Abstract
The modified two-sublattice pseudospin lattice coupled mode model Hamiltonian is extended by adding third- and fourth-order phonon anharmonic interactions, extra spin–lattice interactions, direct spin–spin interaction and an applied electric field terms considered for the study of deuterated Rochelle salt crystal. The double-time thermal-dependent Green function, Dyson equation and symmetric decoupling scheme have been used to derive the expressions for energy shift, line width, ferroelectric soft mode frequency, dielectric constant, dielectric tangent loss and spontaneous polarization. Model values of various physical parameters are fitted in the obtained expressions; the thermal variations of ferroelectric soft mode frequency, dielectric constant, loss tangent and spontaneous polarization have been calculated for deuterated Rochelle salt crystal. Theoretical results with model values compare well with experimental data reported by others for deuterated Rochelle salt. Our expressions contain all possible interactions as compared to the earlier authors.
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References
W.P. Mason, Theory of the ferroelectric effect and clamped dielectric constant of Rochelle salt. Phys. Rev. 72(9), 854 (1947)
A.F. Devonshire, Theory of Rochelle salt. Philos. Mag. 2(20), 1027–1039 (1957)
T. Mitsui, Theory of the ferroelectric effect in Rochelle salt. Phys. Rev. 111(5), 1259 (1958)
F. Jona, G. Shirane, Ferroelectrics Crystals (Pergamon Press, New York, 1962)
R. Blinc, B. Zeks, Dynamics of order-disorder-type ferroelectrics and anti-ferroelectrics. Adv. Phys. 21(93), 693–757 (1972)
R.R. Levitskii, R.O. Sokolovskii, Relaxation dynamics of disordered ising-like models. Condens. Matter Phys. 2(3), 393–400 (1999)
R.R. Levitskii et al., Investigation of Ferroelectric Order-Disorder type Compounds with Asymmetric Double-Well Potential. arXiv:cond-mat/0106351 (2001)
R.R. Levitskii et al., Isotopic effects in partially deuterated piezoelectric crystals of Rochelle salt. Condens. Matter Phys. 7(1), 111–139 (2004)
F. Sandy, R.V. Jones, Dielectric relaxation of Rochelle salt. Phys. Rev. 168(2), 481 (1968)
M. Horioka, R. Abe, Dielectric relaxation of deuterated Rochelle salt. Jpn. J. Appl. Phys. 18(11), 2065 (1979)
B.K. Chaudhuri et al., Study of ferroelectric phase transitions in the Rochelle salt with the pseudo-spin-lattice coupled mode model. J. Phys. Soc. Jpn. 49(2), 608–618 (1980)
S. Kamba, G. Schaack, J. Petzelt, Vibrational spectroscopy and soft-mode behavior in Rochelle salt. Phys. Rev. B 51(21), 14998 (1995)
J. Kobayashi, K. Uchino, T. Asahi, Optical properties of Rochelle salt. Phys. Rev. B 43(7), 5706 (1991)
I.A. Malyshkina, N.D. Gavrilova, Low-frequency dielectric properties of the Rochelle salt and its deuterated analogue. Ferroelectrics 268(1), 41–46 (2002)
I.V. Stasyuk, O.V. Velychko, Theory of Rochelle salt: beyond the Mitsui model. Ferroelectrics 316(1), 51–58 (2005)
Z. Guoxiang et al., Investigation of ferroelectric phase transition of Rochelle salt. Ferroelectrics 366(1), 67–73 (2008)
F. Mo et al., Rochelle salt—a structural reinvestigation with improved tools: I-The high-temperature paraelectric phase at 308K. IUCRJ 2(1), 19–28 (2015)
Y.K. Kim, J.H. Koo, K.S. Lee, Quantized polariton in ferroelectric Rochelle salt. Ferroelectrics 493(1), 79–84 (2016)
R.P. Singh, M. Singh, Self-consistent of calculation of magnetization in oxide superconductors. Phys. Rev. B 46(21), 14069 (1992)
V.I. Yukalov, M.G. Cottam, M.R. Singh, Nonlinear spin dynamics in ferromagnets with electron–nulear coupling. Phys. Rev. B 60(2), 1227 (1999)
T.C. Upadhyay, B. Kandpal, Temperature dependence of microwave loss in Rochelle salt crystal. Indian J. Pure Appl. Phys. 47, 134–140 (2009)
A. Rawat, T.C. Upadhyay, Temperature dependence of soft mode frequency, dielectric constant and loss tangent of deuterated Rochelle salt crystal. Indian J. Pure Appl. Phys. 57, 144–146 (2019)
D.N. Zubarev, Double-time green functions in statistical physics. Sov. Phys. Uspekhi 3(3), 320 (1960)
R.A. Cowley, The lattice dynamics of an anharmonic crystal. Adv. Phys. 12(48), 421–480 (1963)
W. Cochran, Crystal stability and the theory of ferroelectricity. J. Phys. Rev. Lett. 3(9), 412 (1959)
R. Kubo, Statistical-mechanical theory of irreversible processes: I–general theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12(6), 570–586 (1957)
Acknowledgements
The authors are grateful to Prof. S.C. Bhatt for his kind suggestions and valuable discussion in the work and thankful to the Department of Physics, Hemvati Nandan Bahuguna Garhwal University (A Central University), for availing facility and support.
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Khan, M.I., Upadhyay, T.C. Phase transitions in H-bonded deuterated Rochelle salt crystal. Eur. Phys. J. Plus 136, 101 (2021). https://doi.org/10.1140/epjp/s13360-020-01058-4
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DOI: https://doi.org/10.1140/epjp/s13360-020-01058-4