Advertisement

Magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder with modulated along legs Dzyaloshinskii-Moriya interaction

  • Niko Avalishvili
  • Bachana Beradze
  • George I. JaparidzeEmail author
Regular Article
  • 20 Downloads

Abstract

We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder with period two lattice units modulated Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto an effective spin σ = 1/2 XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M = 0 and to its saturation value per rung M = Msat = 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M = 0.5Msat. The width of the magnetization plateau at M = 0.5Msat, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (D0D1/J2)α where D0, D1 are uniform and staggered components of the DM term, J is the intraleg exchange and α ≤ 3∕4 and weakly depends on the DM couplings.

Graphical abstract

Keywords

Solid State and Materials 

References

  1. 1.
    H. Bethe, Z. Phys. 71, 205 (1931) CrossRefADSGoogle Scholar
  2. 2.
    H.-J. Mikeska, A.K. Kolezhuk, inQuantum Magnetism, edited by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop, Lecture Notes in Physics (Springer, Berlin, 2004), Vol. 645 Google Scholar
  3. 3.
    A. Vasiliev, O. Volkova, E. Zvereva, M. Markina, npj Quant. Mater. 3, 18 (2018) CrossRefADSGoogle Scholar
  4. 4.
    S. Sachdev, Nat. Phys. 4, 173 (2008) CrossRefGoogle Scholar
  5. 5.
    C. Broholm, et al., Magnetized States of Quantum Spin Chains, inHigh Magnetic Fields, Lecture Notes in Physics (Springer, 2008), Vol. 595, p. 211 Google Scholar
  6. 6.
    M. Takigawa, F. Mila, inIntroduction to Frustrated Magnetism, edited by C. Lacroix, P. Mendels, F. Mila (Springer, 2011) Google Scholar
  7. 7.
    L. Savary, L. Balents, Rep. Prog. Phys. 80, 016502 (2017) CrossRefADSGoogle Scholar
  8. 8.
    J.H.H. Perk, H.W. Capel, Phys. Lett. A 58, 115 (1976) CrossRefADSGoogle Scholar
  9. 9.
    J.H.H. Perk, H.W. Capel, Physica A92, 163 (1978) MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    A.A. Zvyagin, Fiz. Niz. Temp. 15, 977 (1989) Google Scholar
  11. 11.
    A.A. Zvyagin, Zh. Eksp. Teor. Fiz. 98, 1396 (1990) Google Scholar
  12. 12.
    F.C. Alkaraz, W.F. Wreszinski, J. Stat. Phys. 58, 45 (1990) CrossRefADSGoogle Scholar
  13. 13.
    H.-P. Eckle, C.J. Hamer, J. Phys. A: Math. Gen. 24, 191 (1991) CrossRefADSGoogle Scholar
  14. 14.
    A.A. Zvyagin, J. Phys.: Condens. Matter 3, 3865 (1991) ADSGoogle Scholar
  15. 15.
    L. Shekhtman, O. Entin-Wohlman, A. Aharony, Phys. Rev. Lett. 69, 836 (1992) CrossRefADSGoogle Scholar
  16. 16.
    M. Oshikawa, I. Affleck, Phys. Rev. Lett. 79, 2883 (1997) CrossRefADSGoogle Scholar
  17. 17.
    I. Affleck, M. Oshikawa, Phys. Rev. B 60, 1038 (1999) CrossRefADSGoogle Scholar
  18. 18.
    J.Z. Zhao, X.Q. Wang, T. Xiang, Z.B. Su, L. Yu, Phys. Rev. Lett. 90, 207204 (2003) CrossRefADSGoogle Scholar
  19. 19.
    D.N. Aristov, S.V. Maleyev, Phys. Rev. B 62, R751 (2000) CrossRefADSGoogle Scholar
  20. 20.
    M. Bocquet, F.H.L. Essler, A.M. Tsvelik, A.O. Gogolin, Phys. Rev. B 64, 094425 (2001) CrossRefADSGoogle Scholar
  21. 21.
    S.A. Zvyagin, A.K. Kolezhuk, J. Krzystek, R. Feyerherm, Phys. Rev. Lett. 93, 027201 (2004) CrossRefADSGoogle Scholar
  22. 22.
    S.A. Zvyagin, A.K. Kolezhuk, J. Krzystek, R. Feyerherm, Phys. Rev. Lett. 95, 017207 (2005) CrossRefADSGoogle Scholar
  23. 23.
    S. Gangadharaiah, J. Sun, O.A. Starykh, Phys. Rev. B 78, 054436 (2008) CrossRefADSGoogle Scholar
  24. 24.
    I. Garate, I. Affeck, Phys. Rev. B 81, 144419 (2010) CrossRefADSGoogle Scholar
  25. 25.
    Z. Hao, Y. Wan, I. Rousochatzakis, J. Wildeboer, A. Seidel, F. Mila, O. Tchernyshyov, Phys. Rev. B 84, 094452 (2011) CrossRefADSGoogle Scholar
  26. 26.
    S. Peotta, L. Mazza, E. Vicari, M. Polini, R. Fazio, D. Rossini, J. Stat. Mech. 2014, P09005 (2014) CrossRefGoogle Scholar
  27. 27.
    Y.-H. Chan, W. Jin, H.-C. Jiang, O.A. Starykh, Phys. Rev. B 96, 214441 (2017) CrossRefADSGoogle Scholar
  28. 28.
    O. Baran, V. Ohanyan, T. Verkholyak, Phys. Rev. B 98, 064415 (2018) CrossRefADSGoogle Scholar
  29. 29.
    I.E. Dzyaloshinskii, Sov. Phys. JETP, 5, 1259 (1957) Google Scholar
  30. 30.
    T. Moriya, Phys. Rev. Lett. 4, 288 (1960) CrossRefADSGoogle Scholar
  31. 31.
    H.J. Schulz, Phys. Rev. B 34, 6372 (1986) CrossRefADSGoogle Scholar
  32. 32.
    I. Affleck, J. Phys.: Condens. Matter 1, 3047 (1991) ADSGoogle Scholar
  33. 33.
    D.G. Shelton, A.A. Nersesyan, A.M. Tsvelik, Phys. Rev. B 53, 8521 (1996) CrossRefADSGoogle Scholar
  34. 34.
    C.A. Hayward, D. Poilblanc, L.P. Lévy, Phys. Rev. B 54, R12649 (1996) CrossRefADSGoogle Scholar
  35. 35.
    E. Dagotto, T.M. Rice, Science, 271, 618 (1996) CrossRefADSGoogle Scholar
  36. 36.
    E. Dagotto, Rep. Prog. Phys. 62, 1525 (1999) CrossRefADSGoogle Scholar
  37. 37.
    F. Mila, Eur. Phys. J. B 6, 201 (1998) CrossRefADSGoogle Scholar
  38. 38.
    K. Totsuka, Phys. Rev. B 57, 3454 (1998) CrossRefADSGoogle Scholar
  39. 39.
    R. Chitra, T. Giamarchi, Phys. Rev. B 55, 5816 (1997) CrossRefADSGoogle Scholar
  40. 40.
    D.C. Cabra, A. Honecker, P. Pujol, Phys. Rev. Lett. 79, 5126 (1997) CrossRefADSGoogle Scholar
  41. 41.
    D.C. Cabra, A. Honecker, Phys. Rev. B 58, 6241 (1998) CrossRefADSGoogle Scholar
  42. 42.
    M. Usami, S.I. Suga, Phys. Rev. B 58, 14401 (1998) CrossRefADSGoogle Scholar
  43. 43.
    T. Giamarchi, A.M. Tsvelik, Phys. Rev. B 59, 11398 (1999) CrossRefADSGoogle Scholar
  44. 44.
    Y.-J. Wang, F.H.L. Essler, M. Fabrizio, A.A. Nersesyan, Phys. Rev. B 66, 024412 (2002) CrossRefADSGoogle Scholar
  45. 45.
    Y.-J. Wang, Phys. Rev. B 68, 214428 (2003) CrossRefADSGoogle Scholar
  46. 46.
    T. Vekua, G.I. Japaridze, H.-J. Mikeska, Phys. Rev. B 67, 064419 (2003) CrossRefADSGoogle Scholar
  47. 47.
    K. Hida, M. Shino, W. Chen, J. Phys. Soc. Jpn. 73, 1587 (2004) CrossRefADSGoogle Scholar
  48. 48.
    T. Vekua, G.I. Japaridze, H.-J. Mikeska, Phys. Rev. B 70, 014425 (2004) CrossRefADSGoogle Scholar
  49. 49.
    J.-B. Fouet, F. Mila, D. Clarke, H. Youk, O. Tchernyshyov, P. Fendley, R.M. Noack, Phys. Rev. B 73, 214405 (2006) CrossRefADSGoogle Scholar
  50. 50.
    G.I. Japaridze, E. Pogosyan, J. Phys. C: Condens. Matter 18, 9297 (2006) ADSGoogle Scholar
  51. 51.
    G.I. Japaridze, A. Langari, S. Mahdavifar, J. Phys. C: Condens. Matter 19, 076201 (2007) ADSGoogle Scholar
  52. 52.
    G.I. Japaridze, S. Mahdavifar, Eur. Phys. J. B 68, 59 (2009) CrossRefADSGoogle Scholar
  53. 53.
    K.Yu. Povarov, W.E.A. Lorenz, F. Xiao, C.P. Landee, Y. Krasnikova, A. Zheludev, J. Magn. Magn. Mater. 370, 62 (2014) CrossRefADSGoogle Scholar
  54. 54.
    M. Ozerov, M. Maksymenko, J. Wosnitza, A. Honecker, C.P. Landee, M.M. Turnbull, S.C. Furuya, T. Giamarchi, S.A. Zvyagin, Phys. Rev. B 92, 241113 (2015) CrossRefADSGoogle Scholar
  55. 55.
    V.N. Glazkov, M. Fayzullin, Yu. Krasnikova, G. Skoblin, D. Schmidiger, S. Mühlbauer, A. Zheludev, Phys. Rev. B 92, 184403 (2015) CrossRefADSGoogle Scholar
  56. 56.
    A.N. Ponomaryov, M. Ozerov, L. Zviagina, J. Wosnitza, K.Yu. Povarov, F. Xiao, A. Zheludev, C. Landee, E. Čižmár, A.A. Zvyagin, S.A. Zvyagin, Phys. Rev. B 93, 134416 (2016) CrossRefADSGoogle Scholar
  57. 57.
    O.M. Volkov, D.D. Sheka, Y. Gaididei, V.P. Kravchuk, U.K. Rössler, J. Fassbender, D. Makarov, Sci. Rep. 8, 866 (2018) CrossRefADSGoogle Scholar
  58. 58.
    H. Yang, O. Boulle, V. Cros, A. Fert, M. Chshiev, Sci. Rep. 8, 12356 (2018) CrossRefADSGoogle Scholar
  59. 59.
    W. Zhang et al., Appl. Phys. Lett. 113, 122406 (2018) CrossRefADSGoogle Scholar
  60. 60.
    T. Srivastava et al., Nano Lett. 18, 4871 (2018) CrossRefADSGoogle Scholar
  61. 61.
    N. Avalishvili, G.I. Japaridze, G. Rossini, Phys. Rev. B 99, 205159 (2019) CrossRefADSGoogle Scholar
  62. 62.
    T. Verkholyak, O. Derzhko, T. Krokhmalskii, J. Stolze, Phys. Rev. B 76, 144418 (2007) CrossRefADSGoogle Scholar
  63. 63.
    D.V. Dmitriev, V.Ya. Krivnov, Phys. Rev. B 86, 134407 (2012) CrossRefADSGoogle Scholar
  64. 64.
    P. Jordan, E. Wigner, Z. Phys. 47, 631 (1928) CrossRefADSGoogle Scholar
  65. 65.
    A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik,Bosonization and strongly correlated systems (Cambridge University Press, Cambridge, 1998) Google Scholar
  66. 66.
    T. Hikihara, A. Furusaki, Phys. Rev. B 63, 134438 (2001) CrossRefADSGoogle Scholar
  67. 67.
    A. Luther, I. Peschel, Phys. Rev. B 12, 3908 (1975) CrossRefADSGoogle Scholar
  68. 68.
    G.I. Japaridze, A.A. Nersesyan, JETF Pis’ma 27, 356 (1978) [JETP Lett. 27, 334 1978] Google Scholar
  69. 69.
    V.L. Pokrovsky, A.L. Talapov, Phys. Rev. Lett. 42, 65 (1979) CrossRefADSGoogle Scholar
  70. 70.
    G.I. Japaridze, A.A. Nersesyan, J. Low Temp. Phys. 37, 95 (1979) CrossRefADSGoogle Scholar
  71. 71.
    G.I. Japaridze, A.A. Nersesyan, P.B. Wiegmann, Nucl. Phys. B 230, 511 (1984) CrossRefADSGoogle Scholar
  72. 72.
    R.F. Dashen, B. Hasslacher, A. Neveu, Phys. Rev. D 10 1449 (1974) Google Scholar
  73. 73.
    R.F. Dashen, B. Hasslacher, A. Neveu, Phys. Rev. D 11 3424 (1975) CrossRefADSGoogle Scholar
  74. 74.
    V.E. Korepin, L.D. Faddeev, Sov. Theor. Math. Phys. 25, 147 (1975) Google Scholar
  75. 75.
    Al.B. Zamolodchikov, Int. J. Mod. Phys. A 10, 1125 (1995) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Niko Avalishvili
    • 1
    • 2
  • Bachana Beradze
    • 3
  • George I. Japaridze
    • 1
    • 2
    Email author
  1. 1.Ilia State University, Faculty of Natural Sciences and MedicineTbilisiGeorgia
  2. 2.Andronikashvili Institute of PhysicsTbilisiGeorgia
  3. 3.Ivane Javakhishvili Tbilisi State University, Faculty of Exact and Natural SciencesTbilisiGeorgia

Personalised recommendations