Abstract: Engineering of domains and domain boundaries is quintessential
for technological exploitation of numerous functional materials.
However, it has only recently realized that the configuration of these
domains/domain boundaries can have non-trivial topology. We will discuss
a new topological classification scheme of domain/domain boundary
configurations with Ising-type or two-dimensional order parameters:
Zm×Zn domains (m directional variants and n translational antiphases)
and Zl vortices (where l number of domains and that of domain boundaries
merge). This classification, with the concept of topological protection
and topological charge conservation, has been applied to a wide range of
materials such as improper ferroelectric R(Mn,Fe)O3, antipolar
In(Mn,Ga)O3, hybrid improper ferroelectric (Ca,Sr)3Ti2O7, chiral (and
ferromagnetic) Fe1/3TaS2, and magnetic-superconducting Sr2VO3FeAs. We
will also discuss the emergent physical properties of domain boundaries,
distinct from those of domains. The presented topological consideration
provides a basis in understanding the formation, kinetics, manipulation
and property optimization of domains/domain boundaries in quantum materials.