Skip to main content
Log in

Ising model with staggered Dzyaloshinsky–Moriya interaction

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

We have studied the effect of staggered Dzyaloshinsky–Moria (DM) interaction on the ground state phase diagram of the Ising model using variational matrix product state and numerical Lanczos methods. Variational matrix product state results show that the ground state phase diagram of the model consists of two ferromagnetic (FM) and staggered spiral phases in FM case. The quantum corrections of the staggered DM interaction on the ground state phase diagram are determined by a very accurate numerical method and its results confirm our analytic prediction.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. H Bethe Z. Phys. 71 205 (1931)

    Article  ADS  Google Scholar 

  2. U Schollweck, J O Richter, D J J Farnell and R F BishopQuantum (eds.) Magnetism Lecture Notes in Physics p 645

  3. S Sachdev Nat. Phys. 4 173 (2008)

    Article  Google Scholar 

  4. T Giamarchi, C Regg and O Tchernyshyov Nat. Phys. 4 198 (2008)

    Article  Google Scholar 

  5. G I Japaridze and S Mahdavifar Eur. Phys. J. B 68 59 (2009)

    Article  ADS  Google Scholar 

  6. F Soheilian and M R Soltani Indian J. Phys. 84 257 (2010)

    Article  ADS  Google Scholar 

  7. I Dzyaloshinsky J. Phys. Chem. Solids 4 241 (1958)

    Article  ADS  Google Scholar 

  8. T Moriya Phys. Rev. Lett. 4 228 (1960)

    Article  ADS  Google Scholar 

  9. T Moriya Phys. Rev. 120 91 (1960)

    Article  ADS  Google Scholar 

  10. J Sudan, A Luscher and A M Lauchli Phys. Rev. B 80 140402 (2009)

    Article  ADS  Google Scholar 

  11. S Seki, Y Yamasaki, M Soda, M Matsuura, K Hirota and Y Tokura Phys. Rev. Lett. 100 127201 (2008)

    Article  ADS  Google Scholar 

  12. D Huvonen, U Nagel, T Room, Y J Choi, C L Zhang, S Park and S W Cheong Phys. Rev. B 80 100402 (2009)

    Article  ADS  Google Scholar 

  13. M Oshikawa and I Affleck Phys. Rev. Lett. 79 2883 (1997)

    Article  ADS  Google Scholar 

  14. M Oshikawa and I Affleck Phys. Rev. B 60 1038 (1999)

    Article  ADS  Google Scholar 

  15. O Derzhko, T Verkholyak, T Krokhmalskii and H Buttner Phys. Rev. B 73 214407 (2006)

    Article  ADS  Google Scholar 

  16. M Tovar, K S Raman and K Shtengel Phys. Rev. B 79 024405 (2009)

    Article  ADS  Google Scholar 

  17. N Nayak, B Ghosh and A S Majumdar Indian J. Phys. 84 1039 (2010)

    Article  ADS  Google Scholar 

  18. C T Gonzalez-H, R Franco and J Silva-Valencia Eur. J. Phys. 31 681 (2010)

    Article  MATH  Google Scholar 

  19. I Garate and I Affleck Phys. Rev. B 81 144419 (2010)

    Article  ADS  Google Scholar 

  20. V N Kotov, M Elhajal, M E Zhitomirsky and F Mila Phys. Rev. B 72 014421 (2005)

    Article  ADS  Google Scholar 

  21. M R Soltani, S Mahdavifar, A Akbari and A A Masoudi J. Supercond. Nov. Magn. 23 1369 (2010)

    Article  Google Scholar 

  22. R Jafari, M Kargarian, A Langari and M Siahatgar Phys. Rev. B 78 214414 (2008)

    Article  ADS  Google Scholar 

  23. S Mahdavifar, M R Soltani and A A Masoudi Eur. Phys. J. B 62 215 (2008)

    Article  ADS  Google Scholar 

  24. X Y Zhao and X W Lei Indian J. Phys. 86 137 (2012)

    Article  ADS  Google Scholar 

  25. L Ayache, L Bahmad, A Benyoussef and H Ez-Zahraouy Indian J. Phys. 86 31 (2012)

    Article  ADS  Google Scholar 

  26. T Klumper et al. J. Phys. A 24 L955 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  27. T Klumper et al. Z. Phys. B 87 281 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  28. T Klumper et al. Europhys. Lett. 24 293 (1993)

    Article  ADS  Google Scholar 

  29. M Fannes, B Nachtergaele and R F Werner Europhys. Lett. 10 633(1989)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. R. Soltani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Soltani, M.R., Vahedi, J., Sadremomtaz, A.R. et al. Ising model with staggered Dzyaloshinsky–Moriya interaction. Indian J Phys 86, 1073–1077 (2012). https://doi.org/10.1007/s12648-012-0166-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-012-0166-3

Keywords

PACS Nos.

Navigation