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Register a new userShear effects in lateral piezoresponse force microscopy at 180$^circ$ ferroelectric domain walls
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In studies using piezoresponse force microscopy, we observe a non-zero lateral piezoresponse at 180$^circ$ domain walls in out-of-plane polarized, c-axis-oriented tetragonal ferroelectric Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ epitaxial thin films. We attribute these observations to a shear strain effect linked to the sign change of the $d_{33}$ piezoelectric coefficient through the domain wall, in agreement with theoretical predictions. We show that in monoclinically distorted tetragonal BiFeO$_3$ films, this effect is superimposed on the lateral piezoresponse due to actual in-plane polarization, and has to be taken into account in order to correctly interpret the ferroelectric domain configuration.
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Frequency dependent dynamic behavior in Piezoresponse Force Microscopy (PFM) implemented on a beam-deflection atomic force microscope (AFM) is analyzed using a combination of modeling and experimental measurements. The PFM signal comprises contributions from local electrostatic forces acting on the tip, distributed forces acting on the cantilever, and three components of the electromechanical response vector. These interactions result in the bending and torsion of the cantilever, detected as vertical and lateral PFM signals. The relative magnitudes of these contributions depend on geometric parameters of the system, the stiffness and frictional forces of tip-surface junction, and operation frequencies. The dynamic signal formation mechanism in PFM is analyzed and conditions for optimal PFM imaging are formulated. The experimental approach for probing cantilever dynamics using frequency-bias spectroscopy and deconvolution of electromechanical and electrostatic contrast is implemented.
To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside the material are derived for the cases of weak and strong indentation. In the weak indentation case, electrostatic field distribution is calculated using image charge model. In the strong indentation case, the solution of the coupled electroelastic problem for piezoelectric indentation is used to obtain the electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM contact mechanics and imaging mechanism. The electroelastic field distribution allows signal generation volume in PFM to be determined. These rigorous solutions are compared with the electrostatic point charge and sphere-plane models, and the applicability limits for asymptotic point charge and point force models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.
In purely c-axis oriented PbZr$_{0.2}$Ti$_{0.8}$O$_3$ ferroelectric thin films, a lateral piezoresponse force microscopy signal is observed at the position of 180{deg}domain walls, where the out-of-plane oriented polarization is reversed. Using electric force microscopy measurements we exclude electrostatic effects as the origin of this signal. Moreover, our mechanical simulations of the tip/cantilever system show that the small tilt of the surface at the domain wall below the tip does not satisfactorily explain the observed signal either. We thus attribute this lateral piezoresponse at domain walls to their sideways motion (shear) under the applied electric field. From simple elastic considerations and the conservation of volume of the unit cell, we would expect a similar lateral signal more generally in other ferroelectric materials, and for all types of domain walls in which the out-of-plane component of the polarization is reversed through the domain wall. We show that in BiFeO$_3$ thin films, with 180, 109 and 71{deg}domain walls, this is indeed the case.
Domain dynamics in the Piezoresponse Force Spectroscopy (PFS) experiment is studied using the combination of local hysteresis loop acquisition with simultaneous domain imaging. The analytical theory for PFS signal from domain of arbitrary cross-section is developed and used for the analysis of experimental data on Pb(Zr,Ti)O3 polycrystalline films. The results suggest formation of oblate domain at early stage of the domain nucleation and growth, consistent with efficient screening of depolarization field within the material. The fine structure of the hysteresis loop is shown to be related to the observed jumps in the domain geometry during domain wall propagation (nanoscale Barkhausen jumps), indicative of strong domain-defect interactions.
Nanoscale polarization switching in ferroelectric materials by Piezoresponse Force Microscopy (PFM) in weak and strong indentation limits is analyzed using exact solutions for electrostatic and coupled electroelastic fields below the tip. It is proposed that the tip-induced domain switching can be mapped on the Landau theory of phase transitions with the domain size as an order parameter. For a point charge interacting with a ferroelectric surface, switching of both first and second order is possible depending on the charge-surface separation. For a realistic tip shape, the domain nucleation process is first order in charge magnitude and polarization switching occurs only above a critical tip bias. In pure ferroelectric or ferroelastic switching, the late stages of the switching process can be described using point charge/force model and arbitrarily large domains can be created; however, the description of the early stages of nucleation process when domain size is comparable with the tip radius of curvature requires exact field structure to be taken into account.
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