Abstract
The ferroelectric critical size and microscopic domain structure of PbTiO3 nanodots with unit cells of N × N × N (N = 1–3) have been investigated by ab initio (first-principles) density functional theory calculations. Nanodots with PbO and TiO surface terminations are investigated, and the ground state of TiO-terminated nanodots is found to be paraelectric regardless of the size. However, for PbO-terminated nanodots, the ferroelectric state is energetically favorable even in the smallest nanodot, indicating the absence of an intrinsic critical size for ferroelectricity in the nanodot structure. Moreover, the distributions of polarizations in nanodots with different sizes are analyzed. The vortex polarizations rotating around both the central [001] axis and diagonal [11¯1] directions of nanodots can stably exist. The vortex polarization arises from the opposite rotation between the cations and anions around the [001] and the [11¯1] directions of nanodots, respectively. On the other hand, the toroidal moments of vortex polarizations both around the [001] and [11¯1] directions increase with the increment of nanodot size, and these vortex polarizations are energetically favorable in small and large nanodots, respectively.
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