Soft mode analysis and ferroelectric transition in spherical nanoparticles |
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| Authors: | Preeti Khare Debanand Sa |
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| Institution: | 1. School of Physics and Physical Engineering, Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Qufu Normal University, Qufu 273165, China;2. School of Material Science and Engineering, Materials Research Center for Energy and Photoelectrochemical Conversion, University of Jinan, Jinan 250022, China;1. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA;2. Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA;3. Institute for Superconducting and Electronic Materials, Australian Institute of Innovative Materials, University of Wollongong, NSW 2500, Australia |
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| Abstract: | We address the dielectric behavior in a free standing spherical particle using the phenomenological Landau theory. Considering the equations of motion and small perturbation against uniform polarization, we obtain the size driven ferroelectricity. The size driven polarization is shown to diverge at a new correlation length which turns out to be the extrapolation length. Mode analysis in such systems is carried out and it is found that the size driven ferroelectricity is associated with a soft mode which takes a minimum value at the new transition temperature similar to that of the bulk system. We suggested that such a mode can be tested in Raman measurement. |
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