Skip to main content
SpringerLink
Log in

Antiferromagnetic spin-1 XYZ model with the Dzyaloshinskii–Moriya interaction

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Antiferromagnetic spin-1 XYZ model is examined by using a mean-field approach with the introduction of spin operators on the simple cubic lattice. The model includes the crystal field interaction \((D_z)\) along the z-axis, the Dzyaloshinskii–Moriya interaction \((\Delta _m)\) and an external magnetic field with the components of \(H_x=H_y=H_z=H\). The bilinear exchange interaction parameter \((J_z)\) is taken as a scaling parameter chosen to be negative to simulate the antiferromagnetic interactions between the nearest-neighbor spins. Thermal variations of the total magnetization and its components are investigated in detail to obtain the phase diagrams on the \((H/|J_z|, T/|J_z|)\), \((D_z/|J_z|, T/|J_z|)\) and \((\Delta _m/|J_z|, T/|J_z|)\) planes. The model exhibits antiferromagnetic, paramagnetic and random phase regions. Very interesting various phase lines and critical points are observed including the tricritical points, bicritical points, critical end points and two more. The reentrant behavior is also observed for appropriate values of the system parameters.

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

Similar content being viewed by others

References

  1. M.L. Néel, Ann. Phys. 12, 137 (1948)

    Article  Google Scholar 

  2. X.-Y. Gao, Y.-J. Guo, W.-R. Shan, Appl. Math. Lett. 120, 107161 (2021)

    Article  Google Scholar 

  3. M. Wang, B. Tian, C.-C. Hu, S.-H. Liu, Appl. Math. Lett. 119, 106936 (2021)

    Article  Google Scholar 

  4. Y. Shen, B. Tian, Appl. Math. Lett. 122, 107301 (2021)

    Article  Google Scholar 

  5. X.-Y. Gao, Y.-J. Guo, W.-R. Shan, Eur. Phys. J. Plus 136, 893 (2021)

    Article  Google Scholar 

  6. X.-Y. Gao, Y.-J. Guo, W.-R. Shan, Chaos Solitons Fract. 150, 111066 (2021)

    Article  Google Scholar 

  7. X.-T. Gao, B. Tian, Y. Shen, C.-H. Feng, Chaos Solitons Fract. 151, 111222 (2021)

    Article  Google Scholar 

  8. C.Z. Yang, J.L. Zhong, Phys. Stat. Sol. B 153, 323 (1989)

    Article  ADS  Google Scholar 

  9. J.L. Zhong, J.L. Li, C.Z. Yang, Phys. Stat. Sol. B 160, 329 (1990)

    Article  ADS  Google Scholar 

  10. M. Saber, J.W. Tucker, J. Magn. Magn. Mater. 102, 287 (1991)

    Article  ADS  Google Scholar 

  11. J.W. Tucker, J. Magn. Magn. Mater. 119, 161 (1993)

    Article  ADS  Google Scholar 

  12. J.P. Fittipaldi, E.F. Sarmento, T. Kaneyoshi, Physica A 186, 591 (1992)

    Article  ADS  Google Scholar 

  13. E.F. Sarmento, J.P. Fittipaldi, T. Kaneyoshi, J. Magn. Magn. Mater. 104–107, 233 (1992)

    Article  ADS  Google Scholar 

  14. X.F. Jiang, J.L. Li, J. Zhong, C.Z. Yang, Phys. Rev. B 47, 827 (1993)

    Article  ADS  Google Scholar 

  15. Y.Q. Ma, Y.G. Ma, C.D. Gong, Phys. Stat. Sol. B 177, 215 (1993)

    Article  ADS  Google Scholar 

  16. A. Benyoussef, H.E. Zahraouy, J. Phys. Condens. Matter 6, 3411 (1994)

    Article  ADS  Google Scholar 

  17. C.Z. Yang, W.J. Song, Phys. Stat. Sol. B 177, K21 (1993)

    Article  ADS  Google Scholar 

  18. E. Albayrak, Acta Phys. Pol. A 127, 818 (2015)

    Article  ADS  Google Scholar 

  19. E. Albayrak, Chin. Phys. B 22, 077501 (2013)

    Article  Google Scholar 

  20. E. Albayrak, Chin. Phys. Lett. 35, 037501 (2018)

    Article  ADS  Google Scholar 

  21. Q. Zhang, Y.W. Gu, G.Z. Wei, Proceedings of the third International Syposium on Magnenetic Industries (ISMI’04) and First International Symposium on Physical and IT Industries (ISITI’04) pp. 40–42 (2005)

  22. E. Albayrak, M. Keskin, J. Magn. Magn. Mater. 206, 83 (1999)

    Article  ADS  Google Scholar 

  23. H. Ez-Zahraouy, H. Mahboub, M.J. Ouazzani, Int. J. Mod. Phys. B 18, 4129 (2004)

    Article  ADS  Google Scholar 

  24. J.R. Viana, O.D.R. Salmon, M.A. Neto, D.C. Carvalho, Int. J. Mod. Phys. B 32, 1850038 (2018)

    Article  Google Scholar 

  25. J. Ricardo de Sousa, F. Lacerda, I.P. Fittipaldi, Physica A 258, 221 (1998)

    Article  ADS  Google Scholar 

  26. G. Mert, J. Magn. Magn. Mater. 394, 126 (2015)

    Article  ADS  Google Scholar 

  27. A. Bobák, V. Pokorný, J. Dely, Physica A 388, 2157 (2009)

    Article  ADS  Google Scholar 

  28. A. Bobák, J. Dely, M. Žukovič, Physica A 390, 1953 (2011)

    Article  ADS  Google Scholar 

  29. A. Bobák, V. Pokorny, J. Dely, J. Phys. Conf. Ser. 200, 022001 (2010)

    Article  Google Scholar 

  30. A. Bobák, Z. Fecková, M. Žukovič, J. Magn. Magn. Mater. 323, 813 (2011)

    Article  ADS  Google Scholar 

  31. D.S. Takou, M. Karimou, F. Hontinfinde, E. Albayrak, Cond. Matter Phys. 24, 13704 (2021)

    Article  Google Scholar 

  32. E. Albayrak, Physica A 486, 161 (2017)

    Article  ADS  Google Scholar 

  33. E. Albayrak, J. Supercond. Nov. Magn. 30, 2555 (2017)

    Article  Google Scholar 

  34. J. Strečka, L. Čanová, J. Phys. Conf. Ser. 145, 012012 (2009)

    Article  Google Scholar 

  35. W.E.F. Parente, J.T.M. Pacobahyba, I.G. Araújo, M.A. Neto, J.R. de Sousa, Ü. Akinci, J. Magn. Magn. Mater. 355, 235 (2014)

    Article  ADS  Google Scholar 

  36. A.S. Freitas, D.F. de Albuquerque, Phys. Rev. E 91, 012117 (2015)

    Article  ADS  Google Scholar 

  37. G.-H. Liu, W.-L. You, W. Li, G. Su, J. Phys. Condens. Matter 27, 165602 (2015)

    Article  ADS  Google Scholar 

  38. A. Sera, Y. Kousaka, J. Akimitsu, M. Sera, T. Kawamata, Y. Koike, K. Inoue, Phys. Rev. B 94, 214408 (2016)

    Article  ADS  Google Scholar 

  39. Y.-H. Chan, W. Jin, H.-C. Jiang, O.A. Starykh, Phys. Rev. B 96, 214441 (2017)

    Article  ADS  Google Scholar 

  40. J. Strečka, L. Čanová, K. Minami, Phys. Rev. E 79, 051103 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  41. W.E.F. Parente, J.T.M. Pacobahyba, M.A. Neto, I.G. Araújo, J.A. Plascak, J. Magn. Magn. Mater. 462, 8 (2018)

    Article  ADS  Google Scholar 

  42. G.-H. Sun, X.-M. Kong, Physica A 370, 585 (2006)

    Article  ADS  Google Scholar 

  43. L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 320, 2316 (2008)

    Article  ADS  Google Scholar 

  44. G.-H. Liu, J.-Y. Dou, P. Lu, J. Magn. Magn. Mater. 401, 796 (2016)

    Article  ADS  Google Scholar 

  45. F.-Y. Li, G. Chen, Phys. Rev. B 98, 045109 (2018)

    Article  ADS  Google Scholar 

  46. H. Tschirhart, E.T.S. Ong, P. Sengupta, T.L. Schmidt, Phys. Rev. B 100, 195111 (2019)

    Article  ADS  Google Scholar 

  47. H. Komatsu, Y. Nonomura, M. Nishino, Phys. Rev. B 103, 214404 (2021)

    Article  ADS  Google Scholar 

  48. W.-N. Shi, F. Ming, D. Wang, L. Ye, Quantum Inf. Process. 18, 70 (2019)

    Article  ADS  Google Scholar 

  49. K.-H. Miitted, A. Schmidt, J. Phys. A Math. Gen. 28, 2265 (1995)

    Article  ADS  Google Scholar 

  50. C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, T. Byrnes, Sci. Rep. 7, 13865 (2017)

    Article  ADS  Google Scholar 

  51. L.A. Takhtajan, Physica 3D 1–2, 231 (1981)

    Google Scholar 

  52. E. Albayrak, Opt. Commun. 284, 1631 (2011)

    Article  ADS  Google Scholar 

  53. E. Albayrak, Eur. Phys. J. Plus, Submitted

Download references

Acknowledgements

This work was supported by the Research Fund of Erciyes University with Project Identification Number: FBA-2021-11571.

Author information

Authors and Affiliations

  1. Department of Physics, Erciyes University, 38039, Kayseri, Turkey

    Erhan Albayrak

Authors
  1. Erhan Albayrak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erhan Albayrak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albayrak, E. Antiferromagnetic spin-1 XYZ model with the Dzyaloshinskii–Moriya interaction. Eur. Phys. J. Plus 137, 618 (2022). https://doi.org/10.1140/epjp/s13360-022-02830-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02830-4

Search

Navigation