What is a ferroelectric–a materials designer perspective

ABSTRACT

Ferroelectrics are usually defined as polar materials that display polarisation hysteresis. This is a functional definition. A structural definition exists too, based solely on symmetry arguments. The structural definition, useful e.g. for design of new materials, says that a ferroelectric is a material that underwent a phase transition from a parent higher-symmetry phase into a ferroelectric phase, such that the polar directions in the ferroelectric phase are linked to each other by lost symmetry operations of the parent phase.

Ferroelectrics are discussed in this paper from a structural point of view. The structural definition helps also in clarifying the relationship between ferroelectrics and antiferroelectrics, conducive for the design of new antiferroelectrics or tuning of existing ones. Relaxor ferroelectrics are discussed too, in the structural context. The contemporary material (Na_1/2Bi_1/2)TiO₃ is then used to illustrate the subjects discussed, the existing knowledge, and the missing understanding. This paper, on the occasion of the 500^th volume of the journal Ferroelectrics has the limited scope of (a) reemphasizing the structural aspects of ferroelectricity and (b) serving as a primer on ferroelectric materials for the novice.

KEYWORDS:

• Ferroelectric
• antiferroelectric
• relaxor-ferroelectric
• symmetry
• PbTiO₃
• PbZrO₃
• Pb(Mg_1/3Nb_2/3)O₃
• (Na_1/2Bi_1/2)TiO₃

Acknowledgments

I wish to acknowledge my numerous teachers, above all Eric Cross and Alexander Tagantsev, to whom I am profoundly indebted. Ample thanks to Jan Petzelt for discussion and clarifications. Barbara Fraygola is acknowledged for providing the unpublished data of Fig. 2c. Thanks to Arnaud Crassus for the preparation of the figures. The Swiss National Science Foundation is acknowledged for support (project 200021_149495).

Comments

(1)

In ref. [1] Megaw writes “Ferroelectrics are a special group of pyroelectric crystals (implying polar crystals, (ns)) in which the spontaneous polarisation is reversible” von Hippel, ref. [2], who during the years 1946–1950 defined ferroelectricity as “the spontaneous alignment of electric dipoles by mutual interaction” emphasized only in 1952 “For the ferroelectric crystal, in contrast (to the polar non-ferroelectric crystal (ns)), the possibility of reversal is inherent because the (polar (ns)) axis evolves at the Curie point from a state of higher symmetry. Only in ferroelectric crystals, therefore, can domain structures appear and the moment can be reversed by a sufficiently strong opposing field.” The term ‘ferroelectric’ was used of course earlier but without explicit definition. E.g.: Schroedinger, who was the first to propose the term ‘ferroelectric’ did not mention the polarisation switching (Studien über Kinetik der Dielektrika, den Schmelzpunkt, Pyro-und Piezoelektrizität von Erwin Schrödinger. in Sitzungsberichten der Kaiserl. Akademie der Wissenschaften in Wien. Mathem.-Naturw. Klasse; Bd. CXXI, Abt. Iia, November 1912. P.1945). Valasek, in 1921, in his report on the first ferroelectric material did not use the term ferroelectric (J.Valasek: Piezoelectric and allied phenomena in Rochelle salt. Phys. Rev. 1921; 17:475–481). Muller, in 1935 used the term without referring to the need in a phase transition into a polar state to obtain ferroelectricity (Muller H: Properties of Rochelle salt. Phys. Rev. 1935; 47: 175–191.). Jaffe, in 1937 emphasized that inversion from pyroelectric to nonpyroelectric crystal class is essential, but did not discuss polarisation neither used the term ferroelectricity (Jaffe HvR: Polymorphism of Rochelle Salt. Phys. Rev. 1937; 51:43–47).

(2)

Aizu, in ref. [3], considering no ferroelectric with paraelectric polar phase was known in his time, omitted from the list of species those with a polar prototype, but commented: “This should not be considered as a foregone conclusion. It is to be disputed whether or not a spontaneous polarisation can emerge (at a transition temperature) in a direction perpendicular to the unique polar axis of a paraelectric crystal which belongs to a polar point group.”