Disentangling ferroelectric domain wall geometries and pathways in dynamic piezoresponse force microscopy via unsupervised machine learning

Abstract

Domain switching pathways in ferroelectric materials visualized by dynamic piezoresponse force microscopy (PFM) are explored via variational autoencoder, which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure.

Latent Mechanisms of Polarization Switching from In Situ Electron Microscopy Observations

“…An alternative approach is developed based on rotationally invariant variational autoencoders (rVAE), a class of unsupervised machine learning methods projecting discrete large‐dimensional spaces on a continuous latent space. Previously, we applied the rVAE approach to explore the evolution of atomic‐scale structures in graphene under electron beam irradiation, [ 43 ] analyze the self‐assembly of protein nanorods, [ 44 ] investigate the domain wall dynamics in piezoresponse force microscopy, [ 45 ] and create a bottom‐up symmetry analysis workflow for atom‐resolved data. [ 46 ] Here, we demonstrate that this approach can be extended to explore domain evolution mechanisms via detailed analysis of the latent spaces of rVAE.…”

Nanoscale Activation Energy Mapping and Leveraging for Accelerating Ferroelectric Domain Nucleation and Growth

“…Pixel by pixel analysis of domain wall motion [ 39 ] can similarly improve apparent switching energy maps for domain growth, increasingly assisted by data‐science approaches. [ 40,41 ] There have been many other efforts to characterize relative nucleation or growth activation energies as well, [ 31,42–46 ] albeit independently. The combination, as implemented here, is important for real device switching in a typical parallel plate geometry, as it is the balance between nucleation and growth that ultimately controls the actual switching progression.…”

Disentangling Ferroelectric Wall Dynamics and Identification of Pinning Mechanisms via Deep Learning

“…The second step of the workflow is feature engineering. Previously, we have introduced an approach where the features were image patches centered on a uniform spatial grid [ 61 ] and specific atomic location. [ 64 ] Here, we show that specific aspects of domain wall dynamics can be probed via selection of the patches centered at the specific domain wall types and introducing a time‐delayed description.…”

“…The third step of the workflow is unsupervised learning of low‐dimensional representations of the data, realized here using a multilayer rotationally invariant autoencoder. [ 61 ] The individual elements of this workflow are discussed in detail below.…”

“…Here, we explore the time‐dependent domain wall dynamics in ferroelectric materials via latent representation of the time‐dependent data. [ 61–63 ] We propose the feature‐engineering approach that effectively encodes time‐dependent wall dynamics and demonstrate the applicability of rotationally invariant variational autoencoder to establish the salient features of the domain wall dynamics. The individual elements of this workflow as well as the integrated approach per se can be universally applied to the multitude of PFM applications.…”