11/20/2023 0 Comments Tdgl equation piezo electric![]() ![]() ![]() However, these studies are time-consuming (several minutes per image), and only relatively large, stable domains can be addressed (lifetimes of >100 s). Imaging of the domain size dependence of the voltage pulse duration and magnitude has yielded information on domain wall mobilities and disorder in ferroelectrics ( 12) and on domain wall pinning on defects ( 13, 14). Application of a dc field to a conductive tip results in local polarization reversal, while subsequent imaging allows visualization of the switched domain. Beyond imaging applications, PFM can be used to study domain dynamics and polarization switching on the nanoscale. The development of piezoresponse force microscopy (PFM) has enabled high-resolution (≈10 nm) imaging of static domain structures ( 10, 11). Dynamic domain behavior and nucleation and growth mechanisms in low-dimensional ferroelectrics, including the switching mechanism in the ideal case, and the role of surfaces, interfaces, and defects in the thermodynamics and kinetics of elementary processes in polarization reversal are the keys to these applications. Furthermore, novel types of ferroelectric ordering stabilized by the spatial constraints and depolarization field effects can emerge ( 8, 9). As the size of the system is reduced, the effects of interfaces and structural defects become statistically more significant. Because of the restrictions imposed by the size of the active region, only a limited number of domains can nucleate. Furthermore, these systems open a pathway toward device applications including nonvolatile memories ( 5) and electrically controlled magnetic tunneling junctions, combining nonvolatile electrical writing and magnetic or resistive read-out schemes ( 6, 7).Īpplications of ferroelectric and multiferroic materials in nanoscale devices necessitate the understanding of switching processes in confined and low-dimensional geometries. Studies of these systems provide insight into fundamental mechanisms of coupling between the lattice, spin, and electronic degrees of freedom and resulting order parameters in the bulk and at the interfaces. The electrical control of magnetic ordering in multiferroic materials and self-assembled nanostructures has recently propelled these materials to the forefront of condensed matter physics and materials science ( 1 – 4). These measurements open a pathway for quantitative studies of the role of a single defect on kinetics and thermodynamics of first order bias-induced phase transitions and electrochemical reactions. The role of atomic-scale defects and long-range elastic fields on nucleation bias lowering is discussed. The switching mechanism is modeled by using the phase-field method, and comparison with experimental results shows that the nucleation biases are within a factor of ≈2 of the intrinsic thermodynamic limit. The critical parameters of the nucleating domain and the activation energy for nucleation are determined. The domain parameters are calculated self-consistently from the decoupled Green function theory by using tip geometry determined from the domain wall profile. Variation of local electromechanical response with dc tip bias is used to determine the size of the domain formed below the conductive scanning probe tip. Ferroelectric domain nucleation and growth in multiferroic BiFeO 3 is studied on a single-domain level by using piezoresponse force spectroscopy.
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