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Transition-state-theory-based interpretation of Landau double well potential for ferroelectrics

Md Nur K. Alam, S. Clima, B. Kaczer, Ph. Roussel, B. Truijen, L. - A. Ragnarsson, N. Horiguchi, M. Heyns, J. Van Houdt

TL;DR

This work addresses the contentious idea of quasi-static negative capacitance (QSNC) in ferroelectrics by reframing the Landau double-well potential through transition-state theory. By linking atomistic NEB/DFT insights to phenomenological hysterons and to master-equation switching, the authors show how Landau fits naturally with Preisach and nucleation-based models, while simultaneously arguing that the depolarization field in FE–DE stacks does not stabilize a negative-capacitance state. Their transition-state interpretation yields equal occupation of the two ferroelectric minima under electric-field conditions, leading to zero net polarization and no QSNC, and provides a unified framework connecting first-principles, Landau, and statistical models. The findings clarify that QSNC is not an intrinsic feature of the Landau description, with implications for designing FE-based devices such as HfO$_2$-type ferroelectrics.

Abstract

Existence of quasi-static negative capacitance (QSNC) was proposed from an interpretation of the widely accepted Landau model of ferroelectrics. However, many works showed not to support the QSNC theory, making it controversial. In this letter we show the Landau model when used together with transition-state-theory, can connect various models including first-principles, Landau, Preisach and nucleation limited switching while it does not predict the existence of QSNC.

Transition-state-theory-based interpretation of Landau double well potential for ferroelectrics

TL;DR

This work addresses the contentious idea of quasi-static negative capacitance (QSNC) in ferroelectrics by reframing the Landau double-well potential through transition-state theory. By linking atomistic NEB/DFT insights to phenomenological hysterons and to master-equation switching, the authors show how Landau fits naturally with Preisach and nucleation-based models, while simultaneously arguing that the depolarization field in FE–DE stacks does not stabilize a negative-capacitance state. Their transition-state interpretation yields equal occupation of the two ferroelectric minima under electric-field conditions, leading to zero net polarization and no QSNC, and provides a unified framework connecting first-principles, Landau, and statistical models. The findings clarify that QSNC is not an intrinsic feature of the Landau description, with implications for designing FE-based devices such as HfO-type ferroelectrics.

Abstract

Existence of quasi-static negative capacitance (QSNC) was proposed from an interpretation of the widely accepted Landau model of ferroelectrics. However, many works showed not to support the QSNC theory, making it controversial. In this letter we show the Landau model when used together with transition-state-theory, can connect various models including first-principles, Landau, Preisach and nucleation limited switching while it does not predict the existence of QSNC.
Paper Structure (6 sections, 9 equations, 4 figures)

This paper contains 6 sections, 9 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Atomistic model to Landau model
  3. Phenomenological/Statistical model
  4. Transition-state-theory
  5. Ferroelectric-Dielectric stack
  6. Conclusion

Figures (4)

  • Figure 1: Two possible minimum energy atomic configurations of orthorhombic $HfO_2$ with up and down polarization.
  • Figure 2: a) Polarization in the $m^{th}$ image of the NEB simulation, given by equation 1. Different parallel branches are created due to the uncertainty imposed by the quantum of polarization, b) Energy profile as a function of $P$ (from Fig. \ref{['Landau_profile_from_NEB']}a) fitted with Landau model, c) Minimization of the Landau potential gives the S-curve
  • Figure 3: a) Double well energy profile under applied electric field. Solution of master equation in FE-DE stack gives b) $P-E$ behavior of FE, c) $P_r$ as a function of dielectric thickness
  • Figure 4: Difference in the interpretation of zero net-polarization state of ferroelectric-dielectric stack caused by the depolarization field $E$ (eq. \ref{['E_depolarization']})- a) according to QSNC theory, $E$ pushes FE from the minima to the TOB b) according to transition-state theory, $E$ equally distributes the hysterons in both wells.