Skip to main content
SpringerLink
Log in

Current-driven magnetization reversal dynamics and breather-like EM soliton propagation in biaxial anisotropic weak ferromagnetic nanowire

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We investigate the effect of spin torque on the switching dynamics of magnetic solitons in a weak ferromagnetic nanowire under the influence of an electromagnetic wave (EMW). The magnetization dynamics of the current-driven ferromagnetic nanowire and the EMW propagation is governed by the celebrated Landau-Lifshitz-Gilbert (LLG) vector equation and the Maxwell’s equations, respectively. We recast the set of LLG and Maxwell equations onto the extended derivative nonlinear Schr\(\ddot{o}\)dinger (EDNLS) equation. We employ the nonlinear perturbation analysis along the lines of Kodama and Ablowitz and analyze the interplay of the Dzyaloshinskii-Moriya interaction (DMI) along with the spin transfer torque on the magnetization reversal dynamics by solving the associated evolution equations for the soliton parameters. We also demonstrate the spin-polarized current triggers an ultrafast switching of EM solitons in the ferromagnetic nanowire in the range of \(0.58-0.12~ns\), and the Gilbert damping supports the EM soliton switching to sustain indefinitely. We invoke the Jacobi elliptic function method to explore the propagation of breather-like solitonic localized modes along the ferromagnetic nanowire.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

The data that support the findings of this study are available within the article.

References

  1. Martin, C.R.: Template synthesis of polymeric and metal microtubules. Adv. Mater. 3, 457–459 (1991)

    Article  Google Scholar 

  2. de Visser, A., Louis, E., Franse, J.J.M., Menovsky, A.: Forced magnetostriction of heavy-fermion UPt3. J. Magn. Magn. Mater. 54, 387–388 (1986)

    Article  Google Scholar 

  3. Ferré, R., Ounadjela, K., George, J.M., Piraux, L., Dubois, S.: Magnetization processes in nickel and cobalt electrodeposited nanowires. Phys. Rev. B 56, 14066–14075 (1997)

    Article  Google Scholar 

  4. Berger, L.: Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B 54, 9353–9358 (1996)

    Article  Google Scholar 

  5. Slonczewski, J.C.: Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater. 159, L1–L7 (1996)

    Article  Google Scholar 

  6. Sun, J.Z.: Spin-current interaction with a monodomain magnetic body: a model study. Phys. Rev. B 62, 570–578 (2000)

    Article  Google Scholar 

  7. Wegrowe, J.E.: Thermokinetic approach of the generalized Landau-Lifshitz-Gilbert equation with spin-polarized current. Phys. Rev. B 62, 1067–1078 (2000)

    Article  Google Scholar 

  8. Berger, L.: New origin for spin current and current-induced spin precession in magnetic multilayers. J. Appl. Phys. 89, 5521–5532 (2001)

    Article  Google Scholar 

  9. Heide, C.: Spin currents in magnetic films. Phys. Rev. Lett. 87, 197201–197204 (2001)

    Article  Google Scholar 

  10. Katine, J.A., Albert, F.J., Buhrman, R.A., Myers, E.B., Ralph, D.C.: Current-driven magnetization reversal and spin-wave excitations in Co /Cu/Co pillars phys. Rev. Lett. 84, 3149–3152 (2000)

    Article  Google Scholar 

  11. Tsoi, M., Jansen, A.G.M., Bass, J., Chiang, W.C., Tsoi, V., Wyder, P.: Generation and detection of phase-coherent current-driven magnons in magnetic multilayers. Nature 406, 46–48 (2000)

    Article  Google Scholar 

  12. Anil Kumar, P.S., Jansen, R., van ’t Erve, O.M.J., Vlutters, R., de Haan, P., CLodder, J.: Low-field magneto current above 200% in a spin valve transistor at room temperature. J. Magn. Magn. Mater. 214, 1–6 (2000)

  13. Ralph, D.C., Stiles, M.D.: Spin transfer torques. J. Magn. Magn. Mater. 320, 1190–1216 (2008)

    Article  Google Scholar 

  14. Li, Z., Zhang, S.: Magnetization dynamics with a spin-transfer torque. Phys. Rev. B 68, 024404 (2003)

    Article  Google Scholar 

  15. Dzyaloshinsky, I.: A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids. 4, 241–255 (1958)

  16. Moriya, T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228–230 (1960)

    Article  Google Scholar 

  17. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960)

    Article  Google Scholar 

  18. Fert, A., Levy, Peter M.: Role of anisotropic exchange interactions in determining the properties of spin-glasses. Phys. Rev. Lett. 44, 1538–1541 (1980)

    Article  Google Scholar 

  19. Chen, G., Zhu, J., Quesada, A., Li, J., N’Diaye, A.T., Huo, Y., Ma, T.P., Chen, Y., Kwon, H.Y., Won, C., Qiu, Z.Q., Schmid, A.K., Wu, Y.Z.: Novel chiral magnetic domain wall structure in Fe/Ni/Cu(001) films. Phys. Rev. Lett. 110, 177204 (2013)

  20. Tretiakov, O.A., Liu, Y., Abanov, Ar.: Minimization of ohmic losses for domain wall motion in a ferromagnetic nanowire. Phys. Rev. Lett. 105, 217203 (2010)

    Article  Google Scholar 

  21. Komine, T., Aono, T., Ando, R.: Influence of classical electromagnetic effects on current-induced domain wall motion in a perpendicularly magnetized nanowire. J. Appl. Phys. 117, 17D512 (2015)

    Article  Google Scholar 

  22. Senthil Kumar, V., Kavitha, L., Boopathy, C., Gopi, D.: Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowire. Comm. Non. Sci. Num. Sim. 51, 50–65 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  23. Senthil Kumar, V., Kavitha, L., Gopi, D.: Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire. J. Magn. Magn. Mater. 441, 660–671 (2017)

    Article  Google Scholar 

  24. Pavithra, T., Ravichandran, R., Sunny, G.., Kavitha, L.: Electromagnetic lump soliton solution of (2+1) dimensional ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction. Mater. Today Proc. 25, 192–198 (2020)

    Article  Google Scholar 

  25. Kavitha, L., Saravanan, M., Srividya, B., Gopi, D.: Breatherlike electromagnetic wave propagation in an antiferromagnetic medium with Dzyaloshinsky-Moriya interaction. Phys. Rev. E 84, 066608 (2011)

    Article  Google Scholar 

  26. Kavitha, L., Saravanan, M., Gopi, D.: Propagation of electromagnetic soliton in anisotropic biquadratic ferromagnetic medium. Chin. Phys. B 22, 030512 (2013)

    Article  Google Scholar 

  27. Veerakumar, V., Daniel, M.: Propagation of an electromagnetic soliton in a ferromagnetic medium. ANZIAM J. 44, 103–110 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  28. Veerakumar, V.: Modified Kadomtsev-Petviashvili (MKP) equation and electromagnetic soliton. Math. Comput. Simulat. 62, 163–169 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  30. Yang, C., Zhou, Q., Triki, H., Mirzazadeh, M., Ekici, M., Liu, W.-J., Biswas, A., Belic, M.: Bright soliton interactions in a (2+1)- dimensional fourth-order variable-coefficient nonlinear Schrodinger equation for the Heisenberg ferromagnetic spin chain. J. Nonlinear Dyn. 95, 983–994 (2019)

    Article  MATH  Google Scholar 

  31. Chen, Y.-X., Fang-Qian, X., Yi-Liang, H.: Excitation control for three-dimensional Peregrine solution and combined breather of a partially nonlocal variable-coefficient nonlinear Schrodinger equation. J. Nonlinear Dyn. 95, 1957–1964 (2019)

    Article  MATH  Google Scholar 

  32. Nikolic, S.N., Ashour, O.A., Aleksic, N.B., Belic, M.R., Chin, S.A.: Breathers, solitons and roque waves of the quintic nonlinear Schrodinger equation on various backgrounds. J. Nonlinear Dyn. 95, 2855–2865 (2019)

    Article  MATH  Google Scholar 

  33. Yang, Z.-J., Zhhang, S.-M., Li, X.-L., Pang, Z.-G., Hong-Xia, Bu.: High-order revivable complex-valued hyperbolic-sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality. J. Nonlinear Dyn. 94, 2563–2573 (2018)

    Article  Google Scholar 

  34. Wegrowe, J.-E., Kelly, D., Jaccard, Y., Guittienne, Ph., Ansermet, J.-Ph.: Current-induced magnetization reversal in magnetic nanowires. Europhys. Lett. 45(5), 626 (1999)

    Article  Google Scholar 

  35. Pham, H., Cimpoesu, D., Stancu, A., Spinu, L.: Switching behavior of a Stoner-Wohlfarth particle subjected to spin-torque effect. J. Appl. Phys. 103, 07B105 (2008)

    Article  Google Scholar 

  36. Daniel, M., Sabareesan, P.: Spin-transfer induced ultrafast precessional switching enhanced by interface anisotropy in a ferromagnetic nanopillar. J. Magn. Magn. Mater. 322(6), 675–680 (2012)

    Article  Google Scholar 

  37. Saravanan, M.: Current-driven electromagnetic soliton collision in a ferromagnetic nanowire. Phys. Rev. E 92, 012923 (2015)

    Article  MathSciNet  Google Scholar 

  38. Daniel, M., Kavitha, L.: Magnetization reversal through soliton flip in a biquadratic ferromagnet with varying exchange interactions. Phys. Rev. B 66(1–6), 184433 (2002)

    Article  Google Scholar 

  39. Kavitha, L., Sathishkumar, P., Saravanan, M., Gopi, D.: Soliton switching in an anisotropic Heisenberg ferromagnetic spin chain with octupole-dipole interaction. Physica Scripta 83(3pp), 055701 (2011)

    Article  MATH  Google Scholar 

  40. Kavitha, L., Saravanan, M., Sathishkumar, P., Gopi, D.: Magnetization reversal through soliton in a site dependent weak ferromagnet. Chin. J. Phys. 51, 265 (2013)

    MathSciNet  Google Scholar 

  41. Kavitha, L., Saravanan, M., Senthil Kumar, V., Gopi, D.: Magnetization reversal in a site dependent anisotropic Heisenberg ferromagnet under electromagnetic wave propagation. J. Assoc. Arab Univ. Basic Appl. Sci. 19, 80–90 (2014)

    Google Scholar 

  42. Kavitha, L., Saravanan, M., Senthil kumar, V., Gopi, D.: Effect of varying Dzyloshinskii-Moriya interaction on the bistablesoliton switching. Commun. Theor. Phys. 60, 658–662 (2013)

    Article  Google Scholar 

  43. Yin, F., Tang, B.: Electromagnetic breathers and periodic loops in a ferromagnet with the uniaxial anisotropy. Int. J. Theor. Phys. 57, 2843–2853 (2018)

    Article  MATH  Google Scholar 

  44. Taniuti, T., Yajima, N.: Perturbation method for a nonlinear wave modulation. J. Math. Phys. 10, 1369–1372 (1969)

    Article  MathSciNet  Google Scholar 

  45. Zhang, R.-F., Li, M.-C., Yin, H.-M.: Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo-Miwa equation. J. Nonlinear Dyn. 103, 1071–1079 (2021)

    Article  Google Scholar 

  46. Zhang, R.-F., Li, M.-C., Albishari, M., Zheng, F.-C., Lan, Zhong-Zhou.: Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation. Appl. Math. Comput. 403, 126201 (2021)

    MathSciNet  MATH  Google Scholar 

  47. Runfa, Z., Sudao, B., Temuer, C.: Fractal solitons, arbitrary function solutions, exact periodic wave and breathers for a nonlinear partial differential equation by using bilinear neural network method. J. Syst. Sci. Complex 34, 122–139 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhang, R.-F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. J. Nonlinear Dyn. 95, 3041–3048 (2019)

    Article  MATH  Google Scholar 

  49. Zhang, R.-F., Bilige, S., Liu, J.-G., Li, M.: Bright-dark solitons and interaction phenomenon for p-gBKP equation by using bilinear neural network method. Phys. Scr. 96, 025224 (2021)

    Article  Google Scholar 

  50. Kaup, D.J., Newell, A.C.: An exact solution for a derivative nonlinear Schrödinger equation. J. Math. Phys. 19, 798–801 (1978)

    Article  MATH  Google Scholar 

  51. Leblond, H.: Focusing and defocusing of electromagnetic waves in a ferromagnet. J. Phys. A Math. Gen. 27, 3245–3256 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  52. Guo, D., Tian, S.-F., Zhang, T.-T., Li, J.: Modulational instability analysis and soliton solutions of an integrable coupled nonlinear Schrodinger system. J. Nonlinear Dyn. 94, 2749–2761 (2018)

    Article  Google Scholar 

  53. Yang, C., Liu, W., Zhou, Q., Mihalache, D., Malomed, Boris A.: One-soliton shaping and two soliton interaction in the fifth-order variable-coefficient nonlinear Schrodinger equation. J. Nonlinear Dyn. 95, 369–380 (2019)

    Article  Google Scholar 

  54. Kavitha, L., Saravanan, M., Senthilkumar, V., Ravichandran, R., Gopi, D.: Collision of electromagnetic solitons in a weak ferromagnetic medium. J. Magn. Magn. Mater. 355, 37–50 (2014)

    Article  Google Scholar 

  55. Veerakumar, V., Daniel, M.: Simultaneous propagation of many electromagnetic signals without loss in a ferromagnetic medium. Phys. Lett. A 295, 259–266 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  56. Kodama, Y., Ablowitz, M.J.: Perturbations of solitons and solitary waves. Stud. Appl. Math. 64, 225–245 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  57. Novikov, S.P., Manakov, S.V., Pitaevskii, L.B., Zakharov, V.E.: Theory of Solitons: The Inverse Scattering Method. Plenum Press, New York (1984)

    MATH  Google Scholar 

  58. Chappert, C., Fert, A., Van Dau, F.N.: The emergence of spin electronics in data storage. Nature 6, 813–823 (2009)

    Article  Google Scholar 

  59. Allwood, D.A., Xiong, G., Faulkner, C.C., Atkinson, D., Petit, D., Cowburn, R.P.: Magnetic domain-wall logic. Science 309, 1688–1692 (2005)

    Article  Google Scholar 

  60. Parkin, S.S.P., Hayashi, M., Thomas, L.: Magnetic domain-wall racetrack memorym. Science 320, 190–194 (2008)

    Article  Google Scholar 

  61. Daniel, M., Kavitha, L.: Magnetization reversal through soliton flip in a biquadratic ferromagnet with varying exchange interactions. Phys. Rev. B 66, 184433 (2002)

    Article  Google Scholar 

  62. Shen, J., et al.: Magnetism in one dimension: Fe on Cu(111). J. Phys. Rev. B 56, 2340 (1997)

    Article  Google Scholar 

  63. Wernsdorfer, W., et al.: Nucleation of magnetization reversal in individual nanosized nickel wires. Phys. Rev. Lett. 77, 1873 (1996)

    Article  Google Scholar 

  64. Whitney, T., et al.: Fabrication and magnetic properties of arrays of metallic nanowires. Science 261, 1316 (1993)

    Article  Google Scholar 

  65. Spaldin, N.A.: Magnetic Materials: Fundamentals and Applications, 2nd edn. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  66. Ohandley, R.C.: Modern Magnetic Materials: Principles and Applications. Wiley, New York (2000)

    Google Scholar 

  67. Chen, H.M., Hsin, C.F., Chen, P.Y., Liu, R.-S., Hu, S.-F., Huang, C.-Y., Lee, J.-F., Jang, L.-Y.: Ferromagnetic CoPt3 nanowires: structural evolution from fcc to ordered L1(2). J. Am. Chem. Soc. 131(43), 15794–15801 (2009)

    Article  Google Scholar 

  68. Yang, L., Zhu, Z., Wang, Y.: Exact solutions of nonlinear equations. Phys. Lett. A 260, 55–59 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  69. Kavitha, L., Sathish kumar, P., Gopi, D.: Creation and annihilation of solitons in a ferromagnet with competing nonlinear inhomogeneities. Phys. Scr. 81, 035404 (2010)

    Article  MATH  Google Scholar 

  70. Kavitha, L., Saravanan, M., Akila, N., Bhuvaneswari, S., Gopi, D.: Solitonic transport of energy-momentum in a deformed magnetic medium. Phys. Scr. 85, 035007 (2012)

    Article  MATH  Google Scholar 

  71. Kavitha, L., Sathish kumar, P., Gopi, D.: Shape changing soliton in a site-dependent ferromagnet using tanh-function method. Phys. Scr. 79, 015402 (2009)

    Article  MATH  Google Scholar 

  72. Kavitha, L., Srividya, B., Gopi, D.: Effect of nonlinear inhomogeneity on the creation and annihilation of magnetic soliton. J. Magn. Magn. Mater. 322, 1793–1810 (2010)

    Article  Google Scholar 

  73. Liu, S.K., Fu, Z.T., Liu, S.D., Zhao, Q.: A simple fast method in finding particular solutions of some nonlinear PDE. Appl. Math. Mech. 22, 326–331 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

L.K. gratefully acknowledges the financial support in the form of Major Research Projects by CSIR (Ref.No.:03(1418)/17/EMR-II), India, DST-SERB (Ref.No.: MTR/2017/000314/MS), India, and ICTP, Italy, in the form of a Regular Associateship. LK and TP acknowledge the financial support from UGC-DAE (Ref.No.:CSR-KN/CRS-102/2019-20) in the form of a major research project.

Author information

Authors and Affiliations

  1. Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610 005, India

    L. Kavitha & T. Pavithra

  2. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

    L. Kavitha

  3. Department of Physics, Periyar University, Salem, Tamil Nadu, 636 011, India

    C. Boopathy & V. Senthil Kumar

  4. Condensed Matter Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, India

    Awadhesh Mani

  5. Department of Chemistry, Periyar University, Salem, Tamil Nadu, 636 011, India

    D. Gopi

Authors
  1. L. Kavitha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Pavithra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Boopathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. Senthil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Awadhesh Mani
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. D. Gopi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Kavitha.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kavitha, L., Pavithra, T., Boopathy, C. et al. Current-driven magnetization reversal dynamics and breather-like EM soliton propagation in biaxial anisotropic weak ferromagnetic nanowire. Nonlinear Dyn 107, 2667–2687 (2022). https://doi.org/10.1007/s11071-021-06997-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06997-w

Keywords

Search

Navigation