title: Order parameters for phase transitions to structures with one-dimensional incommensurate modulations.
abstract: Phase transitions that result in incommensurate structural modulations are widely observed in crystalline solids and are relevant to a broad range of physical phenomena in magnetic, electronic, optical and structural materials. While the (3+1)-dimensional superspace-group symmetries associated with one-dimensional modulations have been tabulated, the order parameters that produce these modulations have not been explored in detail. Here, using group-theoretical methods, we present a unique and exhaustive enumeration of the isotropy subgroups (and their corresponding order-parameter directions) belonging to irreducible representations of the (3+1)-dimensional superspace extensions of the 230 crystallographic space groups at all incommensurate k points. The vast majority of experimentally observed incommensurately modulated structures have order parameters belonging to one of these subgroups.
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA. stokesh@byu.edu
authors.forename: Harold T
authors.initials: HT
authors.lastname: Stokes
authors.forename: Branton J
authors.initials: BJ
authors.lastname: Campbell
authors.forename: Dorian M
authors.initials: DM
authors.lastname: Hatch