Classification of laminate domain patterns in ferroelectrics

Ferroelectric crystals are known to adopt low-energy, compatible domain configurations. Observations show that these configurations are commonly multirank laminate patterns. In this work, a method to classify and enumerate the laminate domain patterns that can form is presented. The criteria of exact compatibility for laminates structures in a ferroelectric single crystal are used to find all the rank-2 arrangements of domains in the polar tetragonal crystal system. Surprisingly, only eight distinct rank-2 laminate patterns that satisfy compatibility conditions at all domain walls are found. These patterns are classified and correlated with observations of domains in single crystals, showing good agreement.