NJIT Physics Department Seminar

October 6th, 2014, Monday

Domain Topology and Color Theorems

Prof. Sang-Wook Cheong

Rutgers Center for Emergent Materials

Rutgers University, New Brunswick

(Condensed Matter Physics, Host: Sirenko)

Time: 11:45am-12:45pm with 11:30am tea time

Room: ECE 202

Abstract:

Understanding and controlling domains and domain walls is quintessential for identifying the origin of the macroscopic physical properties of functional materials and exploiting them for technological applications. Domains are associated with different orientations of directional order parameters such as magnetization, polarization, and ferroelastic distortions. Even though the local conditions at, for example, ferroelastic boundaries and liquid crystal defects have been often studied, research on the macroscopic topological constraints in complex domain patterns has been scarce.

The four color theorem, which was empirically known to cartographers before the 17th century, states that four colors are sufficient to identify the countries on a planar map with proper coloring (without bordering countries sharing the same color, except for intersections). It is only recently found that this color theorem and its tensorial variation (two-step proper coloring) are directly relevant to global domain topology of a wide range of materials such as multiferroic hexagonal RMnO₃ (R-rare earths), ferromagnetic layered Fe_1/3TaS₂, and rhombohedral ferroelectrics such as BiFeO₃ and GeTe.

The relevance of color theorems to the domain patterns resembles the relation between the order without periodicity in the Fibonacci sequence, Penrose tiling and the formation of quasicrystals; it is also similar to the way that self-similarity plays the key role in the formation of fractals and dendrites.