1986
DOI: 10.1107/s0108767386099920
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Ferroelectric space groups

Abstract: The 440 ferroelectric space groups, viz the Heesch-Shubnikov (magnetic) space groups, which are symmetry groups of ferroelectric electric-dipole arrangements in crystals, are derived and tabulated. By considering automorphisms induced by the automorphisms of the discrete space-time group, we show that although ferroelectric, ferromagnetic and ferrocurrent point groups all number 31, the number of ferroelectric space groups differs from 275, which is that of both ferromagnetic and ferrocurrent space groups.

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Cited by 21 publications
(24 citation statements)
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“…[9][10][11][12][13][14][15][16][17] However, considering the occurrence of ferroelectricity in Y:HfO 2 thin films, a simple monoclinic=cubic phase mixture or intermediate tetragonal phases seem contradictory, since neither the cubic=tetragonal nor the monoclinic phases in HfO 2 possess ferroelectric space groups. 29 A close examination of the GI-XRD diffractograms presented in Fig. 7 revealed the presence of an orthorhombic phase, whose phase fraction increases against the monoclinic phase until a full stabilization of the cubic phase is reached for high YO 1.5 content.…”
Section: Resultsmentioning
confidence: 99%
“…[9][10][11][12][13][14][15][16][17] However, considering the occurrence of ferroelectricity in Y:HfO 2 thin films, a simple monoclinic=cubic phase mixture or intermediate tetragonal phases seem contradictory, since neither the cubic=tetragonal nor the monoclinic phases in HfO 2 possess ferroelectric space groups. 29 A close examination of the GI-XRD diffractograms presented in Fig. 7 revealed the presence of an orthorhombic phase, whose phase fraction increases against the monoclinic phase until a full stabilization of the cubic phase is reached for high YO 1.5 content.…”
Section: Resultsmentioning
confidence: 99%
“…Even though the crystal structure of MAPbI 3 belongs to the centrosymmetric tetragonal space group I4/mcm, the reorientation of the organic groups and the distortion of the PbI 6 cages can result in a polarization, which is one of the prerequisites for any ferroelectric behavior. [123,124] A second criterion is the ability to switch this polarization by an external field. Several groups, such as Chen et al, [125] Coll et al [126] and Kutes et al, [127] have demonstrated switching of spontaneous polarization, that is a piezoresponse hysteresis loop in both amplitude and phase by using piezoelectric force microscopy (PFM).…”
Section: Ferroelectricitymentioning
confidence: 99%
“…The scarcity of such materials stems from the almost mutually exclusive origin of the two orders: magnetism requires partially unfilled d or f electron orbitals, while ferroelectric distortions occur primarily though hybridization with completely empty d shells [3]. Furthermore, the requirement that the crystalline structure has a noncentrosymmetric space group to support ferroelectricity places further restrictions on possible material candidates [6]. Even in those rare cases where both orders exist [7], useful systems require significant magnetoelectric coupling between ferroelectric and magnetic moments that is often found to be quite weak or is significant only at cryogenic temperatures [4].…”
Section: Introductionmentioning
confidence: 99%