Study of thermodynamic fluctuations of two-dimensional multiferroic systems using the renormalized Gaussian approach


In this paper, we investigate the influence of the thermodynamic fluctuations of order parameters and their coupling on the physical quantities of a 2D-multiferroic system using the renormalized Gaussian approach. Correction to magnetization, polarization, inverse susceptibilities, correlation lengths, specific heat, and critical temperatures are found taking into account order parameters thermodynamic fluctuations and their coupling. The specific heat exhibits two λ-type anomalies; this highlights second-order phase transitions in the system. The results obtained from this approach are in good accordance with the experimental ones found in the literature.

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  1. 1.

    Y. Imry, D.J. Scalapino, Phase transitions in systems with coupled order parameters. Phys. Rev. B 10, 2900 (1974).

    ADS  Article  Google Scholar 

  2. 2.

    G.V. Bezrukov, A.N. Men, V.M. Talanov, Theory of isotructural phase transistions described by two order parameters. Phys. Stat. sol. (a) 116(603), 603–613 (1989)

    ADS  Article  Google Scholar 

  3. 3.

    A. Planes, T. Castán, A. Saxena, Thermodynamics of multicaloric effects of multiferroic materials: application to metamagnetic shape-memory alloys and ferrotoroidics. Philos. Trans. R. Soc. A 374, 20150304 (2016).

    ADS  Article  Google Scholar 

  4. 4.

    C.M. Chang, B.K. Mani, S. Lisenkov, I. Ponomareva, Thermally mediated mechanism to enhance magnetoelectric coupling in multiferroics. Phys. Rev. Lett. 114, 177205 (2015).

    ADS  Article  Google Scholar 

  5. 5.

    A. Dixit, G. Lawes, A.B. Harris, Magnetic structure and magnetoelectric coupling in bulk and thin film FeVO4. Phys. Rev. B 82, 024430 (2010).

    ADS  Article  Google Scholar 

  6. 6.

    A.A. Belik, E. Takayama-Muramachi, Magnetic properties of BiMnO3 studies with DC and AC magnetization and specific heat. Inorg. Chem. 45, 10224–10229 (2006)

    Article  Google Scholar 

  7. 7.

    G.R. Boyd, P. Kumar, S.R. Phillpot, Multiferroic thermodynamic. arXiv:1101.5403v1 [cond-Mat. Mtrl-sci]

  8. 8.

    A.B. Harris, Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics. Phys. Rev. B 76, 054447 (2007).

    ADS  Article  Google Scholar 

  9. 9.

    G. Howczack, J. Spalek, Ferroelectric-ferromagnetic correlations in BiMnO3 perovskite within Landau theory: comparison with experiment. Eur Phys. J. B 78, 417–428 (2010).

    ADS  Article  Google Scholar 

  10. 10.

    J.K. Harada, L. Balhorn, J. Hazi, M.C. Kemei, R. Seshadri, Magnetodielectric coupling in the ilmenites MTiO3 (M = Co, Ni). Phys. Rev. B 93, 104404 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    L. Seixas, A.S. Rodin, A. Carvalho, A.H. Castro Neto, Multiferroic two-dimensional materials. Phys. Rev. Lett. 116, 206803 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    M. Kenzelmann, A.B. Harris, S. Jonas, C. Broholm, J. Schefer, S.B. Kim, C.L. Zhang, S.-W. Cheong, O.P. Vajk, J.W. Lynn, Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3. Phys. Rev. Lett. 95, 087206 (2005).

    ADS  Article  Google Scholar 

  13. 13.

    G.E. Tongue Magne, R.M. Keumo Tsiaze, A.J. Fotué, L.C. Fai, Theoretical study of two biquadratically order parameters: application to two-dimensional mulferroics. J. JMMM 504, 166661 (2020).

    Article  Google Scholar 

  14. 14.

    K.F. Wang, J.-M. Liu, Z.F. Ren, Multiferroicity: the coupling between magnetic and orders. Adv. Phys. 58(4), 321–448 (2009).

    ADS  Article  Google Scholar 

  15. 15.

    J. Ma, J. Hu, Z. Li, C.W. Nan, Recent progress in multiferroic magnetoelectric composites: from bulk to thin films. Adv. Matter 23, 1062–1087 (2011)

    Article  Google Scholar 

  16. 16.

    J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, Epiaxial BiFeO3 multiferroic thin film heterostructes. Science (2003).

    Article  Google Scholar 

  17. 17.

    T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Amira, Y. Tokura, Magnetic control of ferroelectric polarization. Nature (2003).

    Article  Google Scholar 

  18. 18.

    R.M. Keumo Tsiaze, S.E. Mkam Tchouobiap, J.E. Danga, S. Domngang, M.N. Hounkonnou, Renormalized Gaussian approach to critical fluctuations in the Landau–Ginzburg–Wilson model and finite-size scaling. J Phys. A Math. Theor. 44, 285002 (2011).

    Article  MATH  Google Scholar 

  19. 19.

    R.M. Keumo Tsiaze, A.V. Wirngo, S.E. Nkam Tchouobiap, E. Baloîtcha, M.N. Hounkonnou, Renormalized Gaussian, approach to finite size effects and exchange interactions: application to localized ferromagnets and amorphous magnets. JMMM 465, 611–620 (2018).

    ADS  Article  Google Scholar 

  20. 20.

    A.M. Alrub, Study of switching phenomenon of weak magnetoelectric coupling in proper multiferroics using Landau theory. J. Appl. Phys. 126, 154102 (2019).

    ADS  Article  Google Scholar 

  21. 21.

    Y. Liu, L.-J. Zhai, H.-Y. Wang, Theoretical study of mutual control mechanism between magnetization and polarization in multiferroic materials. Chin. Phys. B 24, 037510 (2015).

    ADS  Article  Google Scholar 

  22. 22.

    J.-P. Zhou, Y.-X. Zhang, Q. Liu, P. Liu, Magnetoelectric effects on ferromagnetic and ferroelectric phase transitions in multiferroic materials. Acta Mater. 76, 355–370 (2014).

    ADS  Article  Google Scholar 

  23. 23.

    M.A. Subramanian, T. He, J. Chen, N.S. Rogado, T.G. Calvarese, A.W. Sleight, Giant room—temperature magnetodielectric response in the electronic ferroelectric LuFe2O4. Adv. Mater. 18, 1737–1739 (2006).

    Article  Google Scholar 

  24. 24.

    H. Mo, C.S. Nelson, L.N. Bezmaternykh, V.T. Temerov, Magnetic structure of the field-induced multiferroicGdFe3(BO3)4. Phys. Rev. B (2008).

    Article  Google Scholar 

  25. 25.

    G. Venkataiah, Y. Shirahata, M. Itoh, T. Taniyama, Manipulation of magnetic coercivity of Fe film in Fe/BaTiO3 heterostructure by electric field. Appl. Phys. Lett. 99, 102506 (2011).

    ADS  Article  Google Scholar 

  26. 26.

    W. Eerenstein, M. Wiora, J.L. Prieto, J.F. Scott, N.D. Mathur, Giant sharp and persistent converse magnetoelectric effects in multiferroic epitaxial heterostructures. Nat. Mater. 6, 348–351 (2007).

    ADS  Article  Google Scholar 

  27. 27.

    Y. Imry, On the statistical mechanics of coupled order parameters. J. Phys. C Sol. State Phys. 8, 567 (1975).

    ADS  Article  Google Scholar 

  28. 28.

    A. Dixit, G. Lawes, Development of electrical polarization at an antiferromagnetic transition in FeVO4. J. Phys. Condens. Matter 21, 456003 (2009).

    ADS  Article  Google Scholar 

  29. 29.

    N. Pavan Kumar, E. Sagar, P.D. Babu, A. Srinivas, M. Manivel Raja, Investigation of tow temperature magnetization, specific heat and magnetocaloric effect in Ho doped TnMnO3 multiferroic system. J. Sol. Stat. Sci. 94, 54–63 (2019).

    ADS  Article  Google Scholar 

  30. 30.

    A. Kumarasiri, E. Abdelhamid, A. Dixit, G. Lawes, Effect of transition metal doping on multiferroic ordering in FeVO4. Phys. Rev. B 91, 014420 (2015).

    ADS  Article  Google Scholar 

  31. 31.

    D.O. Flynn, M.R. Less, G. Balakrishnan, Magnetis susceptibility and heat capacity measurements of single crystal TbMnO3. J. Phys. Condens. Matter 26, 25600 (2014).

    Article  Google Scholar 

  32. 32.

    J.G. Cheng, Y. Sui, X.L. Liu, J.P. Miao, X.Q. Huang, Specific heat of single-crystal PrMnO3. J. Phys. Condens. Matter 17, 5869–5879 (2005).

    ADS  Article  Google Scholar 

  33. 33.

    N. Pavan Kumar, G. Lalitha, P. Venugopal Reddy, Specific heat and magnetization studies of RMnO3 (R = Sm, Eu, Gd, Tb, Dy) multiferroics. Phys. Scr. 83, 045701 (2011).

    ADS  Article  Google Scholar 

  34. 34.

    N. Zhang, S. Dong, Z. Fu, Z. Yan, F. Chang, J. Liu, Phase transition and separation in multiferroic orthorhombic Dy1−xHoxMnO3 (0 ≤ x ≤1). Sci. Rep. 4, 6506 (2014).

    ADS  Article  Google Scholar 

  35. 35.

    S.N. Kallev, R.G. Mitarov, Z.M. Omarov, G.G. Gadzhiev, L.A. Reznichenka, Heat capacity of BiFeO-based multiferroics. J. Exp. Phys. 118(2), 279–283 (2014).

    ADS  Article  Google Scholar 

  36. 36.

    M. Ackermann, D. Brüning, T. Lorenz, P. Becker, Thermodynamic properties of the new multiferroic material (NH4)2[FeCl5(H2O)]. New J. Phys. 15, 123001 (2013).

    ADS  Article  Google Scholar 

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Tongue, M.G.E., Fotue, A.J., Tsiaze, R.M.K. et al. Study of thermodynamic fluctuations of two-dimensional multiferroic systems using the renormalized Gaussian approach. Eur. Phys. J. Plus 136, 199 (2021).

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