Kinetics of nano-size Ferroelectrics

TL;DR

This paper provides a theoretical analysis of the finite-temperature polarization dynamics in nano-sized ferroelectrics, highlighting the importance of thermal fluctuations in phase stability and switching behavior.

Contribution

It extends the Landau-Khalatnikov model to include thermal fluctuations and compares results with analytical formulas and established models, offering new insights into size-dependent ferroelectric behavior.

Findings

Thermal fluctuations induce phase instability at reduced sizes.

The extended model aligns with classical switching time formulas.

Thermal effects are crucial for accurate ferroelectric modeling at the nanoscale.

Abstract

We analyze theoretically the finite-temperature polarization dynamic in displacive-type ferroelectrics. In particular we consider the thermally-activated switching time of a single-domain ferroelectric polarization studied by means of the Landau-Khalatnikov equation, extended as to capture thermal fluctuations. The results are compared with the switching time formula that follows from the analytical solution of Pauli master equations. In a second step we focus on the phase diagram of a prototypical ferroelectric as described by the temperature-dependent Landau-Devonshire model including thermal fluctuations. Our simulations show the emergence of phase instability at reduced sizes which we attribute to thermal fluctuations in the order parameter in the respective phase. We conclude that, along with the temperature-dependent potential coefficients, thermal fluctuations should be taken into account to achieve a comprehensive description of the thermal behavior of reduced-size ferroelectrics. To endorse our conclusions, we simulated the electric-field activated switching time for a multi-domain system and compared the results to the predictions of well-established models such as the Kolmogorov-Avrami-Ishibashi.