Journal of Materials Science

, Volume 44, Issue 19, pp 5235–5248 | Cite as

Hypertoroidal moment in complex dipolar structures

  • S. Prosandeev
  • L. Bellaiche


The very recent use of atomistic simulations to investigate low-dimensional ferroelectrics and ferromagnets has led to the discovery of a new order parameter that is associated with the formation and evolution of many complex dipolar structures (such as onion and flower states or double vortices). Such new order parameter has been named as the hypertoidal moment, involves a double cross product of the local dipoles with the vectors locating their positions, and provides a measure of subtle microscopic features. Here, the recent studies devoted to the discovery of such order parameter and how to control it in zero-dimensional systems are reviewed. We also give additional information, such as the symmetry, conjugate field and associated susceptibility of the electric and magnetic hypertoidal moments. A discussion about the existence of the hypertoidal moment and its evolution as a function of temperature and applied field, as well as its possible multi-values, is also provided for complex states (such as nanostripes and nanobubbles) in periodic dipolar systems.


Vortex Monte Carlo Vortex State Ferroelectric Thin Film Local Dipole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We hope that this article will be of benefits to scientists interested in complex dipolar states, and acknowledge support from ONR grants N00014-04-1-0413 and N00014-08-1-0915, NSF grants DMR-0701558, DMR-0404335, and DMR-0080054 (C-SPIN) and DOE grant DE-FG02-05ER46188. Some computations were made possible thanks to the MRI Grants 0421099 and 0722625 from NSF. S.P. also appreciates the support of grants RFBR-07-02-00099&08-02-92006NNS.


  1. 1.
    Dubovik VM, Tugushev VV (1990) Phys Rep 187:145CrossRefADSGoogle Scholar
  2. 2.
    Naumov I, Bellaiche L, Fu H (2004) Nature 432:737PubMedCrossRefADSGoogle Scholar
  3. 3.
    Bader SD (2006) Rev Mod Phys 78:1CrossRefADSGoogle Scholar
  4. 4.
    Prosandeev S, Bellaiche L (2008) Phys Rev B 77:060101 (R)Google Scholar
  5. 5.
    Prosandeev S, Bellaiche L (2008) Phys Rev Lett 101:097203PubMedCrossRefADSGoogle Scholar
  6. 6.
    Dubovik VM, Cheshkov AA (1975) Sov J Part Nucl 5:318Google Scholar
  7. 7.
    Ascher E (1975) In: Freeman A, Schmidt H (eds) Magnetoelectric interaction phenomena in crystals. New YorkGoogle Scholar
  8. 8.
    Malashevich A, Vanderbilt D (2008) Phys Rev Lett 101:037210PubMedCrossRefADSGoogle Scholar
  9. 9.
    Dzyaloshinskii I (1958) J Phys Chem Solids 4:241CrossRefADSGoogle Scholar
  10. 10.
    Moriya T (1960) Phys Rev 120:91CrossRefADSGoogle Scholar
  11. 11.
    Dubovik VM, Martsenyuk MA, Saha B (2000) Phys Rev E 61:7087CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Callen HB, Welton TA (1951) Phys Rev 83:34MATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Resta R (1994) Rev Mod Phys 66:899CrossRefADSGoogle Scholar
  14. 14.
    Chien CL, Zhu FQ, Zhu J-G (2007) Phys Today 92:40CrossRefGoogle Scholar
  15. 15.
    Prosandeev S, Ponomareva I, Kornev I, Bellaiche L (2008) Phys Rev Lett 100:047201PubMedCrossRefADSGoogle Scholar
  16. 16.
    Hoffmann H, Steinbauera F (2002) J Appl Phys 92:5463CrossRefADSGoogle Scholar
  17. 17.
    Antropov VP, Tretyakov SV, Harmon BN (1997) J Appl Phys 81:3961CrossRefADSGoogle Scholar
  18. 18.
    Vedmedenko EY, Ghazali A, Levy J-CS (1998) Surf Sci 391:402Google Scholar
  19. 19.
    Cowburn RP, Koltsov DK, Adeyeye AO, Welland ME, Tricker DM (1999) Phys Rev Lett 83:1042CrossRefADSGoogle Scholar
  20. 20.
    Shinjo T, Okuno T, Hassdorf R, Shigeto K, Ono T (2000) Science 289:930PubMedCrossRefADSGoogle Scholar
  21. 21.
    Zhong W, Vanderbilt D, Rabe KM (1995) Phys Rev Lett 73:1861CrossRefADSGoogle Scholar
  22. 22.
    Zhong W, Vanderbilt D, Rabe KM (1994) Phys Rev B 52:6301CrossRefADSGoogle Scholar
  23. 23.
    Bellaiche L, Garcìa A, Vanderbilt D (2002) Phys Rev Lett 84:5427CrossRefADSGoogle Scholar
  24. 24.
    Bellaiche L, Garcìa A, Vanderbilt D (2002) Ferroelectrics 266:41CrossRefGoogle Scholar
  25. 25.
    Naumov II, Fu H (2005) cond-mat/0505497Google Scholar
  26. 26.
    Ponomareva I, Naumov II, Kornev I, Huaxiang F, Bellaiche L (2005) Phys Rev B 72:140102(R)ADSGoogle Scholar
  27. 27.
    Ponomareva I, Naumov II, Bellaiche L (2005) Phys Rev B 72:214118 (2005)CrossRefADSGoogle Scholar
  28. 28.
    Fu H, Bellaiche L (2003) Phys Rev Lett 91:257601PubMedCrossRefADSGoogle Scholar
  29. 29.
    Almahmoud E, Navtsenya Y, Kornev I, Fu H, Bellaiche L (2004) Phys Rev B 70:220102(R)CrossRefADSGoogle Scholar
  30. 30.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) J Chem 21:1087ADSGoogle Scholar
  31. 31.
    Alder BJ, Wainwright TE (1959) J Chem Phys 31:459CrossRefADSMathSciNetGoogle Scholar
  32. 32.
    Rothman J, Kläui M, Lopez-Diaz L, Vaz CAF, Bleloch A, Bland JAC, Cui Z, Speaks R (2001) Phys Rev Lett 86:1098PubMedCrossRefADSGoogle Scholar
  33. 33.
    Zhu FQ, Chern GW, Tchernyshyov O, Zhu XC, Zhu JG, Chien CL (2006) Phys Rev Lett 96:027205PubMedCrossRefADSGoogle Scholar
  34. 34.
    Huber M, Zweck J, Weiss D (2008) Phys Rev B 77:054407CrossRefADSGoogle Scholar
  35. 35.
    Arrott AS (2003) J Magn Magn Mater 258–259:25CrossRefGoogle Scholar
  36. 36.
    Buchanan KS, Roy PE, Fradin FY, Guslienko KYu, Grimsditch M, Bader SD, Novosad V (2006) J Appl Phys 99:08C707CrossRefGoogle Scholar
  37. 37.
    Okuno T, Mibu K, Shinjo T (2004) J Appl Phys 95:3612CrossRefADSGoogle Scholar
  38. 38.
    Giesen F, Podbielski J, Botters B, Grundler D (2007) Phys Rev B 75:184428CrossRefADSGoogle Scholar
  39. 39.
    Hubert A, Schafer R (1998) Magnetic domains: the analysis of magnetic microstructures. Springer, BerlinGoogle Scholar
  40. 40.
    Schabes ME, Bertram HN (1988) J Appl Phys 64:1347CrossRefADSGoogle Scholar
  41. 41.
    Prosandeev S, Bellaiche L (2007) Phys Rev B 75:094102CrossRefADSGoogle Scholar
  42. 42.
    Prosandeev S, Kornev I, Bellaiche L (2007) Phys Rev B 76:012101CrossRefADSGoogle Scholar
  43. 43.
    Lai B-K, Ponomareva I, Naumov V, Kornev I, Huaxiang Fu, Bellaiche L, Salamo GJ (2006) Phys Rev Lett 96:137602PubMedCrossRefADSGoogle Scholar
  44. 44.
    Kornev I, Fu H, Bellaiche L (2004) Phys Rev Lett 93:196104PubMedCrossRefADSGoogle Scholar
  45. 45.
    Streiffer SK, Eastman JA, Fong DD, Thompson C, Munkholm A, Ramana Murty MV, Auciello O, Bai GR, Stephenson GB (2002) Phys Rev Lett 89:067601PubMedCrossRefADSGoogle Scholar
  46. 46.
    Landau L, Lifshitz E (1935) Phys Z Sowjetunion 8:153MATHGoogle Scholar
  47. 47.
    King-Smith RD, Vanderbilt D (1993) Phys Rev B 47:1651Google Scholar
  48. 48.
    Ederer C, Spaldin NA (2007) Phys Rev B 76:214404CrossRefADSGoogle Scholar
  49. 49.
    Vanderbilt D, King-Smith RD (1993) Phys Rev B 48:4442CrossRefADSGoogle Scholar
  50. 50.
    Resta R (1994) Rev Mod Phys 66:899CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of ArkansasFayettevilleUSA
  2. 2.Southern Federal UniversityRostov na DonuRussia

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