Abstract
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.
Similar content being viewed by others
References
Y. Imry, D.J. Scalapino, Phase transitions in systems with coupled order parameters. Phys. Rev. B 10, 2900 (1974). https://doi.org/10.1103/PhysRevB.10.290
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)
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). https://doi.org/10.1098/rsta.2015.0304
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). https://doi.org/10.1103/PhysRevLett.114.177205
A. Dixit, G. Lawes, A.B. Harris, Magnetic structure and magnetoelectric coupling in bulk and thin film FeVO4. Phys. Rev. B 82, 024430 (2010). https://doi.org/10.1103/PhysRevB.82.024430
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)
G.R. Boyd, P. Kumar, S.R. Phillpot, Multiferroic thermodynamic. arXiv:1101.5403v1 [cond-Mat. Mtrl-sci]
A.B. Harris, Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics. Phys. Rev. B 76, 054447 (2007). https://doi.org/10.1103/PhysRevB.76.054447
G. Howczack, J. Spalek, Ferroelectric-ferromagnetic correlations in BiMnO3 perovskite within Landau theory: comparison with experiment. Eur Phys. J. B 78, 417–428 (2010). https://doi.org/10.1140/EPJB/E2010-10583-0
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). https://doi.org/10.1103/PhysRevB.93.104404
L. Seixas, A.S. Rodin, A. Carvalho, A.H. Castro Neto, Multiferroic two-dimensional materials. Phys. Rev. Lett. 116, 206803 (2016). https://doi.org/10.1103/PhysRevLett.116.206803
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). https://doi.org/10.1103/PhysRevLett.95.087206
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). https://doi.org/10.1016/j.jmmm.2020.166661
K.F. Wang, J.-M. Liu, Z.F. Ren, Multiferroicity: the coupling between magnetic and orders. Adv. Phys. 58(4), 321–448 (2009). https://doi.org/10.1080/00018730902920554
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)
J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, Epiaxial BiFeO3 multiferroic thin film heterostructes. Science (2003). https://doi.org/10.1126/science.1080615
T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Amira, Y. Tokura, Magnetic control of ferroelectric polarization. Nature (2003). https://doi.org/10.1038/nature02018
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). https://doi.org/10.1088/1751-8113/44/28/285002
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). https://doi.org/10.1016/J.Jmmm.2018.06.001
A.M. Alrub, Study of switching phenomenon of weak magnetoelectric coupling in proper multiferroics using Landau theory. J. Appl. Phys. 126, 154102 (2019). https://doi.org/10.1063/1.5110921
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). https://doi.org/10.1088/1674-1056/24/3/037510
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). https://doi.org/10.1016/j.actamat.2014.05.038
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). https://doi.org/10.1002/adma.200600071
H. Mo, C.S. Nelson, L.N. Bezmaternykh, V.T. Temerov, Magnetic structure of the field-induced multiferroicGdFe3(BO3)4. Phys. Rev. B (2008). https://doi.org/10.1103/physrevb.78.214407
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). https://doi.org/10.1063/1.3628464
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). https://doi.org/10.1038/nmat1886
Y. Imry, On the statistical mechanics of coupled order parameters. J. Phys. C Sol. State Phys. 8, 567 (1975). https://doi.org/10.1088/0022-3719/8/5/005
A. Dixit, G. Lawes, Development of electrical polarization at an antiferromagnetic transition in FeVO4. J. Phys. Condens. Matter 21, 456003 (2009). https://doi.org/10.1088/0953-8984/21/45/456003
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). https://doi.org/10.1016/J.Solidstatsciences.2015.05.06
A. Kumarasiri, E. Abdelhamid, A. Dixit, G. Lawes, Effect of transition metal doping on multiferroic ordering in FeVO4. Phys. Rev. B 91, 014420 (2015). https://doi.org/10.1103/PhysRevB.91.014420
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). https://doi.org/10.1088/0953-8984/25/25/256002
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). https://doi.org/10.1088/0953-8084/17/37/022
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). https://doi.org/10.1088/0031-8949/83/04/045701
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). https://doi.org/10.1038/srep06506
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). https://doi.org/10.1134/51063776114020099
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). https://doi.org/10.1088/13672630/15/12/12300
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1140/epjp/s13360-021-01178-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-021-01178-5