Color theorems, chiral domain topology and magnetic properties of   FexTaS2
  Common mathematical theory can have profound applications in understanding real materials. The intrinsic connection between aperiodic orders observed in the Fibonacci sequence, Penrose tiling, and quasicrystals is a well-known example. Another example is the self-similarity in fractals and dendrites. From transmission electron microscopy experiments, we found that FexTaS2 crystals with x=1/4 and 1/3 exhibit complicated antiphase and chiral domain structures related to ordering of intercalated Fe ions with 2a*2a and sqrt3a*sqrt3a superstructures, respectively. These complex domain patterns are found to be deeply related with the four color theorem, stating that four colors are sufficient to identify the countries on a planar map with proper coloring, and its variations for two-step proper coloring. Furthermore, the domain topology is closely relevant to their magnetic properties. Our discovery unveils the importance of understanding the global topology of domain configurations in functional materials. 
Yoichi Horibe, Junjie Yang, Yong-Heum Cho, Xuan Luo, Sung Baek Kim,   Yoon Seok Oh, Fei-Ting Huang, Toshihiro Asada, Makoto ...
cond-mat.mtrl-sci