Commensurability effects in the critical forces of a superconducting film with Kagomé pinning array at submatching fields

  • Nicolas P. Vizarim
  • Maicon Carlone
  • Lucas G. Verga
  • Pablo A. Venegas
Regular Article
  • 16 Downloads

Abstract

Using molecular dynamics simulations, we find the commensurability force peaks in a two-dimensional superconducting thin-film with a Kagomé pinning array. A transport force is applied in two mutually perpendicular directions, and the magnetic field is increased up to the first matching field. Usually the condition to have pronounced force peaks in systems with periodic pinning is associated to the rate between the applied magnetic field and the first matching field, it must be an integer or a rational fraction. Here, we show that another condition must be satisfied, the vortex ground state must be ordered. Our calculations show that the pinning size and strength may dramatically change the vortex ground state. Small pinning radius and high values of pinning strength may lead to disordered vortex configurations, which fade the critical force peaks. The critical forces show anisotropic behavior, but the same dependence on pinning strength and radius is observed for both driven force directions. Different to cases where the applied magnetic field is higher than the first matching field, here the depinning process begins with vortices weakly trapped on top of a pinning site and not with interstitial vortices. Our results are in good agreement with recent experimental results.

Keywords

Solid State and Materials 

References

  1. 1.
    C. Reichhardt, G.T. Zimányi, N. Grønbech-Jensen, Phys. Rev. B 64, 014501 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    C. Reichhardt, C.J.O. Reichhardt, Phys. Rev. B 76, 064523 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    C. Reichhardt, C.J. Olson Reichhardt, Phys. Rev. B 79, 134501 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    C. Reichhardt, C.J. Olson, F. Nori, Phys. Rev. B 57, 7937 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    C. Reichhardt, N. Grønbech-Jensen, Phys. Rev. B 63, 054510 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    S. Ooi, T. Mochiku, K. Hirata, Phys. C: Supercond. 469, 1113 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    D. Bothner, R. Seidl, V.R. Misko, R. Kleiner, D. Koelle, M. Kemmler, Supercond. Sci. Technol. 27, 065002 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    J. Cuppens, G.W. Ataklti, W. Gillijns, J. Van de Vondel, V.V. Moshchalkov, A.V. Silhanek, J. Supercond. Nov. Magn. 24, 7 (2011)CrossRefGoogle Scholar
  9. 9.
    A.N. Lykov, J. Low Temp. Phys. 164, 61 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    L.G. Verga, M.M. Bonilha, M. Carlone, P.A. Venegas, J. Supercond. Nov. Magn. 26, 2147 (2012)CrossRefGoogle Scholar
  11. 11.
    R. Simões, P. Venegas, D. Mello, J. Supercond. Nov. Magn. (2011)Google Scholar
  12. 12.
    K. Harada, O. Kamimura, H. Kasai, T. Matsuda, A. Tonomura, V.V. Moshchalkov, Science 274, 1167 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    A.N. Grigorenko, G.D. Howells, S.J. Bending, J. Bekaert, M.J. Van Bael, L. Van Look, V.V. Moshchalkov, Y. Bruynseraede, G. Borghs, I.I. Kaya, R.A. Stradling, Phys. Rev. B 63, 052504 (2001)ADSCrossRefGoogle Scholar
  14. 14.
    C. Reichhardt, C.J. Olson, F. Nori, Phys. Rev. Lett. 78, 2648 (1997)ADSCrossRefGoogle Scholar
  15. 15.
    Q.-B. Ren, M.-B. Luo, Phys. Lett. A 377, 1966 (2013)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    R. Cao, T.C. Wu, P.C. Kang, J.C. Wu, T.J. Yang, L. Horng, Solid State Commun. 143, 171 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    M. Baert, V.V. Metlushko, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. Lett. 74, 3269 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    A.N. Grigorenko, S.J. Bending, M.J. Van Bael, M. Lange, V.V. Moshchalkov, H. Fangohr, P.A.J. de Groot, Phys. Rev. Lett. 90, 237001 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    S.B. Field, S.S. James, J. Barentine, V. Metlushko, G. Crabtree, H. Shtrikman, B. Ilic, S.R.J. Brueck, Phys. Rev. Lett. 88, 067003 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    B.Y. Zhu, M. Liu, D.Y. Xing, B.R. Zhao, Z.X. Zhao, Phys. C: Supercond. 361, 107 (2001)ADSCrossRefGoogle Scholar
  21. 21.
    T.C. Wu, P.C. Kang, L. Horng, J.C. Wu, T.J. Yang, J. Appl. Phys. 95, 6696 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    M. Velez, D. Jaque, J.I. Martín, M.I. Montero, I.K. Schuller, J.L. Vicent, Phys. Rev. B 65, 104511 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    D. Jaque, E.M. González, J.I. Martin, J.V. Anguita, J.L. Vicent, Appl. Phys. Lett. 81, 2851 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    P.-J. Cuadra-Solís, A. García-Santiago, J.M. Hernandez, J. Tejada, J. Vanacken, V.V. Moshchalkov, Phys. Rev. B 89, 054517 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    C. Reichhardt, G.T. Zimányi, R.T. Scalettar, A. Hoffmann, I.K. Schuller, Phys. Rev. B 64, 052503 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    G.R. Berdiyorov, M.V. Milošević, F.M. Peeters, Phys. Rev. B 74, 174512 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    G.R. Berdiyorov, M.V. Milošević, F.M. Peeters, Europhys. Lett. 74, 493 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    M. Vélez, J.I. Martín, J.E. Villegas, A. Hoffmann, E.M. González, J.L. Vicent, I.K. Schuller, J. Magn. Magn. Mater. 320, 2547 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    H. Shi-Kun, Z. Wei-Jun, W. Zhen-Chao, X. Hong, H. Xiu-Feng, G. Chang-Zhi, Q. Xiang-Gang, Chin. Phys. B 21, 087401 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    M.F. Laguna, C.A. Balseiro, D. Domínguez, F. Nori, Phys. Rev. B 64, 104505 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    R. Simões, P. Venegas, D. Mello, J. Supercond. Nov. Magn. (2011)Google Scholar
  32. 32.
    R.P. Simões, P.A. Venegas, D.F. Mello, J. Supercond. Nov. Magn. 26, 2277 (2013)CrossRefGoogle Scholar
  33. 33.
    S.K. He, W.J. Zhang, H.F. Liu, G.M. Xue, B.H. Li, H. Xiao, Z.C. Wen, X.F. Han, S.P. Zhao, C.Z. Gu, X.G. Qiu, J. Phys.: Condens. Matter 24, 155702 (2012)ADSGoogle Scholar
  34. 34.
    L.G. Verga, M.C. da Silva, R.P. Simões, D.F. Mello, P.A. Venegas, J. Supercond. Nov. Magn. 26, 351 (2013)CrossRefGoogle Scholar
  35. 35.
    D.J. Morgan, J.B. Ketterson, Phys. Rev. Lett. 80, 3614 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    N.P. Vizarim, M. Carlone, L.G. Verga, P.A. Venegas, Mater. Res. (2017)Google Scholar
  37. 37.
    I.A. Sadovskyy, Y.L. Wang, Z.-L. Xiao, W.-K. Kwok, A. Glatz, Phys. Rev. B 95, 075303 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    K. Matsumoto, P. Mele, Supercond. Sci. Technol. 23, 014001 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    A.B. Kolton, D. Domínguez, N. Grønbech-Jensen, Phys. Rev. Lett. 83, 3061 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    A.B. Kolton, R. Exartier, L.F. Cugliandolo, D. Domínguez, N. Grønbech-Jensen, Phys. Rev. Lett. 89, 227001 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    V.R. Misko, S. Savel’ev, F. Nori, Phys. Rev. B 74, 024522 (2006)ADSCrossRefGoogle Scholar
  42. 42.
    R.B.G. Kramer, A.V. Silhanek, J. Van de Vondel, B. Raes, V.V. Moshchalkov, Phys. Rev. Lett. 103, 067007 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    A.V. Silhanek, W. Gillijns, V.V. Moshchalkov, B.Y. Zhu, J. Moonens, L.H.A. Leunissen, Appl. Phys. Lett. 89, 152507 (2006)ADSCrossRefGoogle Scholar
  44. 44.
    V.R. Misko, F. Nori, Phys. Rev. B 85, 184506 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    S. Guénon, Y.J. Rosen, A.C. Basaran, I.K. Schuller, Appl. Phys. Lett. 102, 252602 (2013)ADSCrossRefGoogle Scholar
  46. 46.
    C.J. Olson Reichhardt, Y.L. Wang, Z.L. Xiao, W.K. Kwok, D. Ray, C. Reichhardt, B. Jankó, Phys. C: Supercond. Appl. 533, 148 (2017)ADSCrossRefGoogle Scholar
  47. 47.
    D. Ray, C.J. Olson Reichhardt, B. Jankó, C. Reichhardt, Phys. Rev. Lett. 110, 267001 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    Y.L. Wang, M.L. Latimer, Z.L. Xiao, R. Divan, L.E. Ocola, G.W. Crabtree, W.K. Kwok, Phys. Rev. B 87, 220501 (2013)ADSCrossRefGoogle Scholar
  49. 49.
    D. Ray, C. Reichhardt, C.J.O. Reichhardt, Phys. Rev. B 90, 094502 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M.J. Van Bael, K. Temst, Y. Bruynseraede, R. Jonckheere, Phys. Rev. B 57, 3615 (1998)ADSCrossRefGoogle Scholar
  51. 51.
    A.E. Koshelev, I.A. Sadovskyy, C.L. Phillips, A. Glatz, Phys. Rev. B 93, 060508 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    N. Grønbech-Jensen, Comput. Phys. Commun. 119, 115 (1999)ADSCrossRefGoogle Scholar
  53. 53.
    J. Bardeen, M.J. Stephen, Phys. Rev. 140, A1197 (1965)ADSCrossRefGoogle Scholar
  54. 54.
    C. Tsallis, D.A. Stariolo, Physica A (1996)Google Scholar
  55. 55.
    N. Mangan, C. Reichhardt, C.J.O. Reichhardt, Phys. Rev. Lett. 100, 187002 (2008)ADSCrossRefGoogle Scholar
  56. 56.
    C.J. Olson, C. Reichhardt, R.T. Scalettar, G.T. Zimányi, N. Grønbech-Jensen, Phys. Rev. B 67, 184523 (2003)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.POSMAT – Programa de Pós-Graduação em Ciência e Tecnologia de Materiais, Faculdade de Ciências, UNESP – Universidade Estadual PaulistaBauruBrazil
  2. 2.Department of ChemistryUniversity of SouthamptonSouthamptonUK
  3. 3.Departamento de Física, Faculdade de Ciências, UNESP – Universidade Estadual PaulistaBauruBrazil

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