Dependence of Soft Phonon Spectra on Flexoelectric Coupling in Ferroelectrics

Authors

  • A. N. Morozovska Institute of Physics, Nat. Acad. Sci. of Ukraine, Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics
  • C. M. Scherbakov Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics
  • M. D. Glinchuk I.M. Frantsevich Institute for Problems of Materials Science, Nat. Acad. Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe63.2.168

Keywords:

Landau–Ginzburg–Devonshire theory, flexoelectric coupling, soft phonon modes

Abstract

Analytical expressions describing the frequency dispersion of the soft transverse acoustic (TA)
and optic (TO) phonon modes in uniaxial ferroelectrics, as well as their dependence on the
flexoelectric coupling constant f, have been analyzed in the framework of the Landau–Ginzburg–
Devonshire theory. A critical behavior of the TA mode with respect to the f magnitude is
revealed.

References

<ol><li>M.D. Glinchuk, A.V. Ragulya, V.A. Stephanovich. Nano-ferroics. Springer Series in Materials Science (Springer, 2013), p. 378 [DOI: 10.1007/978-94-007-5992-3].
<a href="https://doi.org/10.1007/978-94-007-5992-3">https://doi.org/10.1007/978-94-007-5992-3</a>
</li>
<li>V.S. Mashkevich, K.B. Tolpygo. The interaction of vibrations of nonpolar crystals with electric fields. Zh. Eksp. Teor. Fiz. 31, 520 (1957) (in Russian).
</li>
<li>A.K. Tagantsev. Piezoelectricity and flexoelectricity in crystalline dielectrics. Phys. Rev. B 34, 5883 (1986)
<a href="https://doi.org/10.1103/PhysRevB.34.5883">https://doi.org/10.1103/PhysRevB.34.5883</a>
</li>
<li>P. Zubko, G. Catalan, A.K. Tagantsev. Flexoelectric effect in solids. Annu. Rev. Mater. Res. 43, 387 (2013).
<a href="https://doi.org/10.1146/annurev-matsci-071312-121634">https://doi.org/10.1146/annurev-matsci-071312-121634</a>
</li>
<li>P.V. Yudin, A.K. Tagantsev. Fundamentals of flexoelectricity in solids. Nanotechnology 24, 432001 (2013).
<a href="https://doi.org/10.1088/0957-4484/24/43/432001">https://doi.org/10.1088/0957-4484/24/43/432001</a>
</li>
<li>S.V. Kalinin, A.N. Morozovska. Multiferroics: Focusing the light on flexoelectricity (Comment). Nat. Nanotechnol. 10, 916 (2015).
<a href="https://doi.org/10.1038/nnano.2015.213">https://doi.org/10.1038/nnano.2015.213</a>
</li>
<li>A. Kvasov, A.K. Tagantsev. Dynamic flexoelectric effect in perovskites from first-principles calculations. Phys. Rev. B 92, 054104 (2015).
<a href="https://doi.org/10.1103/PhysRevB.92.054104">https://doi.org/10.1103/PhysRevB.92.054104</a>
</li>
<li>A.K. Tagantsev, L. Eric Cross, J. Fousek. Domains in Ferroic Crystals and Thin Films (Springer, 2010).
<a href="https://doi.org/10.1007/978-1-4419-1417-0">https://doi.org/10.1007/978-1-4419-1417-0</a>
</li>
<li>G. Catalan, L.J. Sinnamon, J.M. Gregg. The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films. J. Phys. Condens. Matter 16, 2253 (2004).
<a href="https://doi.org/10.1088/0953-8984/16/13/006">https://doi.org/10.1088/0953-8984/16/13/006</a>
</li>
<li> M.S. Majdoub, R. Maranganti, P. Sharma. Understanding the origins of the intrinsic dead layer effect in nanocapacitors. Phys. Rev. B 79, 115412 (2009).
<a href="https://doi.org/10.1103/PhysRevB.79.115412">https://doi.org/10.1103/PhysRevB.79.115412</a>
</li>
<li> M.S. Majdoub, P. Sharma, T. Cagin. Enhanced size-dependent piezoelectricity and elasticity in nanostructures 172 ISSN 2071-0186. Ukr. J. Phys. 2018. Vol. 63, No. 2Dependence of Soft Phonon Spectra due to the flexoelectric effect. Phys. Rev. B 77, 125424 (2008).
</li>
<li> R. Maranganti, P. Sharma. Atomistic determination of flexoelectric properties of crystalline dielectrics. Phys. Rev. B 80, 054109 (2009).
<a href="https://doi.org/10.1103/PhysRevB.80.054109">https://doi.org/10.1103/PhysRevB.80.054109</a>
</li>
<li> G. Catalan, A. Lubk, A.H.G. Vlooswijk, E. Snoeck, C. Magen, A. Janssens, G. Rispens, G. Rijnders, D.H.A. Blank, B. Noheda. Flexoelectric rotation of polarization in ferro-electric thin films. Nat. Mater. 10, 963 (2011).
<a href="https://doi.org/10.1038/nmat3141">https://doi.org/10.1038/nmat3141</a>
</li>
<li> W. Cochran, Crystal stability and the theory of ferroelectricity. Phys. Rev. Lett. 3, 412 (1959).
<a href="https://doi.org/10.1103/PhysRevLett.3.412">https://doi.org/10.1103/PhysRevLett.3.412</a>
</li>
<li> G. Shirane, J.D. Axe, J. Harada, J.P. Remeika. Soft ferro-electric modes in lead titanate. Phys. Rev. B 2, 155 (1970).
<a href="https://doi.org/10.1103/PhysRevB.2.155">https://doi.org/10.1103/PhysRevB.2.155</a>
</li>
<li> W. Cochran. Dynamical, scattering and dielectric properties of ferroelectric crystals. Adv. Phys. 18, 157 (1969).
<a href="https://doi.org/10.1080/00018736900101297">https://doi.org/10.1080/00018736900101297</a>
</li>
<li> G. Shirane, Y. Yamada. Lattice-dynamical study of the 110 K phase transition in SrTiO3. Phys. Rev. 177, 858 (1969).
<a href="https://doi.org/10.1103/PhysRev.177.858">https://doi.org/10.1103/PhysRev.177.858</a>
</li>
<li> R. Currat, H. Buhay, C.H. Perry, A.M. Quittet. Inelastic neutron scattering study of anharmonic interactions in orthorhombic KNbO3. Phys. Rev. B 40, 10741 (1989).
<a href="https://doi.org/10.1103/PhysRevB.40.10741">https://doi.org/10.1103/PhysRevB.40.10741</a>
</li>
<li> I. Etxebarria, M. Quilichini, J.M. Perez-Mato, P. Boutrouille, F.J. Zuniga, T. Breczewski. Inelastic neutron scattering investigation of external modes in incommensurate and commensurate A2BX4 materials. J. Phys. Condens. Matter 4, 8551 (1992).
<a href="https://doi.org/10.1088/0953-8984/4/44/016">https://doi.org/10.1088/0953-8984/4/44/016</a>
</li>
<li> J. Hlinka, M. Quilichini, R. Currat, J.F. Legrand. Dynamical properties of the normal phase of betaine calcium chloride dihydrate. I. Experimental results. J. Phys. Condens. Matter 8, 8207 (1996).
<a href="https://doi.org/10.1088/0953-8984/8/43/016">https://doi.org/10.1088/0953-8984/8/43/016</a>
</li>
<li> J. Hlinka, S. Kamba, J. Petzelt, J. Kulda, C.A. Randall, S.J. Zhang. Origin of the "Waterfall" effect in phonon dispersion of relaxor perovskites. Phys. Rev. Lett. 91, 107602 (2003).
<a href="https://doi.org/10.1103/PhysRevLett.91.107602">https://doi.org/10.1103/PhysRevLett.91.107602</a>
</li>
<li> V. Goian, S. Kamba, O. Pacherova, J. Drahokoupil, L. Palatinus, M. Dusek, J. Rohl?cek, M. Savinov, F. Laufek, W. Schranz, A. Fuith, M. Kachl?k, K. Maca, A. Shkabko, L. Sagarna, A. Weidenkaff, A.A. Belik. Antiferrodistortive phase transition in EuTiO3. Phys. Rev. B 86, 054112 (2012).
<a href="https://doi.org/10.1103/PhysRevB.86.054112">https://doi.org/10.1103/PhysRevB.86.054112</a>
</li>
<li> Jong-Woo Kim, P. Thompson, S. Brown, P.S. Normile, J.A. Schlueter, A. Shkabko, A. Weidenkaff, P.J. Ryan. Emergent superstructural dynamic order due to competing antiferroelectric and antiferrodistortive instabilities in bulk EuTiO3. Phys. Rev. Lett. 110, 027201 (2013).
<a href="https://doi.org/10.1103/PhysRevLett.110.027201">https://doi.org/10.1103/PhysRevLett.110.027201</a>
</li>
<li> R.G. Burkovsky, A.K. Tagantsev, K. Vaideeswaran, N. Setter, S.B. Vakhrushev, A.V. Filimonov, A. Shaganov et al. Lattice dynamics and antiferroelectricity in PbZrO3 tested by x-ray and Brillouin light scattering. Phys. Rev. B 90, 144301 (2014).
<a href="https://doi.org/10.1103/PhysRevB.90.144301">https://doi.org/10.1103/PhysRevB.90.144301</a>
</li>
<li> J. Hlinka, I. Gregora, V. Vorl?cek. Complete spectrum of long-wavelength phonon modes in Sn2P2S6 by Raman scattering. Phys. Rev. B 65, 064308 (2002).
<a href="https://doi.org/10.1103/PhysRevB.65.064308">https://doi.org/10.1103/PhysRevB.65.064308</a>
</li>
<li> A. Kohutych, R. Yevych, S. Perechinskii, V. Samulionis, J. Banys, Yu. Vysochanskii. Sound behavior near the Lifshitz point in proper ferroelectrics. Phys. Rev. B 82, 054101 (2010).
<a href="https://doi.org/10.1103/PhysRevB.82.054101">https://doi.org/10.1103/PhysRevB.82.054101</a>
</li>
<li> A. Kohutych, R. Yevych, S. Perechinskii, Y. Vysochanskii. Acoustic attenuation in ferroelectric Sn2P2S6 crystals. Open Phys. 8, 905 (2010).
<a href="https://doi.org/10.2478/s11534-010-0016-x">https://doi.org/10.2478/s11534-010-0016-x</a>
</li>
<li> Yu.M. Vysochanskii, A.A. Kohutych, A.V. Kityk, A.V. Zadorozhna, M.M. Khoma, A.A. Grabar. Tricritical behavior of Sn2P2S6 ferroelectrics at hydrostatic pressure. Ferro-electrics 399, 83 (2010).
<a href="https://doi.org/10.1080/00150193.2010.489866">https://doi.org/10.1080/00150193.2010.489866</a>
</li>
<li> R.M. Yevych, Yu.M. Vysochanskii, M.M. Khoma, S.I. Perechinskii. Lattice instability at phase transitions near the Lifshitz point in proper monoclinic ferroelectrics. J. Phys. Condens. Matter 18, 4047 (2006).
<a href="https://doi.org/10.1088/0953-8984/18/16/011">https://doi.org/10.1088/0953-8984/18/16/011</a>
</li>
<li> A.N. Morozovska, Yu.M. Vysochanskii, O.V. Varenyk, M.V. Silibin, S.V. Kalinin, E.A. Eliseev. Flexocoupling impact on the generalized susceptibility and soft phonon modes in the ordered phase of ferroics. Phys. Rev. B 92, 094308 (2015).
<a href="https://doi.org/10.1103/PhysRevB.92.094308">https://doi.org/10.1103/PhysRevB.92.094308</a>
</li>
<li> A.N. Morozovska, E.A. Eliseev, Ch.M. Scherbakov, Yu.M. Vysochanskii. The influence of elastic strain gradient on the upper limit of flexocoupling strength, spatially-modulated phases and soft phonon dispersion in ferroics. Phys. Rev. B 94, 174112 (2016).
<a href="https://doi.org/10.1103/PhysRevB.94.174112">https://doi.org/10.1103/PhysRevB.94.174112</a>
</li>
<li> A.N. Morozovska, M.D. Glinchuk, E.A. Eliseev, Yu.M. Vysochanskii. Flexocoupling-induced soft acoustic mode and the spatially modulated phases in ferroelectrics. Phys. Rev. B 96, 094111 (2017).
<a href="https://doi.org/10.1103/PhysRevB.96.094111">https://doi.org/10.1103/PhysRevB.96.094111</a>
</li>
<li> L.D. Landau, E.M. Lifshitz. Theory of Elasticity (Butterworth-Heinemann, 1998).
</li>
<li> G.A. Smolenskii, V.A. Bokov, V.A. Isupov, N.N Krainik, R.E. Pasynkov, A.I. Sokolov. Ferroelectrics and Related Materials (Gordon and Breach, 1984).</li></ol>
UJP 2018 V63 #2

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Published

2018-03-02

How to Cite

Morozovska, A. N., Scherbakov, C. M., & Glinchuk, M. D. (2018). Dependence of Soft Phonon Spectra on Flexoelectric Coupling in Ferroelectrics. Ukrainian Journal of Physics, 63(2), 168. https://doi.org/10.15407/ujpe63.2.168

Issue

Vol. 63 No. 2 (2018)

Section

Physics of magnetic phenomena and physics of ferroics

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