Abstract
The Landau theory of phase transitions predicts the presence of a negative capacitance in ferroelectric materials based on a mean-field approach. While recent experimental results confirm this prediction, the microscopic origin of negative capacitance in ferroelectrics is often debated. This study provides a simple, physical explanation of the negative capacitance phenomenon—i.e., ‘S’-shaped polarization vs. electric field curve—without having to invoke the Landau phenomenology. The discussion is inspired by pedagogical models of ferroelectricity as often presented in classic text-books such as the Feynman lectures on Physics and the Introduction of Solid State Physics by Charles Kittel, which are routinely used to describe the quintessential ferroelectric phenomena such as the Curie-Weiss law and the emergence of spontaneous polarization below the Curie temperature. The model presented herein is overly simplified and ignores many of the complex interactions in real ferroelectrics; however, this model reveals an important insight: The polarization catastrophe phenomenon that is required to describe the onset of ferroelectricity naturally leads to the thermodynamic instability that is negative capacitance. Considering the interaction of electric dipoles and saturation of the dipole moments at large local electric fields we derive the full ‘S’-curve relating the ferroelectric polarization and the electric field, in qualitative agreement with Landau theory.
Highlights
Ferroelectric materials possess a spontaneous polarization that can be reversed by the application of an electric field
Most investigations on negative capacitance have utilized the Landau theory of ferroelectric phase transitions without giving an explanation from the microscopic point of view. This has often raised the question whether negative capacitance is an unphysical, artificial construct for the convenience of the phenomenology of Landau theory
A mathematical model for the relation between the electric dipole moment p and local electric field at the dipole Elocal is presented, which reveals the microscopic origin of negative capacitance in ferroelectrics
Summary
Ferroelectric materials possess a spontaneous polarization that can be reversed by the application of an electric field. Feynman presented a pedagogical approach to explain the microscopic origin of ferroelectricity in his classic lectures on physics [14] He did not discuss the resulting negative sign in the polarization-electric field dependence, besides mentioning the presence of a polarization catastrophe which leads to a runaway condition with the dipole moments increasing to infinity, which he described as implausible. A mathematical model for the relation between the electric dipole moment p and local electric field at the dipole Elocal is presented, which reveals the microscopic origin of negative capacitance in ferroelectrics This model is extended to qualitatively reproduce the ‘S’-shaped P-E curve and the double-well energy landscape known from the phenomenological Landau mean-field theory [18]
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