetic seeding fields, Phys. Rev. B 82, 064414 (2010).
  26. P. O. Jubert, M. Kläui, A. Bischof, U. Rüdiger, and R. Allenspach, Velocity of vortex walls moved by current, J. Appl. Phys. 99, 08G523 (2006).
  27. A. Vanhaverbeke, A. Bischof, and R. Allenspach, Control of Domain Wall Polarity by Current Pulses, Phys. Rev. Lett. 101, 107202 (2008).
  28. L. Heyne, M. Kläui, D. Backes, P. Möhrke, T. a. Moore, J. G. Kimling, O. Boulle, U. Rüdiger, L. J. Heyderman, a. F. Rodriguez, F. Nolting, K. Kirsch, and R. Mattheis, Direct imaging of current-induced domain wall motion in CoFeB structures, J. Appl. Phys. 103, 07D928 (2008).
  29. M. Kläui, P. O. Jubert, R. Allenspach, A. Bischof, J. A. C. Bland, G. Faini, U. Rüdiger, C. A. F. Vaz, L. Vila, and C. Vouille, Direct Observation of Domain-Wall Configurations Transformed by Spin Currents, Phys. Rev. Lett. 95, 026601 (2005).
  30. M. Hayashi, L. Thomas, Ya. B. Bazaliy, C. Rettner, R. Moriya, X. Jiang, and S. S. P. Parkin, Influence of Current on Field-Driven Domain Wall Motion in Permalloy Nanowires from Time Resolved Measurements of Anisotropic Magnetoresistance, Phys. Rev. Lett. 96, 197207 (2006).
  31. J. L. Tsai, S. F. Lee, Y. D. Yao, C. Yu, and S. H. Liou, Magnetoresistance study in thin zig zag NiFe wires, J. Appl. Phys. 91, 7983 (2002).
  32. M. Tanase, D. M. Silevitch, C. L. Chien, and D. H. Reich, Magnetotransport properties of bent ferromagnetic nanowires, J. Appl. Phys. 93, 7616 (2003).
  33. L. K. Bogartand and D. Atkinson, Magnetotransport properties of bent ferromagnetic nanowires, Appl. Phys. Lett. 94, 042511 (2009).
  34. L. O’Brien, D. Petit, H. T. Zeng, E. R. Lewis, J. Sampaio, A. V. Jausovec, D. E. Read, and R. P. Cowburn, Near-Field Interaction between Domain Walls in Adjacent Permalloy Nanowires, Phys. Rev. Lett. 103, 077206 (2009).
  35. E. S. Wilhelm, D. McGrouther, L. Heyne, A. Bisig, and M. Kläui, Vortex domain wall chirality rectification due to the interaction with end domain spin structures in permalloy nanowires, Appl. Phys. Lett. 95, 252501 (2009).
  36. M. Donolato, F. Lofink, S. Hankemeier, J. M. Porro, H. P. Oepen, and P. Vavassori, Characterization of domain wall–based traps for magnetic beads separation, J. Appl. Phys. 111, 07B336 (2012).
  37. H. P. Oepen and H. Hopster, Magnetic Microscopy of Nanostructures (Springer-Verlag, Berlin, 2005), ISBN [Amazon][WorldCat].
  38. F. Lofink, S. Hankemeier, R. Frömter, J. Kirschner, and H. P. Oepen, Long-time stability of a low-energy electron diffraction spin polarization analyzer for magnetic imaging, Rev. Sci. Instrum. 83, 023708 (2012).
  39. A. Berger and H. P. Oepen, Magnetic domain walls in ultrathin fcc cobalt films, Phys. Rev. B 45, 12596 (1992).
  40. R. Frömter, S. Hankemeier, H. P. Oepen, and J. Kirschner, Optimizing a low-energy electron diffraction spin-polarization analyzer for imaging of magnetic surface structures, Rev. Sci. Instrum. 82, 033704 (2011).
  41. M. Donahue and D. Porter, Interagency Report NISTIR 6376, National Institute of Standards and Technology, 1999.
  42. Preliminary results for t=10  nm and w=100  nm show transverse walls that do not pin at the bend but at arbitrary positions within the wire. Moreover, the wall structure is highly deformed. The latter is also found for wires with t=10  nm and w=150  nm. Hence, these samples are not investigated in detail and omitted within the paper.
  43. D. Stickler, R. Frömter, W. Li, A. Kobs, and H. P. Oepen, Integrated setup for the fabrication and measurement of magnetoresistive nanoconstrictions in ultrahigh vacuum, Rev. Sci. Instrum. 79, 103901 (2008).
  44. N. Mikuszeit, S. Pütter, R. Frömter, and H. P. Oepen, Magneto-optic Kerr effect: Incorporating the nonlinearities of the analyzer into static photometric ellipsometry analysis, J. Appl. Phys. 97, 103107 (2005).
  45. A. Berger, S. Knappmann, and H. P. Oepen, Magneto-optical Kerr effect study of ac susceptibilities in ultrathin cobalt films, J. Appl. Phys. 75, 5598 (1994).
  46. S. Mendach, J. Podbielski, J. Topp, W. Hansen, and D. Heitmann, Spin-wave confinement in rolled-up ferromagnetic tubes, Appl. Phys. Lett. 93, 262501 (2008).
  47. X. Liu, R. Sooryakumar, C. J. Gutierrez, and G. A. Prinz, Exchange stiffness and magnetic anisotropies in bcc Fe1−xCox alloys, J. Appl. Phys. 75, 7021 (1994).

  48. The exchange stiffness of FexCo100−x alloys has been found to be almost independent of stoichiometry, exhibiting values of 30–35  pJ/m in the composition range of 32<x<70. For a Fe18Co72B10 alloy, a similar value (A=29  pJ/m) has been reported [49], while it has been demonstrated that varying the boron content has no impact on A [50]. The same seems to hold for adding Si to CoFe, as a similar exchange stiffness of 31.5  pJ/m is found for the Heusler compound Co2FeSi despite the huge amount of Si [51]. Hence, it is reasonable to assume a similar exchange stiffness for Co39Fe54Si7.

  49. C. Bilzer, T. Devolder, Joo-Von Kim, G. Counil, C. Chappert, S. Cardoso, and P. P. Freitas, Study of the dynamic magnetic properties of soft CoFeB films, J. Appl. Phys. 100, 053903 (2006).
  50. T. Devolder, J. V. Kim, L. Nistor, R. Sousa, B. Rodmacq, and B. Dieny, Exchange stiffness in ultrathin perpendicularly magnetized CoFeB layers determined using the spectroscopy of electrically excited spin waves, J. Appl. Phys. 120, 183902 (2016).
  51. O. Gaier, J. Hamrle, S. Trudel, B. Hillebrands, H. Schneider, and G. Jakob, Exchange stiffness in the Co2FeSi Heusler compound, J. Phys. D 42, 232001 (2009).
  52. E. Feldtkeller, Ripple hysteresis in thin magnetic films, J. Appl. Phys. 34, 2646 (1963).
  53. H. B. Callen, R. L. Coren, and W. D. Doyle, Magnetization ripple and Arctic foxes, J. Appl. Phys. 36, 1064 (1965).
  54. K. J. Harte, Theory of magnetization ripple in ferromagnetic films, J. Appl. Phys. 39, 1503 (1968).
  55. O. Tchernyshyov and G.-W. Chern, Fractional Vortices and Composite Domain Walls in Flat Nanomagnets, Phys. Rev. Lett. 95, 197204 (2005).
  56. G.-W. Chern, H. Youk, and O. Tchernyshyov, Topological defects in flat nanomagnets: The magnetostatic limit, J. Appl. Phys. 99, 08Q505 (2006).
  57. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 1995).
  58. A. Aharoni, Local demagnetization in a rectangular ferromagnetic prism, Phys. Status Solidi (b) 229, 1413 (2002).
  59. S. Pütter, N. Mikuszeit, E. Y. Vedmedenko, and H. P. Oepen, The effect of tilted edges on the shape anisotropy and stray field coupling of uniformly magnetized rectangular elements, J. Appl. Phys. 106, 043916 (2009).
  60. S Hankemeier, R. Frömter, N. Mikuszeit, D. Stickler, H. Stillrich, S. Pütter, E. Y. Vedmedenko, and H. P. Oepen, The Effect of Tilted Edges on the Shape Anisotropy and Stray Field Coupling of Uniformly Magnetized Rectangular Elements, Phys. Rev. Lett. 103, 147204 (2009).
  61. M. Redjdal, A. Kakay, M. Ruane, and F. Humphrey, Cross-tie walls in thin permalloy films, IEEE Trans. Magn. 38, 2471 (2002).
  62. N. Wiese, S. McVitie, J. N. Chapman, A. Capella-Kort, and F. Otto, On the scaling behaviour of cross-tie domain wall structures in patterned NiFe elements, Europhys. Lett. 80, 57003 (2007).
  63. A. Hubert and R. Schäfer, Magnetic Domains (Springer-Verlag, Berlin, 1998).

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Phys. Rev. Applied 8, 024008– Published 17 August, 2017
  • Received 21 November 2016

© 2017 American Physical Society

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