Domain Patterns in Incommensurate Systems with the Uniaxial Real Order Parameter

TL;DR

This paper reexamines the Landau model for incommensurate-commensurate transitions, revealing a more complex phase diagram with metastable patterns and unstable configurations, which could explain various observed phenomena in related materials.

Contribution

It introduces a detailed numerical analysis showing additional metastable solutions and complex phase behavior beyond previous sinusoidal and homogeneous solutions.

Findings

Discovery of metastable periodic domain patterns

Identification of Lyapunov unstable configurations

Complex phase coexistence and transition phenomena

Abstract

The basic Landau model for the incommensurate-commensurate transition to the uniform or dimerized uniaxial ordering is critically reexamined. The previous analyses identified only sinusoidal and homogeneous solutions as thermodynamically stable and proposed a simple phase diagram with the first order phase transition between these configurations. By performing the numerical analysis of the free energy and the Euler-Lagrange equation we show that the phase diagram is more complex. It also contains a set of metastable solutions present in the range of coexistence of homogeneous and sinusoidal solutions. These new configurations are periodic patterns of homogeneous domains connected by sinusoidal segments. They are Lyapunov unstable, very probably due to the nonintegrability of the free energy functional. We also discuss some other mathematical aspects of the model, and compare it with the essentially simpler sine-Gordon model for the transitions to the states with higher commensurabilities. The present results might be a basis for the explanation of phenomena like thermal hystereses, cascades of phase transitions, and memory effects, observed in materials exhibiting the transitions to uniform or dimerized state. Some particular examples are discussed in detail.