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Tubular Geometries

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Curvilinear Micromagnetism

Part of the book series: Topics in Applied Physics ((TAP,volume 146))

Abstract

Following the recent developments in materials science and sample fabrication magnetic nanowires and nanotubes became an intensively studied research field in magnetism. However, it should be mentioned that the driving force behind can be attributed to the theoretical, both analytical and numerical predictions of novel magnetic textures and interesting features, such as chiral domain wall motion, the Spin-Cherenkov effect or the curvature-induced magnetochiral effects in general. In this chapter, the static properties of tubular nanomagnets will be reviewed, including magnetic configurations, domain walls, their types, and energetics as well as possible reversal mechanisms. The dynamical properties section is divided into two parts. The first part will guide you through the domain wall motion related to magnetochiral effects. The second part will discuss the general aspects of spin wave propagation. Aspects, being static or dynamic, related to magnetochiral effects or curvature and topology will be addressed mostly. For those interested in a summary of experimental methods to fabricate tubular samples, an overview of all possible techniques one can use to characterize or measure magnetic tubes, or in a guide through all the analytical and numerical formalism developed to investigate the static and dynamic properties of magnetic nanotubes, we kindly ask to read these recently published excellent books by M. Vázquez [1, 2].

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References

  1. M. Vázquez, Magnetic Nano-and Microwires: Design, Synthesis, Properties and Applications (Woodhead Publishing, Sawston, 2015)

    Google Scholar 

  2. M. Vázquez, Magnetic Nano-and Microwires: Design, Synthesis, Properties and Applications, 2nd edn. (Woodhead Publishing, Sawston, 2020)

    Google Scholar 

  3. W.F. Brown Jr., Micromagnetics (Interscience Publishers, New York, 1963)

    MATH  Google Scholar 

  4. A. Hubert, R. Schäfer, Magnetic Domains, the Analysis of Magnetic Microstructures (Springer, Berlin, 2009)

    Google Scholar 

  5. R. Hertel, Computational micromagnetism of magnetization processes in nickel nanowires. J. Magn. Magn. Mater. 249(1), 251–256 (2002)

    Article  ADS  Google Scholar 

  6. R. Hertel, J. Kirschner, Magnetization reversal dynamics in nickel nanowires. Phys. B: Condens. Matter 343(1), 206–210 (2004)

    Article  ADS  Google Scholar 

  7. R. Hertel, J. Kirschner, Magnetic drops in a soft-magnetic cylinder. J. Magn. Magn. Mater. 278(3), L291–L297 (2004)

    Article  ADS  Google Scholar 

  8. P. Landeros, S. Allende, J. Escrig, E. Salcedo, D. Altbir, E.E. Vogel, Reversal modes in magnetic nanotubes. Appl. Phys. Lett. 90, 102501 (2007)

    Google Scholar 

  9. H.G. Piao, J.H. Shim, D. Djuhana, D.H. Kim, Intrinsic pinning behavior and propagation onset of three-dimensional Bloch-point domain wall in a cylindrical ferromagnetic nanowire. Appl. Phys. Lett. 102(11), 112405 (2013)

    Google Scholar 

  10. S. Da Col, S. Jamet, N. Rougemaille, A. Locatelli, T.O. Mentes, B.S. Burgos, R. Afid, M. Darques, L. Cagnon, J.C. Toussaint, O. Fruchart, Observation of Bloch-point domain walls in cylindrical magnetic nanowires. Phys. Rev. B 89, 180405 (2014)

    Google Scholar 

  11. P. Landeros, A.S. Núñez, Domain wall motion on magnetic nanotubes. J. Appl. Phys. 108(3), 033917 (2010)

    Google Scholar 

  12. R. Hertel, Curvature-induced magnetochirality. Spin 03(03), 1340009 (2013)

    Google Scholar 

  13. C. Dietrich, R. Hertel, M. Huber, D. Weiss, R. Schäfer, J. Zweck, Influence of perpendicular magnetic fields on the domain structure of permalloy microstructures grown on thin membranes. Phys. Rev. B 77, 174427 (2008)

    Google Scholar 

  14. Z.K. Wang, H.S. Lim, H.Y. Liu, S.C. Ng, M.H. Kuok, L.L. Tay, D.J. Lockwood, M.G. Cottam, K.L. Hobbs, P.R. Larson, J.C. Keay, G.D. Lian, M.B. Johnson, Spin waves in nickel nanorings of large aspect ratio. Phys. Rev. Lett. 94, 137208 (2005)

    Google Scholar 

  15. N.A. Usov, A.P. Chen, A. Zhukov, J. González, Nucleation field of a soft magnetic nanotube with uniaxial anisotropy. J. Appl. Phys. 104, 083902 (2008)

    Google Scholar 

  16. P. Landeros, O.J. Suarez, A. Cuchillo, P. Vargas, Equilibrium states and vortex domain wall nucleation in ferromagnetic nanotubes. Phys. Rev. B 79, 024404 (2009)

    Google Scholar 

  17. D. Rüffer, R. Huber, P. Berberich, S. Albert, E. Russo-Averchi, M. Heiss, J. Arbiol, A. Fontcuberta i Morral, D. Grundler, Magnetic states of an individual Ni nanotube probed by anisotropic magnetoresistance. Nanoscale 4, 4989–4995 (2012)

    Google Scholar 

  18. A. Buchter, J. Nagel, D. Rüffer, F. Xue, D.P. Weber, O.F. Kieler, T. Weimann, J. Kohlmann, A.B. Zorin, E. Russo-Averchi, R. Huber, P. Berberich, A. Fontcuberta i Morral, M. Kemmler, R. Kleiner, D. Koelle, D. Grundler, M. Poggio, Reversal mechanism of an individual Ni nanotube simultaneously studied by torque and squid magnetometry. Phys. Rev. Lett. 111, 067202 (2013)

    Google Scholar 

  19. A. Buchter, R. Wölbing, M. Wyss, O.F. Kieler, T. Weimann, J. Kohlmann, A.B. Zorin, D. Rüffer, F. Matteini, G. Tütüncüoglu, F. Heimbach, A. Kleibert, A. Fontcuberta i Morral, D. Grundler, R. Kleiner, D. Koelle, M. Poggio, Magnetization reversal of an individual exchange-biased permalloy nanotube. Phys. Rev. B 92, 214432 (2015)

    Google Scholar 

  20. M. Yan, C. Andreas, A. Kákay, F. García-Sánchez, R. Hertel, Fast domain wall dynamics in magnetic nanotubes: suppression of Walker breakdown and Cherenkov-like spin wave emission. Appl. Phys. Lett. 99, 122505 (2011)

    Google Scholar 

  21. J.A. Otálora, J.A. López-López, P. Vargas, P. Landeros, Chirality switching and propagation control of a vortex domain wall in ferromagnetic nanotubes. Appl. Phys. Lett. 100, 072407 (2012)

    Google Scholar 

  22. M. Yan, C. Andreas, A. Kákay, F. García-Sánchez, R. Hertel, Chiral symmetry breaking and pair-creation mediated walker breakdown in magnetic nanotubes. Appl. Phys. Lett. 100(25), 252401 (2012)

    Google Scholar 

  23. J.A. Otálora, J.A. López-López, P. Landeros, P. Vargas, A.S. Núñez, Breaking of chiral symmetry in vortex domain wall propagation in ferromagnetic nanotubes. J. Magn. Magn. Mater. 341, 86–92 (2013)

    Article  ADS  Google Scholar 

  24. J.A. Otálora, M. Yan, H. Schultheiss, R. Hertel, A. Kákay, Curvature-induced asymmetric spin-wave dispersion. Phys. Rev. Lett. 117, 227203 (2016)

    Google Scholar 

  25. D.D. Sheka, O.V. Pylypovskyi, P. Landeros, Y. Gaididei, A. Kákay, D. Makarov, Nonlocal chiral symmetry breaking in curvilinear magnetic shells. Commun. Phys. 3(1), 128 (2020)

    Google Scholar 

  26. D. Zhang, Z. Liu, S. Han, C. Li, B. Lei, M.P. Stewart, J.M. Tour, C. Zhou, Magnetite (Fe3O4) core-shell nanowires: synthesis and magnetoresistance. Nano Lett. 4, 2151 (2004)

    Google Scholar 

  27. Z. Liu, D. Zhang, S. Han, C. Li, B. Lei, W. Lu, J. Fang, C. Zhou, Single crystalline magnetite nanotubes. J. Am. Chem. Soc. 127, 6 (2005)

    Google Scholar 

  28. I. Mönch, D. Makarov, R. Koseva, L. Baraban, D. Karnaushenko, C. Kaiser, K.F. Arndt, O.G. Schmidt, Rolled-up magnetic sensor: nanomembrane architecture for in-flow detection of magnetic objects. ACS Nano 5, 7436 (2011)

    Google Scholar 

  29. J. Schumann, K.G. Lisunov, W. Escoffier, B. Raquet, J.M. Broto, E. Arushanov, I. Mönch, D. Makarov, C. Deneke, O.G. Schmidt, Magnetoresistance of rolled-up Fe 3 Si nanomembranes. Nanotechnology 23, 255701 (2012)

    Google Scholar 

  30. C. Müller, D. Makarov, I. Mönch, C.C.B. Bufon, Y. Mei, O.G. Schmidt, Rolled-up magnetic nanomembranes for sensor applications, Handbook of Functional Nanomaterials. Volume 3 - Application and Development (Nova, 2013), pp. 453–472

    Google Scholar 

  31. D. Rüffer, M. Slot, R. Huber, T. Schwarze, F. Heimbach, G. Tütüncüoglu, F. Matteini, E. Russo-Averchi, A. Kovács, R. Dunin-Borkowski, R.R. Zamani, J.R. Morante, J. Arbiol, A. Fontcuberta i Morral, D. Grundler, Anisotropic magnetoresistance of individual CoFeB and Ni nanotubes with values of up to 1.4. APL Mater. 2(7), 076112 (2014)

    Google Scholar 

  32. G. Gioia, R.D. James, Micromagnetics of very thin films. Proc. R. Soc. A 453(1956), 213–223 (1997)

    Article  ADS  Google Scholar 

  33. G. Carbou, Thin layers in micromagnetism. Math. Model. Methods Appl. Sci. 11(09), 1529–1546 (2001)

    Google Scholar 

  34. R. Kohn, V. Slastikov, Effective dynamics for ferromagnetic thin films: a rigorous justification. Proc. R. Soc. A 461, 143–154 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Y. Gaididei, V.P. Kravchuk, D.D. Sheka, Curvature effects in thin magnetic shells. Phys. Rev. Lett. 112, 257203 (2014)

    Google Scholar 

  36. G. Di Fratta, Micromagnetics of curved thin films. Z. Angew. Math. Phys. 71(4), 111 (2020)

    Google Scholar 

  37. J. Dobson, Gene therapy progress and prospects: magnetic nanoparticle-based gene delivery. Gene Ther. 13, 283 (2006)

    Google Scholar 

  38. S.C. McBain, H.H.P. Yiu, J. Dobson, Magnetic nanoparticles for gene and drug delivery. Int. J. Nanomed. 3(2), 169–180 (2008)

    Google Scholar 

  39. Q.A. Pankhurst, N.T.K. Thanh, S.K. Jones, J. Dobson, Progress in applications of magnetic nanoparticles in biomedicine. J. Phys. D: Appl. Phys. 42(22), 224001 (2009)

    Google Scholar 

  40. O.L. Gobbo, K. Sjaastad, M.W. Radomski, Y. Volkov, A. Prina-Mello, Magnetic nanoparticles in cancer theranostics. Theranostics 5(11), 1249–1263 (2015)

    Article  Google Scholar 

  41. D. Letellier, O. Sandre, C. Ménager, V. Cabuil, M. Lavergne, Magnetic tubules. Mater. Sci. Eng. C 5(2), 153 (1997)

    Google Scholar 

  42. V.K. Varadan, L. Chen, J. Xie, Magnetic Nanotubes and Their Biomedical Applications (Wiley, New York, 2008), pp. 273–327

    Google Scholar 

  43. X. Bai, Magnetic Nanotubes as Magnetic Resonance Contrast Agents: Synthesis, Characterization, Cytotoxicity and Cellular Uptake (VDM Publishing, Riga, 2009)

    Google Scholar 

  44. X.W. Lou, L.A. Archer, Z. Yang, Hollow micro-/nanostructures: synthesis and applications. Adv. Mater. 20(21), 3987–4019 (2008)

    Article  Google Scholar 

  45. S.J. Son, J. Reichel, B. He, M. Schuchman, S.B. Lee, Magnetic nanotubes for magnetic-field-assisted bioseparation, biointeraction, and drug delivery. J. Am. Chem. Soc. 127(20), 7316–7317 (2005)

    Article  Google Scholar 

  46. S.J. Son, X. Bai, S.B. Lee, Inorganic hollow nanoparticles and nanotubes in nanomedicine: Part 1. Drug/gene delivery applications. Drug Discov. Today 12(15/16), 650–656 (2007)

    Google Scholar 

  47. D. Lee, R.E. Cohen, M.F. Rubner, Heterostructured magnetic nanotubes. Langmuir 23(1), 123–129 (2007)

    Article  Google Scholar 

  48. K. Žužek Rožman, D. Pečko, S. Šturm, U. Maver, P. Nadrah, M. Bele, S. Kobe, Electrochemical synthesis and characterization of Fe70Pd30 nanotubes for drug-delivery applications. Mater. Chem. Phys. 133(1), 218–224 (2012)

    Article  Google Scholar 

  49. Y. Yang, X.L. Liu, J.B. Yi, Y. Yang, H.M. Fan, J. Ding, Stable vortex magnetite nanorings colloid: micromagnetic simulation and experimental demonstration. J. Appl. Phys. 111, 044303 (2012)

    Google Scholar 

  50. X.L. Liu, Y. Yang, C.T. Ng, L.Y. Zhao, Y. Zhang, B.H. Bay, H.M. Fan, J. Ding, Magnetic vortex nanorings: a new class of hyperthermia agent for highly efficient in vivo regression of tumors. Adv. Mater. 27(11), 1939–1944 (2015)

    Article  Google Scholar 

  51. D.F. Gutierrez-Guzman, L.I. Lizardi, J.A. Otalora, P. Landeros, Hyperthermia in low aspect-ratio magnetic nanotubes for biomedical applications. Appl. Phys. Lett. 110(13), 133702 (2017)

    Google Scholar 

  52. X. Bai, S.J. Son, S. Zhang, W. Liu, E.K. Jordan, J.A. Frank, T. Venkatesan, S. Bok Lee, Synthesis of superparamagnetic nanotubes as MRI contrast agents and for cell labeling. Nanomedicine 3(2), 163–174 (2008)

    Article  Google Scholar 

  53. J. Escrig, S. Allende, D. Altbir, M. Bahiana, Magnetostatic interactions between magnetic nanotubes. Appl. Phys. Lett. 93(2), 023101 (2008)

    Google Scholar 

  54. O.J. Suarez, P. Vargas, E.E. Vogel, Energy and force between two magnetic nanotubes. J. Magn. Magn. Mater. 321(22), 3658–3664 (2009)

    Article  ADS  Google Scholar 

  55. R.F. Neumann, M. Bahiana, J. Escrig, S. Allende, K. Nielsch, D. Altbir, Stability of magnetic nanoparticles inside ferromagnetic nanotubes. Appl. Phys. Lett. 98(2), 022502 (2011)

    Google Scholar 

  56. D.P. Weber, D. Rüffer, A. Buchter, F. Xue, E. Russo-Averchi, R. Huber, P. Berberich, J. Arbiol, A. Fontcuberta i Morral, D. Grundler, M. Poggio, Cantilever magnetometry of individual Ni nanotubes. Nano Lett. 12(12), 6139–6144 (2012)

    Google Scholar 

  57. J. Nagel, A. Buchter, F. Xue, O.F. Kieler, T. Weimann, J. Kohlmann, A.B. Zorin, D. Rüffer, E. Russo-Averchi, R. Huber, P. Berberich, A. Fontcuberta i Morral, D. Grundler, R. Kleiner, D. Koelle, M. Poggio, M. Kemmler, Nanoscale multifunctional sensor formed by a Ni nanotube and a scanning Nb nanoSQUID. Phys. Rev. B 88, 064425 (2013)

    Google Scholar 

  58. V. Magdanz, M. Guix, O. Schmidt, Tubular micromotors: from microjets to spermbots. Robot. Biomim. 1, 11 (2014)

    Google Scholar 

  59. Y. Mei, G. Huang, A.A. Solovev, E. Bermúdez-Ureña, I. Mönch, F. Ding, T. Reindl, R.K.Y. Fu, P.K. Chu, O.G. Schmidt, Versatile approach for integrative and functionalized tubes by strain engineering of nanomembranes on polymers. Adv. Mater. 20, 4085 (2008)

    Google Scholar 

  60. S. Sanchez, A.A. Solovev, S. Schulze, O.G. Schmidt, Controlled manipulation of multiple cells using catalytic microbots. Chem. Commun. 47, 698 (2011)

    Google Scholar 

  61. V. Magdanz, S. Sanchez, O.G. Schmidt, Development of a sperm-flagella driven micro-bio-robot. Adv. Mater. 25, 6581 (2013)

    Google Scholar 

  62. S. Sanchez, W. Xi, A.A. Solovev, L. Soler, V. Magdanz, O.G. Schmidt, Tubular micro-nanorobots: smart design for bio-related applications, in Small-Scale Robotics. From Nano-to-Millimeter-Sized Robotic Systems and Applications. Lecture Notes in Computer Science, vol. 8336, ed. by I. Paprotny, S. Bergbreiter (Springer, Berlin, 2014), pp. 16–27

    Google Scholar 

  63. X.F. Han, S. Shamaila, R. Sharif, Ferromagnetic nanowires and nanotubes, in Electrodeposited Nanowires and Their Applications, ed. by N. Lupu (InTech, 2010), pp. 141–166

    Google Scholar 

  64. Y. Ye, B. Geng, Magnetic nanotubes: synthesis, properties, and applications. Crit. Rev. Solid State Mater. Sci. 37(2), 75–93 (2012)

    Article  ADS  Google Scholar 

  65. X. Wei Wang, Z. Cheng He, J. Shan Li, Z. Hao Yuan, Controllable synthesis and magnetic properties of ferromagnetic nanowires and nanotubes. Curr. Nanosci. 8(5), 801–809 (2012)

    Article  ADS  Google Scholar 

  66. M. Stano, O. Fruchart, Magnetic nanowires and nanotubes. Handb. Magn. Mater. 27, 155 (2018)

    Google Scholar 

  67. R. Streubel, P. Fischer, F. Kronast, V.P. Kravchuk, D.D. Sheka, Y. Gaididei, O.G. Schmidt, D. Makarov, Magnetism in curved geometries. J. Phys. D: Appl. Phys. 49(36), 363001 (2016)

    Google Scholar 

  68. M.P. Proenca, C.T. Sousa, J. Ventura, J.P. Araujo, 6 - cylindrical magnetic nanotubes: synthesis, magnetism and applications, in Magnetic Nano- and Microwires. Woodhead Publishing Series in Electronic and Optical Materials, ed. by M. Vázquez, 2nd edn. (Woodhead Publishing, Sawston, 2020), pp. 135–184

    Google Scholar 

  69. M. Poggio, 17 - determining magnetization configurations and reversal of individual magnetic nanotubes, in Magnetic Nano- and Microwires. Woodhead Publishing Series in Electronic and Optical Materials, ed. by M. Vázquez, 2nd edn. (Woodhead Publishing, Sawston, 2020), pp. 491–517

    Google Scholar 

  70. H. Lim, M. Kuok, Spin waves in ferromagnetic nanowires and nanotubes, Handbook of Nanophysics (CRC Press, Boca Raton, 2010), pp. 1–13

    Google Scholar 

  71. G. Gubbiotti, Three-Dimensional Magnonics: Layered, Micro- and Nanostructures (CRC Press, Boca Raton, 2019)

    Google Scholar 

  72. P. Landeros, J. Escrig, D. Altbir, Vortex structures in cylindrical magnetic nanoparticles, in Electromagnetic, Magnetostatic, and Exchange-Interaction Vortices in Confined Magnetic Structures, ed. by E.O. Kamenetskii (Transworld Research Network, Kerala, 2008)

    Google Scholar 

  73. E.E. Vogel, P. Vargas, D. Altbir, J. Escrig, Magnetic nanotubes, in Handbook of Nanophysics (CRC Press, Boca Raton, 2010)

    Google Scholar 

  74. R. Hertel, Ultrafast domain wall dynamics in magnetic nanotubes and nanowires. J. Phys.: Condens. Matter 28(48), 483002 (2016)

    Google Scholar 

  75. D. Makarov, O.M. Volkov, A. Kákay, O.V. Pylypovskyi, B. Budinská, O.V. Dobrovolskiy, New dimension in magnetism and superconductivity: 3D and curvilinear nanoarchitectures. Adv. Mater. 34, 2101758 (2022)

    Google Scholar 

  76. A. Arrott, B. Heinrich, A. Aharoni, Point singularities and magnetization reversal in ideally soft ferromagnetic cylinders. IEEE Trans. Magn. 15(5), 1228–1235 (1979)

    Article  ADS  Google Scholar 

  77. C.R. Chang, C.M. Lee, J.S. Yang, Magnetization curling reversal for an infinite hollow cylinder. Phys. Rev. B 50, 6461 (1994)

    Google Scholar 

  78. C.M. Lee, C.R. Chang, Coercivity and nucleation field of hollow ferromagnetic particles. Mater. Chem. Phys. 43(2), 183–186 (1996)

    Article  Google Scholar 

  79. A. Saxena, R. Dandoloff, Curvature-induced geometrical frustration in magnetic systems. Phys. Rev. B 55, 11049–11051 (1997)

    Article  ADS  Google Scholar 

  80. E.H. Frei, S. Shtrikman, D. Treves, Critical size and nucleation field of ideal ferromagnetic particles. Phys. Rev. 106, 446 (1957)

    Google Scholar 

  81. A. Aharoni, S. Shtrikman, Magnetization curve of the infinite cylinder. Phys. Rev. 109, 1522 (1958)

    Google Scholar 

  82. A. Aharoni, Introduction to the Theory of Ferromagnetism, vol. 109 (Oxford University Press, Oxford, 2000)

    Google Scholar 

  83. W. Wernsdorfer, B. Doudin, D. Mailly, K. Hasselbach, A. Benoit, J. Meier, J.P. Ansermet, B. Barbara, Nucleation of magnetization reversal in individual nanosized nickel wires. Phys. Rev. Lett. 77, 1873 (1996)

    Google Scholar 

  84. E. Varga, A. Beyer, Magnetic field of a uniformly magnetized hollow cylinder. IEEE Trans. Magn. 34(3), 613–618 (1998)

    Article  ADS  Google Scholar 

  85. P. Landeros, P.R. Guzmán, R. Soto-Garrido, J. Escrig, Magnetostatic fields in tubular nanostructures. J. Phys. D: Appl. Phys. 42, 225002 (2009)

    Google Scholar 

  86. J. Lee, D. Suess, T. Schrefl, K.H. Oh, J. Fidler, Magnetic characteristics of ferromagnetic nanotube. J. Magn. Magn. Mater. 310, 2445 (2007)

    Google Scholar 

  87. A.P. Chen, N.A. Usov, J.M. Blanco, J. Gonzalez, Equilibrium magnetization states in magnetic nanotubes and their evolution in external magnetic field. J. Magn. Magn. Mater. 316, e317 (2007)

    Google Scholar 

  88. A.P. Chen, K.Y. Guslienko, J. Gonzalez, Magnetization configurations and reversal of thin magnetic nanotubes with uniaxial anisotropy. J. Appl. Phys. 108(8), 083920 (2010)

    Google Scholar 

  89. A.P. Chen, J.M. Gonzalez, K.Y. Guslienko, Magnetization configurations and reversal of magnetic nanotubes with opposite chiralities of the end domains. J. Appl. Phys. 109(7), 073923 (2011)

    Google Scholar 

  90. E. Feldtkeller, H. Thomas, Struktur und Energie von Blochlinien in dünnen ferromagnetischenSchichten. Physik der kondensierten Materie 4(1), 8–14 (1965)

    ADS  Google Scholar 

  91. A. Aharoni, Upper bound to a single domain behavior of a ferromagnetic cylinder. J. Appl. Phys. 68(6), 2892–2900 (1990)

    Article  ADS  Google Scholar 

  92. N.A. Usov, S.E. Peschany, Magnetization curling in a fine cylindrical particle. J. Magn. Magn. Mater. 118(3), L290–L294 (1993)

    Article  ADS  Google Scholar 

  93. R.P. Cowburn, D.K. Koltsov, A.O. Adeyeye, M.E. Welland, D.M. Tricker, Single-domain circular nanomagnets. Phys. Rev. Lett. 83, 1042–1045 (1999)

    Article  ADS  Google Scholar 

  94. M. Schneider, H. Hoffmann, J. Zweck, Lorentz microscopy of circular ferromagnetic permalloy nanodisks. Appl. Phys. Lett. 77(18), 2909–2911 (2000)

    Article  ADS  Google Scholar 

  95. K.Y. Guslienko, V. Novosad, Y. Otani, H. Shima, K. Fukamichi, Magnetization reversal due to vortex nucleation, displacement, and annihilation in submicron ferromagnetic dot arrays. Phys. Rev. B 65, 024414 (2001)

    Google Scholar 

  96. K.Y. Guslienko, K.L. Metlov, Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied field. Phys. Rev. B 63, 100403 (2001)

    Google Scholar 

  97. J. d’Albuquerque e Castro, D. Altbir, J.C. Retamal, P. Vargas, Scaling approach to the magnetic phase diagram of nanosized systems. Phys. Rev. Lett. 88, 237202 (2002)

    Google Scholar 

  98. K.L. Metlov, K.Y. Guslienko, Stability of magnetic vortex in soft magnetic nano-sized circular cylinder. J. Magn. Magn. Mater. 242–245, 1015–1017 (2002)

    Article  ADS  Google Scholar 

  99. R. Höllinger, A. Killinger, U. Krey, Statics and fast dynamics of nanomagnets with vortex structure. J. Magn. Magn. Mater. 261(1), 178–189 (2003)

    Article  ADS  Google Scholar 

  100. P.O. Jubert, R. Allenspach, Analytical approach to the single-domain-to-vortex transition in small magnetic disks. Phys. Rev. B 70, 144402 (2004)

    Google Scholar 

  101. S. Savel’ev, F. Nori, Magnetic and mechanical buckling: modified Landau theory approach to study phase transitions in micromagnetic disks and compressed rods. Phys. Rev. B 70, 214415 (2004)

    Google Scholar 

  102. P. Landeros, J. Escrig, D. Altbir, D. Laroze, J. d’Albuquerque e Castro, P. Vargas, Scaling relations for magnetic nanoparticles. Phys. Rev. B 71, 094435 (2005)

    Google Scholar 

  103. J. Mejía-López, D. Altbir, A.H. Romero, X. Batlle, I.V. Roshchin, C.P. Li, I.K. Schuller, Vortex state and effect of anisotropy in sub-100-nm magnetic nanodots. J. Appl. Phys. 100(10), 104319 (2006)

    Google Scholar 

  104. J. Rothman, M. Kläui, L. Lopez-Diaz, C.A.F. Vaz, A. Bleloch, J.A.C. Bland, Z. Cui, R. Speaks, Observation of a bi-domain state and nucleation free switching in mesoscopic ring magnets. Phys. Rev. Lett. 86, 1098–1101 (2001)

    Article  ADS  Google Scholar 

  105. F.J. Castaño, C.A. Ross, C. Frandsen, A. Eilez, D. Gil, H.I. Smith, M. Redjdal, F.B. Humphrey, Metastable states in magnetic nanorings. Phys. Rev. B 67, 184425 (2003)

    Google Scholar 

  106. M. Kläui, C.A.F. Vaz, L. Lopez-Diaz, J.A.C. Bland, Vortex formation in narrow ferromagnetic rings. J. Phys.: Condens. Matter 15(21), R985–R1024 (2003)

    Google Scholar 

  107. M. Kläui, C.A.F. Vaz, J.A.C. Bland, T.L. Monchesky, J. Unguris, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, L.J. Heyderman, Z. Cui, Direct observation of spin configurations and classification of switching processes in mesoscopic ferromagnetic rings. Phys. Rev. B 68, 134426 (2003)

    Google Scholar 

  108. M. Kläui, C.A.F. Vaz, J.A.C. Bland, L.J. Heyderman, C. David, E.H.C.P. Sinnecker, A.P. Guimarães, Multistep switching phase diagram of ferromagnetic ring structures. J. Appl. Phys. 95(11), 6639–6641 (2004)

    Article  ADS  Google Scholar 

  109. P. Landeros, J. Escrig, D. Altbir, M. Bahiana, J. da Albuquerque e Castro, Stability of magnetic configurations in nanorings. J. Appl. Phys. 100(4), 044311 (2006)

    Google Scholar 

  110. M. Beleggia, J. Lau, M. Schofield, Y. Zhu, S. Tandon, M.D. Graef, Phase diagram for magnetic nano-rings. J. Magn. Magn. Mater. 301, 131 (2006)

    Google Scholar 

  111. C.A.F. Vaz, T.J. Hayward, J. Llandro, F. Schackert, D. Morecroft, J.A.C. Bland, M. Kläui, M. Laufenberg, D. Backes, U. Rödiger, F.J. Castaño, C.A. Ross, L.J. Heyderman, F. Nolting, A. Locatelli, G. Faini, S. Cherifi, W. Wernsdorfer, Ferromagnetic nanorings. J. Phys.: Condens. Matter 19(25), 255207 (2007)

    Google Scholar 

  112. J. Escrig, P. Landeros, D. Altbir, E. Vogel, P. Vargas, Phase diagrams of magnetic nanotubes. J. Magn. Magn. Mater. 308(2), 233–237 (2007)

    Article  ADS  Google Scholar 

  113. J. Escrig, P. Landeros, D. Altbir, E. Vogel, Effect of anisotropy in magnetic nanotubes. J. Magn. Magn. Mater. 310(2, Part 3), 2448–2450 (2007)

    Google Scholar 

  114. M. Wyss, A. Mehlin, B. Gross, A. Buchter, A. Farhan, M. Buzzi, A. Kleibert, G. Tütüncüoglu, F. Heimbach, A. Fontcuberta i Morral, D. Grundler, M. Poggio, Imaging magnetic vortex configurations in ferromagnetic nanotubes. Phys. Rev. B 96, 024423 (2017)

    Google Scholar 

  115. N.A. Usov, A. Zhukov, J. González, Domain walls and magnetization reversal process in soft magnetic nanowires and nanotubes. J. Magn. Magn. Mater. 316, 255–261 (2007)

    Article  ADS  Google Scholar 

  116. D. Sanz-Hernández, A. Hierro-Rodriguez, C. Donnelly, J. Pablo-Navarro, A. Sorrentino, E. Pereiro, C. Magén, S. McVitie, J.M. de Teresa, S. Ferrer, P. Fischer, A. Fernández-Pacheco, Artificial double-helix for geometrical control of magnetic chirality. ACS Nano 14(7), 8084–8092 (2020). PMID: 32633492

    Google Scholar 

  117. R. Streubel, E.Y. Tsymbal, P. Fischer, Magnetism in curved geometries. J. Appl. Phys. 129(21), 210902 (2021)

    Google Scholar 

  118. J.A. Fernandez-Roldan, D. Chrischon, L.S. Dorneles, O. Chubykalo-Fesenko, M. Vazquez, C.A. Bran, Comparative study of magnetic properties of large diameter Co nanowires and nanotubes. Nanomaterials 8, 692 (2018)

    Google Scholar 

  119. A. Ruiz-Clavijo, O. Caballero-Calero, M. Martín-González, Revisiting anodic alumina templates: from fabrication to applications. Nanoscale 13, 2227–2265 (2021)

    Article  Google Scholar 

  120. G. Seniutinas, A. Weber, C. Padeste, I. Sakellari, M. Farsari, C. David, Beyond 100nm resolution in 3D laser lithography - post processing solutions. Microelectron. Eng. 191, 25 (2018)

    Google Scholar 

  121. D. Gräfe, S.L. Walden, J. Blinco, M. Wegener, E. Blasco, C. Barner-Kowollik, It’s in the fine print: erasable three-dimensional laser-printed micro- and nanostructures. Angew. Chem. Int. Ed. 59, 2 (2020)

    Google Scholar 

  122. M. Hunt, M. Taverne, J. Askey, A. May, A. Van Den Berg, Y.L. Ho, J. Rarity, S. Ladak, Harnessing multi-photon absorption to produce three-dimensional magnetic structures at the nanoscale. Materials 13, 761 (2020)

    Google Scholar 

  123. J.M. De Teresa, A. Fernández-Pacheco, R. Córdoba, L. Serrano-Ramón, S. Sangiao, M.R. Ibarra, Review of magnetic nanostructures grown by focused electron beam induced deposition (FEBID). J. Phys. D: Appl. Phys. 49(24), 243003 (2016)

    Google Scholar 

  124. R. Winkler, J. Fowlkes, P. Rack, H. Plank, 3D nanoprinting via focused electron beams. J. Appl. Phys. 125(21), 210901 (2019)

    Google Scholar 

  125. L. Skoric, D. Sanz-Hernández, F. Meng, C. Donnelly, S. Merino-Aceituno, A. Fernández-Pacheco, Layer-by-layer growth of complex-shaped three-dimensional nanostructures with focused electron beams. Nano Lett. 20(1), 184 (2020)

    Google Scholar 

  126. O.M. Volkov, D.D. Sheka, Y. Gaididei, V.P. Kravchuk, U.K. Rößler, J. Fassbender, D. Makarov, Mesoscale Dzyaloshinskii-Moriya interaction: geometrical tailoring of the magnetochirality. Sci. Rep. 8(1), 866 (2018)

    Google Scholar 

  127. O.M. Volkov, A. Kákay, F. Kronast, I. Mönch, M.A. Mawass, J. Fassbender, D. Makarov, Experimental observation of exchange-driven chiral effects in curvilinear magnetism. Phys. Rev. Lett. 123, 077201 (2019)

    Google Scholar 

  128. O.M. Volkov, U.K. Rößler, J. Fassbender, D. Makarov, Concept of artificial magnetoelectric materials via geometrically controlling curvilinear helimagnets. J. Phys. D: Appl. Phys. 52(34), 345001 (2019)

    Google Scholar 

  129. M.C. Giordano, K. Baumgaertl, S. Escobar Steinvall, J. Gay, M. Vuichard, A. Fontcuberta i Morral, D. Grundler, Plasma-enhanced atomic layer deposition of nickel nanotubes with low resistivity and coherent magnetization dynamics for 3D spintronics. ACS Appl. Mater. Interfaces 12(36), 40443–40452 (2020). PMID: 32805802

    Google Scholar 

  130. P. Levy, A.G. Leyva, H.E. Troiani, R.D. Sánchez, Nanotubes of rare-earth manganese oxide. Appl. Phys. Lett. 83, 5247 (2003)

    Google Scholar 

  131. K. Nielsch, F. Castaño, S. Matthias, W. Lee, C. Ross, Synthesis of cobalt/polymer multilayer nanotubes. Adv. Eng. Mater. 7(4), 217–221 (2005)

    Google Scholar 

  132. F. Tao, M. Guan, Y. Jiang, J. Zhu, Z. Xu, Z. Xue, An easy way to construct an ordered array of nickel nanotubes: the triblock-copolymer-assisted hard-template method. Adv. Mater. 18(16), 2161 (2006)

    Google Scholar 

  133. M. Knez, K. Nielsch, L. Niinistö, Synthesis and surface engineering of complex nanostructures by atomic layer deposition. Adv. Mater. 19(21), 3425–3438 (2007)

    Article  Google Scholar 

  134. M. Daub, M. Knez, U. Goesele, K. Nielsch, Ferromagnetic nanotubes by atomic layer deposition in anodic alumina membranes. J. Appl. Phys. 101(9), 09J111 (2007)

    Google Scholar 

  135. J. Bachmann, J. Jing, M. Knez, S. Barth, H. Shen, S. Mathur, U. Gösele, K. Nielsch, Ordered iron oxide nanotube arrays of controlled geometry and tunable magnetism by atomic layer deposition. J. Am. Chem. Soc. 129(31), 9554–9555 (2007)

    Article  Google Scholar 

  136. J. Curiale, R.D. Sánchez, H.E. Troiani, C.A. Ramos, H. Pastoriza, A.G. Leyva, P. Levy, Magnetism of manganite nanotubes constituted by assembled nanoparticles. Phys. Rev. B 75, 224410 (2007)

    Google Scholar 

  137. L.A. Rodríguez, C. Bran, D. Reyes, E. Berganza, M. Vázquez, C. Gatel, E. Snoeck, A. Asenjo, Quantitative nanoscale magnetic study of isolated diameter-modulated FeCoCu nanowires. ACS Nano 10(10), 9669–9678 (2016)

    Article  Google Scholar 

  138. J. Escrig, M. Daub, P. Landeros, K. Nielsch, D. Altbir, Angular dependence of coercivity in magnetic nanotubes. Nanotechnology 18(44), 445706 (2007)

    Google Scholar 

  139. D. Li, R.S. Thompson, G. Bergmann, J.G. Lu, Template-based synthesis and magnetic properties of cobalt nanotube arrays. Adv. Mater. 20(23), 4575–4578 (2008)

    Article  Google Scholar 

  140. K. Pitzschel, J.M.M. Moreno, J. Escrig, O. Albrecht, K. Nielsch, J. Bachmann, Controlled introduction of diameter modulations in arrayed magnetic iron oxide nanotubes. ACS Nano 3(11), 3463 (2009)

    Google Scholar 

  141. J.Y. Chen, D.W. Shi, N. Ahmad, D.P. Liu, W.P. Zhou, X.F. Han, Fabrication and magnetic properties of La-X (X = Co, Ni, and Fe) nanotube arrays prepared by electrodeposition methods. J. Appl. Phys. 114(5), 054303 (2013)

    Google Scholar 

  142. J. Chae, H.S. Park, S.W. Kang, Atomic layer deposition of nickel by the reduction of preformed nickel oxide. Electrochem. Solid-State Lett. 5(6), C64 (2002)

    Google Scholar 

  143. H.B. Profijt, S.E. Potts, M.C.M. van de Sanden, W.M.M. Kessels, Plasma-assisted atomic layer deposition: basics, opportunities, and challenges. J. Vac. Sci. Technol. A 29(5), 050801 (2011)

    Google Scholar 

  144. J. Crangle, G.M. Goodman, W. Sucksmith, The magnetization of pure iron and nickel. Proc. R. Soc. A 321(1547), 477–491 (1971)

    ADS  Google Scholar 

  145. Y.P. Wang, Z.J. Ding, Q.X. Liu, W.J. Liu, S.J. Ding, D.W. Zhang, Plasma-assisted atomic layer deposition and post-annealing enhancement of low resistivity and oxygen-free nickel nano-films using nickelocene and ammonia precursors. J. Mater. Chem. C 4, 11059–11066 (2016)

    Article  Google Scholar 

  146. A. Rudolph, M. Soda, M. Kiessling, T. Wojtowicz, D. Schuh, W. Wegscheider, J. Zweck, C. Back, E. Reiger, Ferromagnetic GaAs/GaMnAs core-shell nanowires grown by molecular beam epitaxy. Nano Lett. 9(11), 3860–3866 (2009)

    Article  ADS  Google Scholar 

  147. K. Baumgaertl, F. Heimbach, S. Maendl, D. Rueffer, A. Fontcuberta i Morral, D. Grundler, Magnetization reversal in individual Py and CoFeB nanotubes locally probed via anisotropic magnetoresistance and anomalous Nernst effect. Appl. Phys. Lett. 108 (2016)

    Google Scholar 

  148. J. Kimling, F. Kronast, S. Martens, T. Böhnert, M. Martens, J. Herrero-Albillos, L. Tati-Bismaths, U. Merkt, K. Nielsch, G. Meier, Photoemission electron microscopy of three-dimensional magnetization configurations in core-shell nanostructures. Phys. Rev. B 84, 174406 (2011)

    Google Scholar 

  149. R. Streubel, V.P. Kravchuk, D.D. Sheka, D. Makarov, F. Kronast, O.G. Schmidt, Y. Gaididei, Equilibrium magnetic states in individual hemispherical permalloy caps. Appl. Phys. Lett. 101(13), 132419 (2012)

    Google Scholar 

  150. A. Mehlin, B. Gross, M. Wyss, T. Schefer, G. Tütüncüoglu, F. Heimbach, A. Fontcuberta i Morral, D. Grundler, M. Poggio, Observation of end-vortex nucleation in individual ferromagnetic nanotubes. Phys. Rev. B 97, 134422 (2018)

    Google Scholar 

  151. D. Vasyukov, L. Ceccarelli, M. Wyss, B. Gross, A. Schwarb, A. Mehlin, N. Rossi, G. Tütüncüoglu, F. Heimbach, R.R. Zamani, A. Kovács, A. Fontcuberta i Morral, D. Grundler, M. Poggio, Imaging stray magnetic field of individual ferromagnetic nanotubes. Nano Lett. 18(2), 964–970 (2018)

    Google Scholar 

  152. B. Gross, D.P. Weber, D. Rüffer, A. Buchter, F. Heimbach, A. Fontcuberta i Morral, D. Grundler, M. Poggio, Dynamic cantilever magnetometry of individual CoFeB nanotubes. Phys. Rev. B 93, 064409 (2016)

    Google Scholar 

  153. M. Zimmermann, T.N.G. Meier, F. Dirnberger, A. Kákay, M. Decker, S. Wintz, S. Finizio, E. Josten, J. Raabe, M. Kronseder et al., Origin and manipulation of stable vortex ground states in permalloy nanotubes. Nano Lett. 18(5), 2828–2834 (2018)

    Article  ADS  Google Scholar 

  154. M. Beleggia, D. Vokoun, M. De Graef, Demagnetization factors for cylindrical shells and related shapes. J. Magn. Magn. Mater. 321(9), 1306–1315 (2009)

    Article  ADS  Google Scholar 

  155. H.D. Salinas, J. Restrepo, Ò. Iglesias, Change in the magnetic configurations of tubular nanostructures by tuning dipolar interactions. Sci. Rep. 8(1), 10275 (2018)

    Google Scholar 

  156. R. Streubel, D. Makarov, J. Lee, C. Müller, M. Melzer, R. Schäfer, C.C. Bof Bufon, S.K. Kim, O.G. Schmidt, Rolled-up permalloy nanomembranes with multiple windings. SPIN 03(03), 1340001 (2013)

    Google Scholar 

  157. R. Streubel, L. Han, F. Kronast, A.A. Ünal, O.G. Schmidt, D. Makarov, Imaging of buried 3D magnetic rolled-up nanomembranes. Nano Lett. 14(7), 3981–3986 (2014)

    Article  ADS  Google Scholar 

  158. R. Streubel, J. Lee, D. Makarov, M.Y. Im, D. Karnaushenko, L. Han, R. Schäfer, P. Fischer, S.K. Kim, O.G. Schmidt, Magnetic microstructure of rolled-up single-layer ferromagnetic nanomembranes. Adv. Mater. 26, 316 (2014)

    Google Scholar 

  159. R. Streubel, F. Kronast, P. Fischer, D. Parkinson, O.G. Schmidt, D. Makarov, Retrieving spin textures on curved magnetic thin films with full-field soft x-ray microscopies. Nat. Commun. 6(1), 7612 (2015)

    Google Scholar 

  160. J. Hurst, A. De Riz, M. Staňo, J.C. Toussaint, O. Fruchart, D. Gusakova, Theoretical study of current-induced domain wall motion in magnetic nanotubes with azimuthal domains. Phys. Rev. B 103, 024434 (2021)

    Google Scholar 

  161. S. Mendach, J. Podbielski, J. Topp, W. Hansen, D. Heitmann, Spin-wave confinement in rolled-up ferromagnetic tubes. Appl. Phys. Lett. 93, 262501 (2008)

    Google Scholar 

  162. E. Bermúdez-Ureña, Y. Mei, E. Coric, D. Makarov, M. Albrecht, O.G. Schmidt, Fabrication of ferromagnetic rolled-up microtubes for magnetic sensors on fluids. J. Phys. D: Appl. Phys. 42, 055001 (2009)

    Google Scholar 

  163. C. Müller, M.S. Khatri, C. Deneke, S. Fähler, Y.F. Mei, E. Bermúdez-Ureña, O.G. Schmidt, Tuning magnetic properties by roll-up of Au/Co/Au films into microtubes. Appl. Phys. Lett. 94, 102510 (2009)

    Google Scholar 

  164. F. Balhorn, S. Mansfeld, A. Krohn, J. Topp, W. Hansen, D. Heitmann, S. Mendach, Spin-wave interference in three-dimensional rolled-up ferromagnetic microtubes. Phys. Rev. Lett. 104, 037205 (2010)

    Google Scholar 

  165. E.J. Smith, D. Makarov, S. Sanchez, V.M. Fomin, O.G. Schmidt, Magnetic microhelix coil structures. Phys. Rev. Lett. 107, 097204 (2011)

    Google Scholar 

  166. T. Ueltzhöffer, R. Streubel, I. Koch, D. Holzinger, D. Makarov, O.G. Schmidt, A. Ehresmann, Magnetically patterned rolled-up exchange bias tubes: a paternoster for superparamagnetic beads. ACS Nano 10(9), 8491–8498 (2016)

    Article  Google Scholar 

  167. J.A. López-López, D. Cortés-Ortuño, P. Landeros, Role of anisotropy on the domain wall properties of ferromagnetic nanotubes. J. Magn. Magn. Mater. 324, 2024 (2012)

    Google Scholar 

  168. S. Allende, J. Escrig, D. Altbir, E. Salcedo, M. Bahiana, Angular dependence of the transverse and vortex modes in magnetic nanotubes. Eur. Phys. J. B 66(1), 37–40 (2008)

    Article  ADS  Google Scholar 

  169. D.M. Arciniegas-Jaimes, S. Raviolo, J.M. Carballo, N. Bajales, J. Escrig, Wave reversion mode stability as a function of diameter and wall thickness for permalloy and nickel nanotubes. J. Magn. Magn. Mater. 523, 167578 (2021)

    Google Scholar 

  170. J. Escrig, J. Bachmann, J. Jing, M. Daub, D. Altbir, K. Nielsch, Crossover between two different magnetization reversal modes in arrays of iron oxide nanotubes. Phys. Rev. B 77, 214421 (2008)

    Google Scholar 

  171. J. Bachmann, J. Escrig, K. Pitzschel, J.M. Montero-Moreno, J. Jing, D. Görlitz, D. Altbir, K. Nielsch, Size effects in ordered arrays of magnetic nanotubes: pick your reversal mode. J. Appl. Phys. 105(7), 07B521 (2009)

    Google Scholar 

  172. Y.T. Chong, D. Görlitz, S. Martens, M.Y.E. Yau, S. Allende, J. Bachmann, K. Nielsch, Multilayered core/shell nanowires displaying two distinct magnetic switching events. Adv. Mater. 22(22), 2435 (2010)

    Google Scholar 

  173. O. Albrecht, R. Zierold, C. Patzig, J. Bachmann, C. Sturm, B. Rheinländer, M. Grundmann, D. Görlitz, B. Rauschenbach, K. Nielsch, Tubular magnetic nanostructures based on glancing angle deposited templates and atomic layer deposition. Phys. Status Solidi B 247(6), 1365 (2010)

    Google Scholar 

  174. O. Albrecht, R. Zierold, S. Allende, J. Escrig, C. Patzig, B. Rauschenbach, K. Nielsch, D. Görlitz, Experimental evidence for an angular dependent transition of magnetization reversal modes in magnetic nanotubes. J. Appl. Phys. 109(9), 093910 (2011)

    Google Scholar 

  175. K. Pitzschel, J. Bachmann, J.M. Montero-Moreno, J. Escrig, D. Görlitz, K. Nielsch, Reversal modes and magnetostatic interactions in Fe3O4/ZrO2/Fe3O4 multilayer nanotubes. Nanotechnology 23(49), 495718 (2012)

    Google Scholar 

  176. P.A. Cherenkov, Dokl. Akad. Nauk SSSR 2, 451 (1934)

    Google Scholar 

  177. A. Fernández-Pacheco, R. Streubel, O. Fruchart, R. Hertel, P. Fischer, R.P. Cowburn, Three-dimensional nanomagnetism. Nat. Commun. 8(1), 15756 (2017)

    Google Scholar 

  178. S.S.P. Parkin, M. Hayashi, L. Thomas, Magnetic domain-wall racetrack memory. Science 320(5873), 190–194 (2008)

    Google Scholar 

  179. R.D. McMichael, M.J. Donahue, Head to head domain wall structures in thin magnetic strips. IEEE Trans. Magn. 33(5), 4167–4169 (1997)

    Article  ADS  Google Scholar 

  180. R. Hertel, A. Kákay, Analytic form of transverse head-to-head domain walls in thin cylindrical wires. J. Magn. Magn. Mater. 379, 45–49 (2015)

    Article  ADS  Google Scholar 

  181. D. Bouzidi, H. Suhl, Motion of a Bloch domain wall. Phys. Rev. Lett. 65, 2587–2590 (1990)

    Article  ADS  Google Scholar 

  182. G. Tatara, H. Kohno, Theory of current-driven domain wall motion: spin transfer versus momentum transfer. Phys. Rev. Lett. 92, 086601 (2004)

    Google Scholar 

  183. J.A. Otálora, J.A. López-López, A.S. Núñez, P. Landeros, Domain wall manipulation in magnetic nanotubes induced by electric current pulses. J. Phys.: Condens. Matter 24(43), 436007 (2012)

    Google Scholar 

  184. V. Bar’yakhtar, M.V. Chetkin, B. Ivanov, S.N. Gadetskii, Dynamics of Topological Magnetic Solitons: Experiment and Theory (Springer, Berlin, Heidelberg, 1994)

    Google Scholar 

  185. F. Bloch, Zur Theorie des Ferromagnetismus. Z. Phys. 61(3), 206–219 (1930)

    Google Scholar 

  186. B.A. Kalinikos, A.N. Slavin, Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions. J. Phys. C: Solid State Phys. 19(35), 7013–7033 (1986)

    Article  ADS  Google Scholar 

  187. S. Neusser, D. Grundler, Magnonics: spin waves on the nanoscale. Adv. Mater. 21(28), 2927–2932 (2009)

    Article  Google Scholar 

  188. V.V. Kruglyak, S.O. Demokritov, D. Grundler, Magnonics. J. Phys. D: Appl. Phys. 43(26), 264001 (2010)

    Google Scholar 

  189. A.V. Chumak, V.I. Vasyuchka, A.A. Serga, B. Hillebrands, Magnon spintronics. Nat. Phys. 11(6), 453–461 (2015)

    Article  Google Scholar 

  190. D. Grundler, Reconfigurable magnonics heats up. Nat. Phys. 11(6), 438–441 (2015)

    Article  Google Scholar 

  191. D. Grundler, Spintronics: nanomagnonics around the corner. Nat. Nanotechnol. (2016)

    Google Scholar 

  192. A.V. Chumak, A.A. Serga, B. Hillebrands, Magnonic crystals for data processing. J. Phys. D: Appl. Phys. 50(24), 244001 (2017)

    Google Scholar 

  193. Y. Tserkovnyak, A. Brataas, G.E.W. Bauer, Enhanced gilbert damping in thin ferromagnetic films. Phys. Rev. Lett. 88(11), 117601 (2002)

    Google Scholar 

  194. Y. Kajiwara, K. Harii, S. Takahashi, J.I. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi et al., Transmission of electrical signals by spin-wave interconversion in a magnetic insulator. Nature 464(7286), 262 (2010)

    Google Scholar 

  195. M. Madami, S. Bonetti, G. Consolo, S. Tacchi, G. Carlotti, G. Gubbiotti, F.B. Mancoff, M.A. Yar, J. Åkerman, Direct observation of a propagating spin wave induced by spin-transfer torque. Nat. Nanotechnol. 6(10), 635 (2011)

    Google Scholar 

  196. C.W. Sandweg, Y. Kajiwara, A.V. Chumak, A.A. Serga, V.I. Vasyuchka, M.B. Jungfleisch, E. Saitoh, B. Hillebrands, Spin pumping by parametrically excited exchange magnons. Phys. Rev. Lett. 106, 216601 (2011)

    Google Scholar 

  197. V.E. Demidov, S. Urazhdin, H. Ulrichs, V. Tiberkevich, A. Slavin, D. Baither, G. Schmitz, S.O. Demokritov, Magnetic nano-oscillator driven by pure spin current. Nat. Mater. 11(12), 1028 (2012)

    Google Scholar 

  198. A.V. Chumak, A.A. Serga, B. Hillebrands, Magnon transistor for all-magnon data processing. Nat. Commun. 5 (2014)

    Google Scholar 

  199. K. Vogt, F.Y. Fradin, J.E. Pearson, T. Sebastian, S.D. Bader, B. Hillebrands, A. Hoffmann, H. Schultheiss, Realization of a spin-wave multiplexer. Nat. Commun. 5 (2014)

    Google Scholar 

  200. A.V. Sadovnikov, C.S. Davies, S.V. Grishin, V.V. Kruglyak, D.V. Romanenko, Y.P. Sharaevskii, S.A. Nikitov, Magnonic beam splitter: the building block of parallel magnonic circuitry. Appl. Phys. Lett. 106(19), 192406 (2015)

    Google Scholar 

  201. J. Lan, W. Yu, R. Wu, J. Xiao et al., Spin-wave diode. Phys. Rev. X 5(4), 041049 (2015)

    Google Scholar 

  202. S. Klingler, P. Pirro, T. Brächer, B. Leven, B. Hillebrands, A.V. Chumak, Design of a spin-wave majority gate employing mode selection. Appl. Phys. Lett. 105(15), 152410 (2014)

    Google Scholar 

  203. I.P. Radu, O. Zografos, A. Vaysset, F. Ciubotaru, J. Yan, J. Swerts, D. Radisic, B. Briggs, B. Soree, M. Manfrini et al., Spintronic majority gates, in 2015 IEEE International Electron Devices Meeting (IEDM) (IEEE, 2015), p. 32–5

    Google Scholar 

  204. A. Khitun, M. Bao, K.L. Wang, Magnonic logic circuits. J. Phys. D: Appl. Phys. 43(26), 264005 (2010)

    Google Scholar 

  205. T. Brächer, F. Heussner, P. Pirro, T. Meyer, T. Fischer, M. Geilen, B. Heinz, B. Lägel, A. Serga, B. Hillebrands, Phase-to-intensity conversion of magnonic spin currents and application to the design of a majority gate. Sci. Rep. 6, 38235 (2016)

    Google Scholar 

  206. C.J. Tock, J.F. Gregg, Phase modulation and amplitude modulation interconversion for magnonic circuits. Phys. Rev. Appl. 11, 044065 (2019)

    Google Scholar 

  207. A. Barman, G. Gubbiotti, S. Ladak, A.O. Adeyeye, M. Krawczyk, J. Grafe, C. Adelmann, S. Cotofana, A. Naeemi, V.I. Vasyuchka, B. Hillebrands, S.A. Nikitov, H. Yu, D. Grundler, A. Sadovnikov, A.A. Grachev, S.E. Sheshukova, J.Y. Duquesne, M. Marangolo, C. Gyorgy, W. Porod, V.E. Demidov, S. Urazhdin, S. Demokritov, E. Albisetti, D. Petti, R. Bertacco, H. Schulteiss, V.V. Kruglyak, V.D. Poimanov, A.K. Sahoo, J. Sinha, H. Yang, M. Muenzenberg, T. Moriyama, S. Mizukami, P. Landeros, R.A. Gallardo, G. Carlotti, J.V. Kim, R.L. Stamps, R.E. Camley, B. Rana, Y. Otani, W. Yu, T. Yu, G.E.W. Bauer, C.H. Back, G.S. Uhrig, O.V. Dobrovolskiy, S. van Dijken, B. Budinska, H. Qin, A. Chumak, A. Khitun, D.E. Nikonov, I.A. Young, B. Zingsem, M. Winklhofer, The 2021 magnonics roadmap. J. Phys.: Condens. Matter 33(41), 413001 (2021)

    Google Scholar 

  208. M. Krawczyk, H. Puszkarski, Plane-wave theory of three-dimensional magnonic crystals. Phys. Rev. B 77, 054437 (2008)

    Google Scholar 

  209. M. Krawczyk, J. Klos, M.L. Sokolovskyy, S. Mamica, Materials optimization of the magnonic gap in three-dimensional magnonic crystals with spheres in hexagonal structure. J. Appl. Phys. 108(9), 093909 (2010)

    Google Scholar 

  210. S. Mamica, M. Krawczyk, M.L. Sokolovskyy, J. Romero-Vivas, Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles. Phys. Rev. B 86, 144402 (2012)

    Google Scholar 

  211. G. Gubbiotti, X. Zhou, Z. Haghshenasfard, M.G. Cottam, A.O. Adeyeye, Reprogrammable magnonic band structure of layered permalloy/Cu/permalloy nanowires. Phys. Rev. B 97, 134428 (2018)

    Google Scholar 

  212. E.N. Beginin, A.V. Sadovnikov, A.Y. Sharaevskaya, A.I. Stognij, S.A. Nikitov, Spin wave steering in three-dimensional magnonic networks. Appl. Phys. Lett. 112(12), 122404 (2018)

    Google Scholar 

  213. P.A. Popov, A.Y. Sharaevskaya, D.V. Kalyabin, A.I. Stognii, E.N. Beginin, A.V. Sadovnikov, S.A. Nikitov, Volume magnetostatic spin waves in 3D ferromagnetic structures. J. Commun. Technol. Electron. 63(12), 1431–1438 (2018)

    Google Scholar 

  214. P.A. Popov, A.Y. Sharaevskaya, E.N. Beginin, A.V. Sadovnikov, A.I. Stognij, D.V. Kalyabin, S.A. Nikitov, Spin wave propagation in three-dimensional magnonic crystals and coupled structures. J. Magn. Magn. Mater. 476, 423–427 (2019)

    Article  ADS  Google Scholar 

  215. E.Y. Vedmedenko, R.K. Kawakami, D.D. Sheka, P. Gambardella, A. Kirilyuk, A. Hirohata, C. Binek, O. Chubykalo-Fesenko, S. Sanvito, B.J. Kirby, J. Grollier, K. Everschor-Sitte, T. Kampfrath, C.Y. You, A. Berger, The 2020 magnetism roadmap. J. Phys. D: Appl. Phys. 53(45), 453001 (2020)

    Google Scholar 

  216. O.V. Pylypovskyi, V.P. Kravchuk, D.D. Sheka, D. Makarov, O.G. Schmidt, Y. Gaididei, Coupling of chiralities in spin and physical spaces: the möbius ring as a case study. Phys. Rev. Lett. 114, 197204 (2015)

    Google Scholar 

  217. D.D. Sheka, V.P. Kravchuk, K.V. Yershov, Y. Gaididei, Torsion-induced effects in magnetic nanowires. Phys. Rev. B 92, 054417 (2015)

    Google Scholar 

  218. F. Balhorn, S. Jeni, W. Hansen, D. Heitmann, S. Mendach, Axial and azimuthal spin-wave eigenmodes in rolled-up permalloy stripes. Appl. Phys. Lett. 100, 222402 (2012)

    Google Scholar 

  219. F. Balhorn, L. Nagrodzki, S. Mendach, Spin-wave interference in microscopic permalloy tubes. Appl. Phys. Lett. 102(22), 222403 (2013)

    Google Scholar 

  220. F. Balhorn, C. Bausch, S. Jeni, W. Hansen, D. Heitmann, S. Mendach, Azimuthal spin-wave modes in rolled-up permalloy microtubes: tuneable mode frequency, mode patterns, and mode splitting. Phys. Rev. B 88, 054402 (2013)

    Google Scholar 

  221. M. Yang, B. Yin, Z. Li, X. Zeng, M. Yan, Magnonic activity of ferromagnetic nanocylinders. Phys. Rev. B 103, 094404 (2021)

    Google Scholar 

  222. R. Arias, D. Mills, Theory of spin excitations and the microwave response of cylindrical ferromagnetic nanowires. Phys. Rev. B 63(13), 134439 (2001)

    Google Scholar 

  223. D. Mills, Theory of spin excitations and the microwave response of cylindrical ferromagnetic nanowires, Band-Ferromagnetism (Springer, Berlin, 2001), pp. 297–319

    Google Scholar 

  224. H. Leblond, V. Veerakumar, Magnetostatic spin solitons in ferromagnetic nanotubes. Phys. Rev. B 70, 134413 (2004)

    Google Scholar 

  225. T. Nguyen, M. Cottam, Spin-wave excitations in ferromagnetic nanotubes. Surf. Sci. 600(18), 4151–4154 (2006)

    Google Scholar 

  226. A.L. González, P. Landeros, A.S. Núñez, Spin wave spectrum of magnetic nanotubes. J. Magn. Magn. Mater. 322, 530 (2010)

    Google Scholar 

  227. L. Körber, M. Zimmermann, S. Wintz, S. Finizio, M. Kronseder, D. Bougeard, F. Dirnberger, M. Weigand, J. Raabe, J.A. Otálora, H. Schultheiss, E. Josten, J. Lindner, I. Kézsmárki, C.H. Back, A. Kákay, Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes. Phys. Rev. B 104, 184429 (2021)

    Google Scholar 

  228. M.M. Salazar-Cardona, L. Körber, H. Schultheiss, K. Lenz, A. Thomas, K. Nielsch, A. Kákay, J.A. Otálora, Nonreciprocity of spin waves in magnetic nanotubes with helical equilibrium magnetization. Appl. Phys. Lett. 118(26), 262411 (2021)

    Google Scholar 

  229. A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves (CSC Press, Florida, 1996)

    Google Scholar 

  230. J.A. Otálora, M. Yan, H. Schultheiss, R. Hertel, A. Kákay, Asymmetric spin-wave dispersion in ferromagnetic nanotubes induced by surface curvature. Phys. Rev. B 95, 184415 (2017)

    Google Scholar 

  231. J.A. Otálora, A. Kákay, J. Lindner, H. Schultheiss, A. Thomas, J. Fassbender, K. Nielsch, Frequency linewidth and decay length of spin waves in curved magnetic membranes. Phys. Rev. B 98, 014403 (2018)

    Google Scholar 

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Acknowledgements

The authors acknowledge financial support by Fondecyt 1201153 and Fondecyt Iniciación 11190184, Basal Program for Centers of Excellence grant AFB180001 (CEDENNA), National Science Foundation/EPSCoR RII Track-1: Emergent Quantum Materials and Technologies (EQUATE) under Grant No. OIA-2044049, National Science Foundation under Grant No. 2203933, and Deutsche Forschungsgemeinschaft (KA 5069/1-1 and KA 5069/3-1).

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Authors and Affiliations

  1. Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile

    Pedro Landeros

  2. Center for the Development of Nanoscience and Nanotechnology (CEDENNA), 917-0124, Santiago, Chile

    Pedro Landeros

  3. Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile

    Jorge A. Otálora

  4. Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA

    Robert Streubel

  5. Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA

    Robert Streubel

  6. Helmholtz-Zentrum Dresden - Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany

    Attila Kákay

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  1. Pedro Landeros
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Correspondence to Attila Kákay .

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  1. Helmholtz-Zentrum Dresden-Rossendorf e.V, Dresden, Germany

    Denys Makarov

  2. Faculty of Radiophysics, Electronics and Computer Systems, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Denis D. Sheka

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Landeros, P., Otálora, J.A., Streubel, R., Kákay, A. (2022). Tubular Geometries. In: Makarov, D., Sheka, D.D. (eds) Curvilinear Micromagnetism. Topics in Applied Physics, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-09086-8_4

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