Domain Wall Width in Different Ferroelectrics via Perturbation Route

Affiliation(s)

Department of Electrical Engineering & Computer Science, University of Toledo, Toledo, USA.

Department of Materials Science, Pennsylvania State University, USA.

Department of Materials Science and Engineering, University of Florida, Gainesville, USA.

Dumkal Institute of Engineering and Technology, West Bengal University of Technology, Dumkal, India.

Department of Mathematics, Government College of Engineering & Leather Technology, Kolkata, India.

Department of Electrical Engineering & Computer Science, University of Toledo, Toledo, USA.

Department of Materials Science, Pennsylvania State University, USA.

Department of Materials Science and Engineering, University of Florida, Gainesville, USA.

Dumkal Institute of Engineering and Technology, West Bengal University of Technology, Dumkal, India.

Department of Mathematics, Government College of Engineering & Leather Technology, Kolkata, India.

ABSTRACT

The domains are of fundamental interest for engineering a ferroelectric material. The domain wall and its width control the ferroelectric behavior to a great extent. The stability of polarization in the context of Landau-Ginzburg free energy functional has been worked out in a previous work by a perturbation approach, where two limits of domain wall width were estimated within the stability zone and they were also found to correspond well with the data on lithium niobate and lithium tantalate. In the present work, it is shown that this model is valid for a wide range of ferroelectric materials and also for a given ferroelectric, such as lithium niobate with different levels of impurities, which are known to affect the domain wall width.

The domains are of fundamental interest for engineering a ferroelectric material. The domain wall and its width control the ferroelectric behavior to a great extent. The stability of polarization in the context of Landau-Ginzburg free energy functional has been worked out in a previous work by a perturbation approach, where two limits of domain wall width were estimated within the stability zone and they were also found to correspond well with the data on lithium niobate and lithium tantalate. In the present work, it is shown that this model is valid for a wide range of ferroelectric materials and also for a given ferroelectric, such as lithium niobate with different levels of impurities, which are known to affect the domain wall width.

Cite this paper

A. Bandyopadhyay, A. Sengupta, K. Choudhary, A. Bandyopadhyay and P. Ray, "Domain Wall Width in Different Ferroelectrics via Perturbation Route,"*World Journal of Condensed Matter Physics*, Vol. 2 No. 2, 2012, pp. 91-95. doi: 10.4236/wjcmp.2012.22016.

A. Bandyopadhyay, A. Sengupta, K. Choudhary, A. Bandyopadhyay and P. Ray, "Domain Wall Width in Different Ferroelectrics via Perturbation Route,"

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[20] A. K. Bandyopadhyay, P. C. Ray and V. Gopalan, “Solitons and Critical Breakup Fields in Lithium Niobate Type Uniaxial Ferroelectrics,” European Physical Journal B, Vol. 65, No. 4, 2008, pp. 525-531. doi:10.1140/epjb/e2008-00356-9

[21] A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc and A. R. McGurn, “Multiple-Time-Scale Analysis of Nonlinear Modes in Ferroelectric LiNbO_{3},” Physical Review B, Vol. 81, No. 6, 2010, pp. 064104-064114.
doi:10.1103/PhysRevB.81.064104

[22] A. K. Bandyopadhyay, P. C. Ray and V. Gopalan, “An Approach to the Klein-Gordon Equation for a Dynamic Study in Ferroelectric Materials,” Journal of Physics: Condensed Matter, Vol. 18, No. 16, 2006, pp. 4093-4100. doi:10.1088/0953-8984/18/16/016

[23] P. Giri, S. Ghosh, K. Choudhary, Md. Alam, A. K. Bandyopadhyay and P. C. Ray, “Importance of Damping on Nanoswitching in LiNb O_{3}-Type Ferroelectrics,” Physica Scripta, Vol. 83, No. 1, 2011, p. 015702.
doi:10.1088/0031-8949/83/01/015702.

[24] A. Biswas, K. Choudhary, A. K. Bandyopadhyay, A. K. Bhattacharjee and D. Mandal, “Quantum Pining-Transition Due to Charge Defect in Ferroelectrics,” Journal of Applied Physics, Vol. 110, No. 2, 2011, pp. 024104-024111. doi:10.1063/1.3607298

[1] H. Fu and R. E. Cohen, “Polarization Rotation Mechanism for Ultrahigh Electromechanical Response in Single-Crystal Piezoelectrics,” Nature, Vol. 403, No. 6767, 2000, pp. 281-283. doi:10.1038/35002022

[2] S. Kim, V. Gopalan and A. Gruverman, “Coercive Fields in Ferroelectrics: A Case Study in Lithium Niobate and Lithium Tantalite,” Applied Physics Letters, Vol. 80, No. 15, 2002, pp. 2740-2742. doi:10.1063/1.1470247

[3] D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena and P. J. Swart, “Phenomenological Theory of a Single Domain Wall in Uniaxial Trigonal Ferroelectrics: Lithium Niobate and Lithium Tantalate,” Physical Review B, Vol. 71, No. 18, 2005, pp. 184110-184122. doi:10.1103/PhysRevB.71.184110

[4] A. K. Bandyopadhyay and P. C. Ray, “Perturbation Analysis and Memory in Ferroelectric Materials,” Journal of Applied Physics, Vol. 95, No. 1, 2004, pp. 226-230. doi:10.1063/1.1630698

[5] M. E. Lines and A. M. Glass, “Principles and Applications of Ferroelectrics and Related Materials Clarendon,” Clarendon Press, Oxford, 1977.

[6] V. Gopalan and T. E. Mitchell, “Wall Velocities, Switching Times, and Stabilization Mechanism of 180? Domains in Congruent LiTaO

[7] A. K. Bandyopadhyay, P. C. Ray and V. Gopalan, “Dynamical Systems Analysis for Polarization in Ferroelectrics,” Journal of Applied Physics, Vol. 100, No. 11, 2006, pp. 114106-114109. doi:10.1063/1.2388124

[8] J. Padilla, W. Zhong and D. Vanderbilt, “Heterovalent and A-Atom Effects in A(B'B″) O

[9] B. Meyer and D. Vanderbilt, “Ab initio Study of Ferroelectric Domain Walls in PbTi O

[10] N. Floquet, C. M. Valot, M. T. Mesnier, J. C. Niepce, L. Normand, M. Thorel and R. Kilaas, “Ferroelectric Domain Walls in BaTiO

[11] Y. Girshberg and Y. Yacoby, “Ferroelectric Phase Transitions and Off-Centre Displacements in Systems with Strong Electron-Phonon Interaction,” Journal of Physics: Condensed Matter, Vol. 11, No. 48, 1999, pp. 9807-9822. doi:10.1088/0953-8984/11/48/337.

[12] A. L. Roytburd, “Elastic Domains and Polydomain Phases in Solids,” Phase Transitions B, Vol. 45, 1993, pp. 1-34. doi:10.1080/01411599308203516

[13] W. Zhang and K. Bhattacharya, “A Computational Model of Ferroelectric Domains. Part II: Grain Boundaries and Defect Pinning,” Acta Materialia, Vol. 53, No. 1, 2005, pp. 199-209. doi:10.1016/j.actamat.2004.09.015

[14] W. Zhang and K. Bhattacharya, “A Computational Model of Ferroelectric Domains. Part I: Model Formulation and Domain Switching,” Acta Materialia, Vol. 53, No. 1, 2005, pp. 185-198. doi:10.1016/j.actamat.2004.09.016

[15] Y. Su and C. M. Landis, “Continuum Thermodynamics of Ferroelectric Domain Evolution: Theory, Finite Element Implementation, and Application to Domain Wall Pinning,” Journal of the Mechanics and Physics of Solids, Vol. 55, No. 2, 2007, pp. 280-305. doi:10.1016/j.jmps.2006.07.006

[16] N. Floquet and C. Valot, “Ferroelectric Domain Walls in BaTiO

[17] W. Yan, et al., “The Relationship between the Switching Field and the Intrinsic Defects in Near-Stoichiometric Lithium Niobate Crystals,” Journal of Physics D: Applied Physics, Vol. 39, No. 1, 2006, pp. 21-24. doi:10.1088/0022-3727/39/1/004

[18] L. Tian, V. Gopalan and L. Galambos, “Domain Reversal in Stoichiometric LiTaO

[19] V. Gopalan, V. Dierolf and D. A. Scrymgeour, “Defect-Domain Wall Interactions in Trigonal Ferroelectrics,” Annual Reviews Materials Research, Vol. 37, 2007, pp. 449-489. doi:10.1146/annurev.matsci.37.052506.084247

[20] A. K. Bandyopadhyay, P. C. Ray and V. Gopalan, “Solitons and Critical Breakup Fields in Lithium Niobate Type Uniaxial Ferroelectrics,” European Physical Journal B, Vol. 65, No. 4, 2008, pp. 525-531. doi:10.1140/epjb/e2008-00356-9

[21] A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc and A. R. McGurn, “Multiple-Time-Scale Analysis of Nonlinear Modes in Ferroelectric LiNbO

[22] A. K. Bandyopadhyay, P. C. Ray and V. Gopalan, “An Approach to the Klein-Gordon Equation for a Dynamic Study in Ferroelectric Materials,” Journal of Physics: Condensed Matter, Vol. 18, No. 16, 2006, pp. 4093-4100. doi:10.1088/0953-8984/18/16/016

[23] P. Giri, S. Ghosh, K. Choudhary, Md. Alam, A. K. Bandyopadhyay and P. C. Ray, “Importance of Damping on Nanoswitching in LiNb O

[24] A. Biswas, K. Choudhary, A. K. Bandyopadhyay, A. K. Bhattacharjee and D. Mandal, “Quantum Pining-Transition Due to Charge Defect in Ferroelectrics,” Journal of Applied Physics, Vol. 110, No. 2, 2011, pp. 024104-024111. doi:10.1063/1.3607298