[Paper Review] Studies of Barkhausen Pulses in Ferroelectrics

Chao Dun Tan, Jonathan Gardner+3 more|arXiv (Cornell University)|May 22, 2018

Magnetic Properties and Applications40 references16 citations

TL;DR

This study demonstrates that Barkhausen pulses in lead zirconate titanate (PZT) ferroelectrics follow avalanche statistics, with jerk amplitudes (squared time derivative of current) exhibiting power-law distributions. Critical exponents of 1.73, 1.64, and 1.61 for three PZT samples closely match the theoretical prediction of 1.65, indicating self-organized criticality and validating avalanche theory in ferroelectric domain switching.

ABSTRACT

Systems that produce crackling noises such as Barkhausen pulses are statistically similar and can be compared with one another. In this project, the Barkhausen noise of three ferroelectric lead zirconate titanate (PZT) samples were demonstrated to be compatible with avalanche statistics. The peaks of the slew-rate (time derivative of current $dI/dt$) squared, defined as jerks, were statistically analysed and shown to obey power-laws. The critical exponents obtained for three PZT samples (B, F and S) were 1.73, 1.64 and 1.61, respectively, with a standard deviation of 0.04. This power-law behaviour is in excellent agreement with recent theoretical predictions of 1.65 in avalanche theory. If these critical exponents do resemble energy exponents, they were above the energy exponent 1.33 derived from mean-field theory. Based on the power-law distribution of the jerks, we demonstrate that domain switching display self-organised criticality and that Barkhausen jumps measured as electrical noise follows avalanche theory.

Motivation & Objective

• To investigate whether Barkhausen noise in ferroelectrics follows avalanche statistics and exhibits self-organized criticality.
• To determine if the statistical distribution of jerk amplitudes (dI/dt)² in PZT ferroelectrics follows a power law.
• To measure critical exponents of Barkhausen jerks and compare them with theoretical predictions from avalanche theory.
• To validate the use of maximum-likelihood fitting over linear regression for power-law analysis in noisy experimental data.
• To assess the robustness of power-law behavior across multiple PZT samples with varying microstructures.

Proposed method

• Measured Barkhausen noise via two-pulse electric field cycling on three PZT samples (B, F, S) using a hysteresis apparatus.
• Calculated jerk as the square of the time derivative of current (dI/dt)² to identify sharp domain switching events.
• Applied piecewise cubic Hermite interpolation (PCHIP) to remove smooth baselines from jerk spectra, isolating individual pulses.
• Used maximum-likelihood (ML) fitting to analyze power-law distributions of jerk amplitudes, avoiding biases from linear regression.
• Performed logarithmic binning and ML fitting on normalized and combined jerk data across multiple runs for statistical robustness.
• Compared results with theoretical predictions of 1.65 for avalanche critical exponents and mean-field theory (1.33).

Experimental results

Research questions

• RQ1 Do Barkhausen pulses in PZT ferroelectrics follow a power-law distribution of jerk amplitudes?
• RQ2 Are the critical exponents of these jerks consistent with theoretical predictions from avalanche theory?
• RQ3 How do the critical exponents vary across different PZT samples with distinct microstructures?
• RQ4 Does maximum-likelihood fitting provide more reliable power-law estimation than linear regression in this context?
• RQ5 Can the observed statistical behavior be interpreted as evidence of self-organized criticality in ferroelectric domain dynamics?

Key findings

• The jerk amplitudes in all three PZT samples (B, F, S) exhibited power-law distributions with critical exponents of 1.73, 1.64, and 1.61, respectively.
• The average critical exponent across samples was 1.66 with a standard deviation of 0.04, closely matching the theoretical prediction of 1.65 for avalanche theory.
• The measured exponents were significantly higher than the mean-field theory prediction of 1.33, indicating non-mean-field critical behavior.
• Maximum-likelihood fitting confirmed power-law behavior across multiple runs, with stable plateaus spanning multiple decades in the log-log plots.
• Baseline removal via PCHIP interpolation effectively isolated individual jerk pulses, especially in samples with large spanning avalanche events.
• The consistency of power-law behavior across different samples and measurement runs supports the presence of self-organized criticality in ferroelectric domain switching.