Multidimensional dynamic piezoresponse measurements: Unraveling local relaxation behavior in relaxor-ferroelectrics via big data

Abstract

Compositional and charge disorder in ferroelectric relaxors lies at the heart of the unusual properties of these systems, such as aging and non-ergodicity, polarization rotations, and a host of temperature and field-driven phase transitions. However, much information about the field-dynamics of the polarization in the prototypical ferroelectric relaxor (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) remains unprobed at the mesoscopic level. Here, we use a piezoresponse force microscopy-based dynamic multimodal relaxation spectroscopy technique, enabling the study of ferroelectric switching and polarization relaxation at mesoscopic length scales, and carry out measurements on a PMN-0.28PT sample with minimal polishing. Results indicate that beyond a threshold DC bias the average relaxation increases as the system attempts to relax to the previous state. Phenomenological fitting reveals the presence of mesoscale heterogeneity in relaxation amplitudes and clearly suggests the presence of two distinct amplitudes. Independent component analysis reveals the presence of a disorder component of the relaxation, which is found to be strongly anti-correlated with the maximum piezoresponse at that location, suggesting smaller disorder effects where the polarization reversal is large and vice versa. The disorder in the relaxation amplitudes is postulated to arise from rhombohedral and field-induced tetragonal phase in the crystal, with each phase associated with its own relaxation amplitude. These studies highlight the crucial importance of the mixture of ferroelectric phases in the compositions in proximity of the morphotropic phase boundary in governing the local response and further highlight the ability of PFM voltage and time spectroscopies, in conjunction with big-data multivariate analyses, to locally map disorder and correlate it with parameters governing the dynamic behavior.

Smart machine learning or discovering meaningful physical and chemical contributions through dimensional stacking

“…where A 0 is the response at saturation, R 0 is the amplitude of the change over time, τ is the characteristic time constant, and β is the stretch exponential, describing the width of the time constant distribution. 43 When β → 0, the time constant distribution is the widest, and when β → 1, the τ distribution is the tightest, with a simple exponential decay at the limit of β = 1. The KWW functional has been successfully applied to many out-ofequilibrium systems, with an anticorrelation between the disorder and β.…”

“…In the past, such datasets have been analyzed with conventional DR by slicing the data into voltage datasets for each composition, D pv ;pc ðt; zÞ, and analyzing the two-dimensional slices independently. [42][43][44][45] Conversely, applying DR with dimensional stacking concatenates the D pv ;pc ðt; zÞ slices along appropriate axes prior to DR analysis, based on physical and chemical understanding of the material. Here, we compare the resulting phenomenological insights obtained through traditional statistical analysis, the conventional DR approach, and DR with dimensional stacking.…”

“…Specifically, dimensional reduction (DR) and machine-learning (ML) techniques have been hailed as a groundbreaking paradigm in materials science, 37 and used to identify superimposed physical and chemical contributors to functional behavior within multidimensional datasets in fields as diverse as multiferroics, 38,39 superconductors, 40 oxide interfaces, 41 and electromechanically active materials. [42][43][44][45] However, while these techniques hold significant promise to revolutionize our understanding of the fundamental material science and guide future design of materials, they are inherently limited by a lack of means to impose physical or chemical constraints to the analysis. 46 In particular, conventional DR analysis on high dimensional datasets is often performed through creation of two-dimensional data slices, where only one single parameter is changed within the slice.…”

Electric-Field-Adjustable Time-Dependent Magnetoelectric Response in Martensitic FeRh Alloy

“…Notice that after applying 100 V (Figure 2f) 2θ(110) does not vary at all. Complementary XRD (see Supporting InformationFigure S6) allow disregarding any substrate contribution to the observed relaxation [25][26]. Therefore, the obvious time-dependent position of the 2θ(110) must be related to the dynamics of the FM to AFM phase transition.…”

Frontiers in strain-engineered multifunctional ferroic materials

“…[53] In this example, relaxation in the piezoresponse was measured using BE-PFM as a function of time (in the remanent state) following a DC bias of varying magnitude [ Fig. 3(a)]; and thus the final dataset is 4D A = (x, y, V, t).…”