Universality of domain growth in antiferromagnets with spin-exchange kinetics

  • Prasenjit Das
  • Tanusri Saha-Dasgupta
  • Sanjay Puri
Regular Article
  • 13 Downloads

Abstract.

We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via the antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: \( L_{\sigma}(t)\sim t^{\alpha}\). The asymptotic growth regime has \(\alpha = 1/2\), though there can be prolonged transients with \(\alpha < 1/2\) for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order parameters. The evolution of these order parameters is modeled by using Model C kinetics. As for the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: \(L_{m}(t)\sim t^{1/2}\) at later times, irrespective of the mean value of the conserved order-parameter (composition) field.

Graphical abstract

Keywords

Flowing Matter: Interfacial phenomena 

References

  1. 1.
    S. Puri, V. Wadhawan (Editors), Kinetics of Phase Transitions (CRC Press, Boca Raton, 2009)Google Scholar
  2. 2.
    S. Dattagupta, S. Puri, Dissipative Phenomena in Condensed Matter: Some Applications (Springer-Verlag, Heidelberg, 2004)Google Scholar
  3. 3.
    A.J. Bray, Adv. Phys. 43, 357 (1994)ADSCrossRefGoogle Scholar
  4. 4.
    M. Plischke, B. Bergersen, Equilibrium Statistical Physics, 3rd edition (World Scientific, Singapore, 2006)Google Scholar
  5. 5.
    M. Kessler, W. Dieterich, A. Majhofer, Phys. Rev. B 67, 134201 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    E.P. Feldman, L.I. Stefanovich, K.V. Gumennyk, J. Stat. Phys. 132, 501 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    K. Kaski, M.C. Yalabik, J.D. Gunton, P.S. Sahni, Phys. Rev. B 28, 5263 (1983)ADSCrossRefGoogle Scholar
  8. 8.
    G.S. Grest, S.A. Safran, P.S. Sahni, J. Appl. Phys. 55, 2432 (1984)ADSCrossRefGoogle Scholar
  9. 9.
    J.W. Cahn, S.M. Allen, Acta Metall. 27, 1085 (1979)CrossRefGoogle Scholar
  10. 10.
    T. Ohta, D. Jasnow, K. Kawasaki, Phys. Rev. Lett. 49, 1223 (1982)ADSCrossRefGoogle Scholar
  11. 11.
    S.E. Nagler, R.F. Shannon jr., C.R. Harkless, M.A. Singh, R.M. Nicklow, Phys. Rev. Lett. 61, 718 (1988)ADSCrossRefGoogle Scholar
  12. 12.
    J. Bohr, D. Broddin, A. Loiseau, Phys. Rev. B 42, 1052 (1990)ADSCrossRefGoogle Scholar
  13. 13.
    R.F. Shannon jr., S.E. Nagler, C.R. Harkless, R.M. Nicklow, Phys. Rev. B 46, 40 (1992)ADSCrossRefGoogle Scholar
  14. 14.
    T. Hashimoto, K. Nishimura, Y. Takeuchi, Phys. Lett. 65, 250 (1978)CrossRefGoogle Scholar
  15. 15.
    S. Katano, M. Iizumi, R.M. Nicklow, H.R. Child, Phys. Rev. B 38, 2659 (1988)ADSCrossRefGoogle Scholar
  16. 16.
    O. Malis, K.F. Ludwig jr., Phys. Rev. B 60, 14675 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    R.F. Shannon jr., C.R. Harkless, S.E. Nagler, Phys. Rev. B 38, 9327 (1988)ADSCrossRefGoogle Scholar
  18. 18.
    R. Paul, S. Puri, H. Rieger, Europhys. Lett. 68, 881 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    R. Paul, S. Puri, H. Rieger, Phys. Rev. E 71, 061109 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    E. Lippiello, A. Mukherjee, S. Puri, M. Zannetti, EPL 90, 46006 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    F. Corberi, E. Lippiello, A. Mukherjee, S. Puri, M. Zannetti, Phys. Rev. E 88, 042129 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    S.B. Rivers, W.N. Unertl, H.H. Hung, K.S. Liang, Phys. Rev. B 52, 012601 (2005)CrossRefGoogle Scholar
  23. 23.
    T. Ohta, Ann. Phys. 158, 31 (1984)ADSCrossRefGoogle Scholar
  24. 24.
    V.I. Gorentsveig, P. Fratzl, J.L. Lebowitz, Phys. Rev. B 55, 2912 (1997)ADSCrossRefGoogle Scholar
  25. 25.
    M.K. Phani, J.L. Lebowitz, Phys. Rev. Lett. 45, 366 (1980)ADSCrossRefGoogle Scholar
  26. 26.
    P.S. Sahni, G. Dee, J.D. Gunton, M. Phani, J.L. Lebowitz, M. Kalos, Phys. Rev. B 24, 410 (1981)ADSCrossRefGoogle Scholar
  27. 27.
    M. Porta, T. Castán, Phys. Rev. B 54, 166 (1996)ADSCrossRefGoogle Scholar
  28. 28.
    C. Frontera, E. Vives, T. Castán, A. Planes, Phys. Rev. B 55, 212 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    V.G. Vaks, Phys. Rep. 391, 157 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Z.-W. Lai, Phys. Rev. B 41, 9239 (1990)ADSCrossRefGoogle Scholar
  31. 31.
    A.M. Somoza, C. Sagui, Phys. Rev. E 53, 5101 (1996)ADSCrossRefGoogle Scholar
  32. 32.
    J. Kockelkoren, H. Chaté, Physica D 168-169, 80 (2002)ADSCrossRefGoogle Scholar
  33. 33.
    K. Gumennyk, L. Stefanovich, E. Feldman, Phys. Status Solidi B 246, 56 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    K. Yaldram, K. Binder, Acta Metall. Mater. 39, 707 (1991)CrossRefGoogle Scholar
  35. 35.
    K. Yaldram, K. Binder, Z. Phys. B 82, 405 (1991)ADSCrossRefGoogle Scholar
  36. 36.
    S. Puri, Phys. Rev. E 55, 1752 (1997)ADSCrossRefGoogle Scholar
  37. 37.
    S. Puri, R. Sharma, Phys. Rev. E 57, 1873 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    D. Le Floc’h, P. Bellon, M. Athenes, Phys. Rev. B 62, 3142 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    J. Ye, P. Bellon, Phys. Rev. B 70, 094104 (2004)ADSCrossRefGoogle Scholar
  40. 40.
    M. Sanati, A. Zunger, J. Phys.: Condens. Matter 19, 086201 (2007)ADSGoogle Scholar
  41. 41.
    D. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 4th edition (Cambridge University Press, 2015). Google Scholar
  42. 42.
    J.F. Marko, G.T. Barkema, Phys. Rev. E 52, 2522 (1995)ADSCrossRefGoogle Scholar
  43. 43.
    G. Porod, in Small-Angle X-Ray Scattering, edited by O. Glatter, O. Kratky (Academic Press, New York, 1982) p. 42Google Scholar
  44. 44.
    Y. Oono, S. Puri, Mod. Phys. Lett. B 2, 861 (1988)ADSCrossRefGoogle Scholar
  45. 45.
    P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)ADSCrossRefGoogle Scholar
  46. 46.
    I. Dasgupta, T. Saha, A. Mookerjee, Phys. Rev. B 51, 3413 (1995)ADSCrossRefGoogle Scholar
  47. 47.
    C. Leroux, A. Loiseau, M.C. Cadeville, F. Ducastelle, Europhys. Lett. 12, 155 (1990)ADSCrossRefGoogle Scholar
  48. 48.
    D.G. Morris, Phys. Status Solidi 32, 145 (1975)ADSCrossRefGoogle Scholar
  49. 49.
    C. Ricolleau, A. Loiseau, F. Ducastelle, Phase Trans. 30, 243 (1991)CrossRefGoogle Scholar
  50. 50.
    C. Leroux, A. Loiseau, M.C. Cadeville, D. Broddin, G. Van Tendeloo, J. Phys.: Condens. Matter 2, 3479 (1990)ADSGoogle Scholar
  51. 51.
    W. Köster, T. Gödeke, Z. Metallkd. 71, 765 (1980)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Prasenjit Das
    • 1
  • Tanusri Saha-Dasgupta
    • 2
  • Sanjay Puri
    • 1
  1. 1.School of Physical SciencesJawaharlal Nehru UniversityNew DelhiIndia
  2. 2.S. N. Bose National Centre for Basic SciencesKolkataIndia

Personalised recommendations