Physical description of crystal

Ishitobi, Takayuki

Traditional crystal descriptions rely on space groups, while physical phenomena are more naturally expressed through tensorial quantities. This fundamental difference makes it difficult to directly link symmetry to physical behavior. In this work, we introduce a novel tensor-based approach that represents both crystalline and magnetic structures in a direct and unified manner. A compact set of tensor order parameters describes the symmetry-breaking features, from which other physical quantities can be systematically derived through their combinations and derivatives. By correlating the tensor indices of order parameters with those of coupling tensors, the correspondence between structural symmetry and measurable properties becomes explicit. This formulation streamlines the symmetry analysis and offers a comprehensive framework encompassing structural characterization, macroscopic responses, local symmetries, and electronic band degeneracies.