Free surface domain nucleation in a ferroelectric under an electrically charged tip

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° 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° switching occurs at a higher applied field. We also see that the calculated domain patterns differ significantly from analytical approximations that are often used.