A symmetry approach to domain structures

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Abstract
Whereas the symmetry of the order parameter is specified by operations preserved at the transition, domains are determined by lost symmetry operations. The number and the relations between domains and domain pairs can be found by grouping the lost operations into left and double cosets. Different types of domains, rotational (e.g., ferroelectric, ferroelastic) and translational ones, are related to maximal subgroups retaining a characteristic domain property. The interface between domains is treated as a two-dimensional residue of the parent phase and is described by two-sided plane groups. The existence, orientation and charge of coherent stress-free domain walls between ferroelastic domains can also be determined from left coset decompositions. Junctions and interactions of antiphase boundaries, domain walls and imperfect dislocations are considered. Annihilation of antiphase boundaries by moving domain walls, the creation of antiphase boundaries by reacting domain walls and the selective interactions of dislocations with antiphase boundaries and domain walls are demonstrated on the example of gadolinium molybdate. Goldstone modes as a dynamical counterpart of domain structures in systems described by continuous symmetry groups are briefly mentioned.