Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.

Using Ginzburg-Landau theory and two-dimensional (2D) phase field simulations, we analyze the influence of flexoelectric coupling on the domain patterns in ferroelectrics. The phase field simulations predict that a high strength of the flexoelectric coupling leads to formation of a fine structure in domain patterns in ferroelectrics. The fine structure forms when the coupling strength exceeds a critical value and is related to local transition into an incommensurate phase. Depending on the parameters, a structure with stripe patterns with antiparallel polarizations or another one, not seen before, with two-dimensional arrays of alternating vortices is found. Complex domain configurations with coexisting phases and unusual domain walls between them are observed. Although the incommensurate phase does not form for weaker couplings, the influence of flexoelectricity on bulk domain patterns can still be significant. The results of the calculations are rationalized using an analytical model. Directions for the modulation wave vectors in the fine structure are found in the framework of a linear analysis, while the type of the structure-stripes or vortices-is determined by anharmonicity.

Ferroelectric nanostructures can be formed by local switching of domains using techniques such as piezo-force microscopy (PFM). Understanding lateral size effects is important to determine the minimum feature size for writing ferroelectric nanostructures. To understand these lateral size effects, we use the time-dependent-Ginzburg-Landau equations to simulate localized switching of domains for a PFM type and parallel-plate capacitor configurations.Our investigations indicate that fringing electric fields lead to switching via 90° domain wedge nucleation for thicker films while at smaller thicknesses, the polarization switches directly by 180º rotations. The voltage required to switch the domain increases by decreasing the lateral size and at very small lateral sizes the coercive voltage becomes so large that it becomes virtually impossible to switch the domain. In all cases, the width of the switched region extends beyond the electrodes, due to fringing.

The line width dependence of zero-phonon lines and phonon sidebands on temperature, bath dissipation, and electron-phonon coupling is studied for an underdamped Brownian oscillator model with an Ohmic dissipative bath. Factors determining the line widths vary from the zero-phonon lines to the phonon sidebands. The control-parameter space of line broadening has been mapped out, revealing that the line widths of the zero-phonon lines and phonon sidebands are linearly dependent on both the temperature and the Huang-Rhys factor. It is also found that the dependence of the line widths on the bath damping factor is linear for the zero-phonon lines and quadratic for the phonon sidebands.