Skip to main content
SpringerLink
Log in

Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry

  • Condensed Matter
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler–Lagrange static equations, derived from the Hamiltonian, lead to the inhomogeneous double sine-Gordon equation. Nonetheless, if the magnetic field is coupled to the metric elements of the surface, and consequently to its curvature, the homogeneous double sine-Gordon equation emerges and a \(2\pi \)-soliton solution is obtained. In order to satisfy the self-dual equations, surface deformations are predicted to appear at the sector where the spin direction is opposite to the magnetic field. On the basis of the model, we find the characteristic length of the \(2\pi \)-soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid, and the hyperboloid. On finite surfaces, such as the sphere, torus, and barrels, fractional \(2\pi \)-solitons are predicted to appear.

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

Similar content being viewed by others

References

  1. S. Tanda, T. Tsuneta, H. Okajima, K. Inagaki, K. Yumaya, N. Hatakenaka, Nature 417, 397 (2002)

    Article  Google Scholar 

  2. E. Yazgan, E. Taşci, O.B. Malcioǧlu, Ş. Erkoç, J. Mol. Struct. 681, 231 (2004)

    Article  Google Scholar 

  3. E. Taşci, E. Yazgan, O.B. Malcioǧlu, Ş. Erkoç, Fuller. Nanotub. Carbon Nanostruct. 13(147) (2005)

  4. F.-M. Liu, M. Green, J. Mater. Chem. 14, 1526 (2004)

    Article  Google Scholar 

  5. F.Q. Zhu, G.W. Chern, O. Tchernyshyov, X.C. Zhu, J.G. Zhu, C.L. Chien, Phys. Rev. Lett. 96, 027205 (2006)

    Article  ADS  Google Scholar 

  6. P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 2006). 3rd printing

    Google Scholar 

  7. N.D. Mermin, Rev. Mod. Phys. 51, 591 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  8. M.N.S. Qureshi, J. Shi, H.A. Shah, Bras. J. Phys. 42, 48 (2012)

    Article  ADS  Google Scholar 

  9. V. Vitelli, A.M. Turner, Phys. Rev. Lett. 93, 215–301 (2004)

    Article  Google Scholar 

  10. J. Dai, J.-Q. Wang, C. Sangregorio, J. Fang, E. Carpenter, J. Tang, J. Appl. Phys. 87, 7397 (2000)

    Article  ADS  Google Scholar 

  11. G.A. Prinz, J. Magn. Magn. Mater. 200, 57 (1999)

    Article  ADS  Google Scholar 

  12. S.H. Sun, C.B. Murray, D. Weller, L. Folks, A. Moser, Science 287, 1989 (2000)

    Article  ADS  Google Scholar 

  13. G.A. Prinz, ibid. 282, 1660 (1998)

  14. D.-H. Kim, E. Rozhkova, I. Ulasov, S. Bader, T. Rajh, M. Lesniak, V. Novosad, Nat. Matter (2009). doi:10.1038/NMAT2591

    Google Scholar 

  15. E.A. Rozhkova, V. Novosad, D.-H. Kim, J. Pearson, R. Divan, T. Rajh, S.D. Bader, J. Appl. Phys. 105, 07B306 (2009)

    Article  Google Scholar 

  16. E.A. Rozhkova, I. Ulasov, B. Lai, N.M. Dimitrijevic, M.S. Lesniac, T. Rajh, Nano Lett. 9, 3337 (2009)

    Article  ADS  Google Scholar 

  17. V.L. Carvalho-Santos, W.A. Moura-Melo, A.R. Pereira, J. Appl. Phys. 108, 094310 (2010)

    Article  ADS  Google Scholar 

  18. F.A. Apolonio, W.A. Moura-Melo, F.P. Crisafuli, A.R. Pereira, R.L. Silva, J. Appl. Phys. 106, 084320 (2009)

    Article  ADS  Google Scholar 

  19. A. Vansteenkiste, M. Weigand, M. Curcic, H. Stoll, G. Schütz, B. Van Waeyenberge, New J. Phys. 11, 063006 (2009)

    Article  ADS  Google Scholar 

  20. D. Toscano, S.A. Leonel, R.A. Dias, P.Z. Coura, B.V. Costa, J. Appl. Phys. 109, 076104 (2011)

    Article  ADS  Google Scholar 

  21. V.L. Carvalho-Santos, A.R. Moura, W.A. Moura-Melo, A.R. Pereira, Phys. Rev. B77, 134450 (2008)

    ADS  Google Scholar 

  22. J. Benoit, R. Dandoloff, Phys. Lett. A248, 439 (1998)

    ADS  Google Scholar 

  23. A. Saxena, R. Dandoloff, T. Lookman, Physica A261, 13 (1998)

    Google Scholar 

  24. R. Dandoloff, S. Villain-Guillot, A. Saxena, A.R. Bishop, Phys. Rev. Lett. 74, 813 (1995)

    Article  ADS  Google Scholar 

  25. S. Villain-Guillot, R. Dandoloff, A. Saxena, A.R. Bishop, Phys. Rev. B52, 6712 (1995)

    ADS  Google Scholar 

  26. L.A.N. de Paula, Bras. J. Phys. 39, 711 (2009)

    Google Scholar 

  27. G.S. Milagre, W.A. Moura-Melo, Phys. Lett. A368, 155 (2007)

    ADS  Google Scholar 

  28. L.R.A. Belo, N.M. Oliveira-Neto, W.A. Moura-Melo, A.R. Pereira, E. Ercolessi, Phys. Lett. A365, 463 (2007)

    ADS  Google Scholar 

  29. W.A. Freitas, W.A. Moura-Melo, A.R. Pereira, Phys. Lett. A336, 412 (2005)

    ADS  Google Scholar 

  30. W.A. Moura-Melo, A.R. Pereira, L.A.S. Mól, A.S.T. Pires, Phys. Lett. A360, 472 (2007)

    ADS  Google Scholar 

  31. A. Saxena, R. Dandoloff, Phys. Rev. B66, 104414 (2002)

    ADS  Google Scholar 

  32. M. Lapine, I.V. Shadrivov, D.A. Powell, Y.S. Kivshar, Nat. Mater. 11, 30 (2012)

    Article  ADS  Google Scholar 

  33. G. Napoli, L. Vergori, Phys. Rev. Lett. 108, 207803 (2012)

    Article  ADS  Google Scholar 

  34. T. Georgiou, L. Britnell, P. Blake, R.V. Gorbachev, A. Gholinia, A.K. Geim, C. Casiraghi, K.S. Novoselov, Appl. Phys. Lett. 99, 093103 (2011)

    Article  ADS  Google Scholar 

  35. A. Saxena, R. Dandoloff, Phys. Rev. B58, R563 (1998)

    ADS  Google Scholar 

  36. R. Dandoloff, A. Saxena, Eur. Phys. J. B29, 265 (2002)

    MathSciNet  ADS  Google Scholar 

  37. A. Saxena, R. Dandoloff, Phys. Rev. B66, 104414 (2002)

    ADS  Google Scholar 

  38. R. Dandoloff, A. Saxena, J. Phys. A Math. Theor. 44, 045203 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  39. V.L. Carvalho-Santos, R. Dandoloff, Phys. Lett. A376, 3551 (2012)

    ADS  Google Scholar 

  40. V.L. Carvalho-Santos, R. Dandoloff, On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry. Phys. Lett. A (2013). doi:10.1016/j.physleta.2013.03.028

    Google Scholar 

  41. K.M. Leung, Phys. Rev. B26, 226 (1982)

    ADS  Google Scholar 

  42. K.M. Leung, Phys. Rev. B27, 2877 (1983)

    ADS  Google Scholar 

  43. E.B. Bogomolnyi, Sov. J. Nucl. Phys. 26, 449 (1976)

    MathSciNet  Google Scholar 

  44. E.W. Weisstein, Hyperboloid. (MathWorld—A Wolfram Web Resource, 2013). http://mathworld.wolfram.com/Hyperboloid.html. Accessed 30 Nov 2012

  45. K. Kowalski, J. Rembieliński, A. Szcześniak, J. Phys. A: Math. Theor. 44, 085302 (2011)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We thank the CNPq (grant number 562867/2010-4) and Propes of the IF Baiano, for financial support. Carvalho-Santos thanks J. D. Lima, P. G. Lima-Santos, and G. H. Lima-Santos for their encouragement.

Author information

Authors and Affiliations

  1. Instituto Federal de Educação, Ciência e Tecnologia Baiano - Campus Senhor do Bonfim, 48970-000, Senhor do Bonfim, Bahia, Brazil

    Vagson L. Carvalho-Santos

  2. Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 95302, Cergy-Pontoise, France

    Rossen Dandoloff

Authors
  1. Vagson L. Carvalho-Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rossen Dandoloff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vagson L. Carvalho-Santos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carvalho-Santos, V.L., Dandoloff, R. Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry. Braz J Phys 43, 130–136 (2013). https://doi.org/10.1007/s13538-013-0126-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-013-0126-1

Keywords

Search

Navigation