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Free Surface Domain Nucleation in a Ferroelectric under an Electrically Charged Tip

Kaushik Dayal's picture

This is the preprint of an article that will appear in the Journal of Applied Physics, 111:014106, 2012. (doi:10.1063/1.3674320).

Free Surface Domain Nucleation in a Ferroelectric under an Electrically Charged Tip

by Lun Yang and Kaushik Dayal, Carnegie Mellon University



This paper examines the process of domain nucleation in ferroelectric perovskites at a free surface due to electrical fields applied through a charged tip above the surface.  We use a real-space phase-field model to model the ferroelectric, and apply a boundary element-based numerical method that enables us to accurately account for the stray electric fields outside the ferroelectric and the interactions through electric fields between the external tip and ferroelectric.  We calculate the induced domain patterns, the stress and internal electric fields, and the induced surface displacement for various relative orientations of the crystal lattice with respect to the free surface.  The effect of the external spatially-inhomogeneous electric field leads to the formation of complex domain patterns and nominally incompatible microstructures.  Two key findings are: first, in c-axis films, a new domain forms beneath the tip through 180-degree switching and this new domain has the opposite piezo-response as the original domain, leading to a distinct displacement signature on the surface; and second, in a-axis films, domain nucleation occurs at lower applied field because polarization rotates to align with the applied field, whereas in c-axis films, the polarization magnitude reduces until 180-degree switching occurs at a higher applied field.  We also see that the calculated domain patterns differ significantly from analytical approximations that are often used.

PDF icon yang-dayal_jap2012preprint.pdf4.65 MB


chenlei07's picture

Dear Prof.

 It is a excellent work, espeically for the consideration of the stray electric fields induced by tip using BEM. As you use the FEM solve the equations of the whole mode, your model can solve two layers of materials with wavyness of interface, right?



jiangyuli's picture


  Nice work! Before even worrying about nucleation and switching, have you thought about the correlation between the tip induced displacement and the electromechanical moduli of the sample. As PFM is widely used for characterizing ferroelectric materials at nanoscale, understanding such correlation would be critical in data interpretation and analysis. We did some semi-analytical calculations for highly simpliefied configuration, and it will be interesting to learn from the simulation. Also, how about 3D? We should talk more on this. We have some very interesting PFM data, which I hope to post here in near future.


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