Rapid polarization mapping in ferroelectrics using Fourier masking

Ferroelectric materials, and more specifically ferroelectric domain walls (DWs) have become an area of intense research in recent years. Novel physical phenomena have been discovered at these nanoscale topological polarization discontinuities by mapping out the polarization in each atomic unit cell around the DW in a scanning transmission electron microscope (STEM). However, identifying these features requires an understanding of the polarization in the overall domain structure of the TEM sample, which is often a time-consuming process. Here, a fast method of polarization mapping in the TEM is presented, which can be applied to a range of ferroelectric materials. Due to the coupling of polarization to spontaneous strain, we can isolate different strain states and demonstrate the fast mapping of the domain structure in ferroelectric lead titanate (PTO). The method only requires a high-resolution TEM or STEM image and is less sensitive to zone axis or local strain effects, which may affect other techniques. Thus, it is easily applicable to in-situ experiments. The complimentary benefits of Fourier masking with more advanced mapping strategies and its application to other materials are discussed. These results imply that Fourier masked polarization mapping will be a useful tool for electron microscopists in streamlining their analysis of ferroelectric TEM samples. LAY DESCRIPTION: This paper addresses a problem that often occurs when looking at a ferroelectric material in the Transmission Electron Microscope (TEM). Ferroelectric samples are interesting because they form tiny areas inside themselves with arrow of charge in each one. The thinner the sample, the smaller these regions, called "domains" become. These arrows of charge point in different directions in each domain of the sample. The boundary where these domains meet have interesting properties to study in a TEM but it's important to figure out which way the arrows point in the domains around the boundary. What causes the arrows in the different domains is tiny shifts of different atoms in unit cell away from their neutral position, usually because they're being squeezed by pressure from the domains nearby. The problem is that these tiny atoms moving are difficult to measure and see where the charged arrow is pointing, often it's hard to know how many different domains are even in the sample and where they begin. This paper discusses a method called "Fourier masking" to quickly see what's going on in the overall TEM sample, where the domains are and roughly where the arrows point. It does this by looking at the spacings of the atoms from a magnification where you can just about see the lines of atoms. In lead titanate the unit cell is a rectangle and the arrow always points in line with the long side of the rectangle. The Fourier masking lets you see which direction the long side of the rectangular unit cell is pointing in different parts of your TEM image. The big advantage is that it takes about two minutes to do and uses software that almost every TEM already has. That lets the TEM user quickly know where the domains are in their TEM samples and roughly which way the arrows of charge are pointing. Then they can choose the most interesting features focus on for higher resolution analysis.