Order-parameter symmetries for the phase transitions of nonmagnetic secondary and higher-order ferroics

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Abstract
A theoretical investigation is presented of the order-parameter symmetries of all possible secondary and higher-order ferroic transitions, (nonmagnetic). These structural phase transitions, which are neither ferroelectric nor ferroelastic, involve the onset of a spontaneous macroscopic quantity represented by a polar tensor of rank higher than 2. The investigation is performed on the basis of the Landau's symmetry criteria for continuous transitions. Particular attention is given to transitions accompanied by a change of the number of atoms in the crystal's unit cell (improper ferroic transitions). Accordingly, the irreducible representations of 147 space groups are examined, corresponding to all the relevant high-symmetry points of their respective Brillouin zones. Eight tables summarize the results by indicating the irreducible representations which are compatible with a secondary or higher-order ferroic transition, and specifying the corresponding space-group change. For each of the predicted transitions, a free-energy expansion is constructed. Twelve different types of expansions are encountered, relative to one-, two-, three-, four-, and six-dimensional order parameters. The form of the term representing the coupling between the order-parameter and the spontaneous macroscopic quantity is also determined. These results are discussed, and compared to the existing experimental data relative to the considered type of transitions, such as those in ammonium chloride, iron sulfide, or quartz. The case of niobium dioxide is treated in detail, and a new interpretation is given for its transition's order parameter.

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