General theory on the growth kinetics of topological domain structure in hexagonal manganites

Abstract

Although the dynamics of domain growth has been a long-standing topic in ferroic systems, its science complexity and important guidance to practical applications cannot be overemphasized. Highly anisotropic systems with only domain-wall-type defects and roughly isotropic systems with only vortex-type defects have been extensively studied as two ideal and extreme examples in terms of domain growth dynamics. The domain growth processes in these two types of systems are believed to follow two different scaling laws. The driving forces behind are domain wall motion and vortex–antivortex annihilation, respectively. However, no realistic ferroic systems have ever been found to exhibit a domain growth process that strictly follows these scaling laws. Fortunately, we now have a realistic ferroic system, i.e., the ferroelectric hexagonal manganite family in which the aforementioned two types of defects coexist. This system supports a fascinating topological vortex–antivortex domain structure and is a unique platform for probing a generalized theory on the domain growth dynamics that covers the two extremes. In this work, we investigate this vortex–antivortex domain structure and its growth dynamics within the framework of the Landau theory using phase-field simulations. It is revealed that morphology of this domain structure can be controlled by a correlation length Lc that is different from the conventional correlation length. More importantly, this domain structure can be seen as an intermediate state between the two extremes in terms of domain growth dynamics. When Lc is very small, the domain growth process in this domain structure is driven by domain wall motion and follows the well-known Allen–Cahn scaling law. As Lc increases, vortex–antivortex annihilation will dominate the domain growth process and the scaling law will need a logarithmical correction. The present work provides a comprehensive understanding of the domain growth behavior in such a realistic ferroic system of much attention and represents a substantial extension of domain growth dynamics toward complicated multi-defect systems.