New Symmetries in Crystals and Handed Structures

For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and counterclockwise directions as a distinct symmetry operation, here we show that there are many more structural symmetries than are currently recognized in right- or left-handed handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, though a helix or spiral cannot possess conventional mirror or inversion symmetries, they can possess them in combination with the rotation reversal symmetry. Similarly, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new symmetries predict new forms for "roto" properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They also enable symmetry-based search for new phenomena, such as multiferroicity involving a coupling of spins, electric polarization and static rotations. This work is relevant to structure-property relationships in all material structures with static rotations such as minerals, polymers, proteins, and engineered structures.Comment: 15 Pages, 4 figures, 3 Tables; Fig. 2b has error

Ferroelectric polarization switching with a remarkably high activation energy in orthorhombic GaFeO3 thin films

This work was supported by the National Research Foundation (NRF) Grants funded by the Korea Government (MSIP) (Grant No. 2012R 1A1A2041628 and 2013R 1A2A2A01068274). The work at Cambridge was supported by the Engineering and Physical Sciences Research Council (EPSRC). AG and RG thank the Department of Science and Technology for the financial support (Grant No. SB/S3/ME/29/2013).Orthorhombic GaFeO3 (o-GFO) with the polar Pna21 space group is a prominent ferrite owing to its piezoelectricity and ferrimagnetism, coupled with magnetoelectric effects. Herein, we demonstrate large ferroelectric remanent polarization in undoped o-GFO thin films by adopting either a hexagonal strontium titanate (STO) or a cubic yttrium-stabilized zirconia (YSZ) substrate. The polarization-electric-field hysteresis curves of the polar c-axis-grown o-GFO film on a SrRuO3/STO substrate show the net switching polarization of ~35 μC cm−2 with an unusually high coercive field (Ec) of ±1400 kV cm−1 at room temperature. The positive-up and negative-down measurement also demonstrates the switching polarization of ~26 μC cm−2. The activation energy for the polarization switching, as obtained by density-functional theory calculations, is remarkably high, 1.05 eV per formula unit. We have theoretically shown that this high value accounts for the extraordinary high Ec and the stability of the polar Pna21 phase over a wide range of temperatures up to 1368 K.Publisher PDFPeer reviewe

Advances in ab-initio theory of Multiferroics. Materials and mechanisms: modelling and understanding

Within the broad class of multiferroics (compounds showing a coexistence of magnetism and ferroelectricity), we focus on the subclass of "improper electronic ferroelectrics", i.e. correlated materials where electronic degrees of freedom (such as spin, charge or orbital) drive ferroelectricity. In particular, in spin-induced ferroelectrics, there is not only a {\em coexistence} of the two intriguing magnetic and dipolar orders; rather, there is such an intimate link that one drives the other, suggesting a giant magnetoelectric coupling. Via first-principles approaches based on density functional theory, we review the microscopic mechanisms at the basis of multiferroicity in several compounds, ranging from transition metal oxides to organic multiferroics (MFs) to organic-inorganic hybrids (i.e. metal-organic frameworks, MOFs)Comment: 22 pages, 9 figure

Symmetry considerations in structural phase transitions

The most important symmetry arguments to be considered in the analysis of structural phase transitions are reviewed. A practical approach is used, with the discussion of many examples. In particular, we stress the straightforward application of computer tools freely available in internet to solve these symmetry-related problems. We focus on programs available on the Bilbao Crystallographic Server (www.cryst.ehu.es), but also the use of some programs from the ISOTROPY site (stokes.byu.edu/isotropy.html) is discussed

Symmetry analysis of extinction rules in diffuse-scattering experiments

Structured diffuse-scattering intensities, whether of compositional or of pure displacive origin, static or dynamic, contain important information about the symmetry of the individual compositional and/or displacive modes responsible for the observed intensities. However, the interpretation of the experimental data is very often impeded by the lack of a symmetry-based approach to the analysis of the structured diffuse-scattering distributions. Recently, we have demonstrated the existence of systematic phonon selection rules for diffuse scattering that depend on the symmetries of the mode and the scattering vector, and not on the specific structure. Here, we show that such symmetry analysis can be successfully extended and also applied to structure-dependent diffuse scattering associated with disordered materials: the combination of theoretically determined, diffuse-scattering extinction conditions with the concept of non-characteristic orbits proves to be very useful in the interpretation of the observed diffuse-scattering extinctions. The utility of this approach is illustrated by the analysis of diffuse-scattering data from ThAsSe, FeOF and FeF2. The essential part of the associated calculations are performed by the computer programs NEUTRON (systematic phonon extinction rules in inelastic scattering) and NONCHAR (non-characteristic orbits of space groups) that are available on the Bilbao crystallographic server (http://www.cryst.ehu. es)

An introduction to the tools hosted in the Bilbao Crystallographic Server

The programs hosted in the Bilbao Crystallographic Server (http://www.cryst.ehu.e

Distortion modes and related ferroic properties of the stuffed tridymite-type compounds SrAl 2 O 4 and BaAl 2 O 4

The structural and associated ferroic properties of the stuffed tridymite-type compounds BaAl2 O4 and SrAl2 O4 have been investigated by means of ab initio calculations. Structures and energy landscapes have been analyzed in terms of symmetry-adapted distortion modes. Despite their rather different room-temperature symmetries, a triply-degenerate unstable antiferrodistortive rigid unit mode (RUM) of the Al2 O4 tetrahedral framework is shown to be the dominant instability for both compounds. An orthorhombic configuration resulting from a single wave (1q) distortion mode competes with a hexagonal configuration resulting from three superposed such waves (3q). The very small energy difference between these two configurations in the case of BaAl2 O4 would explain the recent electron microscope observation of orthorhombic symmetry on the nanoscale. A second unstable mode of polar character (also a RUM for the tetrahedral framework) is also present. While this second instability is too weak to condense in BaAl2 O4, in the case of SrAl2 O4 it is fundamental to make the 1q configuration prevail. The condensation of this additional instability is the cause of the symmetry reduction in SrAl2 O4 to monoclinic. In contrast with previous literature, SrAl2 O4 is a proper ferroelectric and a pseudoproper ferroelastic, with an uncommon bilinear coupling between its spontaneous polarization and shear monoclinic strain. One expects direct switching of spontaneous polarization through a shear stress, and conversely switching of the ferroelastic spontaneous shear strain through an electric field. This property must be related to the elasticoluminescent and electroluminiscent properties reported in Eu-doped SrAl2 O4. The calculated energy maps have been systematically compared with variations in the so-called global instability index, introduced within the empirical bond valence model. The similarity of the variation in both quantities (for the most unstable distortion modes) reported in other systems is also observed here

An introduction to the tools hosted in the Bilbao Crystallographic Server

The programs hosted in the Bilbao Crystallographic Server (http://www.cryst.ehu.es) are briefly explained along with worked examples on various cases related to different fields of applications. It is our aim to have this text acting as a primer on the various usage of the crystallographic tools in conjunction with each other due to the modular structure of the server. For this reason, diverse topics such as crystallographic groups and their subgroups, pseudosymmetry, extinction conditions, k-vectors and irreducible representations have been discussed in the context