Scanning of magnetic space groups and the analysis of non-magnetic domain walls

Similarly to atomic positions in a crystal being fixed, or at least constrained by the space group of that crystal, the displacements of atoms in a domain wall are determined or constrained by the symmetry of the wall given by the sectional layer group of the corresponding domain pair. The sectional layer group can be interpreted as comprised of operations that leave invariant a plane transecting two overlapping structures, the domain states of the two domains adhering to the domain wall. The procedure of determining the sectional layer groups for all orientations and positions of a transecting plane is called scanning of the space group. Scanning of non-magnetic space groups has been described and tabulated. It is shown here that the scanning of magnetic groups can be determined from that of non-magnetic groups. The information provided by scanning of magnetic space groups can be utilized in the symmetry analysis of domain walls in non-magnetic crystals since, for any dichromatic space group, which expresses the symmetry of overlapped structures of two non-magnetic domains, there exists an isomorphic magnetic space group. Consequently, a sectional layer group of a magnetic space group expresses the symmetry of a non-magnetic domain wall. Examples of this are given in the symmetry analysis of ferroelectric domain walls in non-magnetic perovskites.