Sequential piezoresponse force microscopy and the \u2018small-data\u2019 problem

Harsh Trivedi,Robert C Pullar,Vladimir V Shvartsman,Marco S A Medeiros,Doru C Lupascu

doi:10.1038/s41524-018-0084-9

Abstract

The term big-data in the context of materials science not only stands for the volume, but also for the heterogeneous nature of the characterization data-sets. This is a common problem in combinatorial searches in materials science, as well as chemistry. However, these data-sets may well be ‘small’ in terms of limited step-size of the measurement variables. Due to this limitation, application of higher-order statistics is not effective, and the choice of a suitable unsupervised learning method is restricted to those utilizing lower-order statistics. As an interesting case study, we present here variable magnetic-field Piezoresponse Force Microscopy (PFM) study of composite multiferroics, where due to experimental limitations the magnetic field dependence of piezoresponse is registered with a coarse step-size. An efficient extraction of this dependence, which corresponds to the local magnetoelectric effect, forms the central problem of this work. We evaluate the performance of Principal Component Analysis (PCA) as a simple unsupervised learning technique, by pre-labeling possible patterns in the data using Density Based Clustering (DBSCAN). Based on this combinational analysis, we highlight how PCA using non-central second-moment can be useful in such cases for extracting information about the local material response and the corresponding spatial distribution.

Highlights

In an age where advanced material characterization techniques offer access to a wide range of information, the problem essentially lies in extracting a sensible meaning out of the large amount of information collected
The BaTiO3–CoFe2O4 system (BTO-CFO) data show a clear distinction between different groups of data-points
In order to understand the different results obtained by Principal Component Analysis (PCA) of the two material systems, we consider the basic properties of PCA, which is minimization of the bivariate second-moments and maximization of the univariate second-moments

Summary

Introduction

In an age where advanced material characterization techniques offer access to a wide range of information, the problem essentially lies in extracting a sensible meaning out of the large amount of information collected. A few examples of such phenomena include electrical conduction at ferroelectric/ferroelastic domain walls,[9,10,11,12] polarization dynamics in ferroelectrics,[13,14,15,16,17,18] temperature/time/ voltage dependent study of ergodicity (time dependence) of polarization in relaxor-ferroelectrics,[14,19] and local magnetoelectricity.[20,21,22,23,24,25,26,27,28] Probing such local phenomena essentially requires measuring a response Iij(xi, Pj) on an X × Y grid, as a function of a spectral parameter Pj (j = 1,...,M); where xi is the spatial coordinate index (i = 1,...,N; N = X × Y) The format of such spectroscopic acquisition could be selected in two different ways: (i) a point-by-point acquisition of the response as a function of Pj, or (ii) a sequence of scans at different values of Pj. The choice between either of the formats largely depends upon the time step necessary to stabilize the spectral parameter, taking into consideration the scanner drift. It is more suitable to opt for the sequential scan format, where a better track of the drift could be kept via simultaneously acquired topography images

Methods

Results

Conclusion