Magnetic, electric and toroidal polarization modes describing the physical properties of crystals. NdFeO case.

The structure and the physical phenomena that occur in a crystal can be described by using a suitable set of symmetry-adapted modes. The classification of magnetic modes in crystals presented in Fabrykiewicz et al. [Acta Cryst.

Magnetic modes compatible with the symmetry of crystals.

A classification of magnetic point groups is presented which gives an answer to the question: which magnetic groups can describe a given magnetic mode? There are 32 categories of magnetic point groups which describe 64 unique magnetic modes: 16 with a ferromagnetic component and 48 without. This classification focused on magnetic modes is helpful for finding the magnetic space group which can describe the magnetic symmetry of the material.

Crystal symmetry for incommensurate helical and cycloidal modulations.

A classification of magnetic superspace groups compatible with the helical and cycloidal magnetic modulations is presented. Helical modulations are compatible with groups from crystal classes 1, 2, 222, 4, 422, 3, 32, 6 and 622, while cycloidal modulations are compatible with groups from crystal classes 1, 2, m and mm2. For each magnetic crystal class, the directions of the symmetry-allowed (non-modulated) net ferromagnetic moment and electric polarization are given.

Neutron Larmor diffraction on powder samples.

A hitherto unrecognized resolution effect in neutron Larmor diffraction (LD) is reported, resulting from small-angle neutron scattering (SANS) in the sample. Small distortions of the neutron trajectories by SANS give rise to a blurring of the Bragg angles of the order of a few hundredths of a degree, leading to a degradation of the momentum resolution. This effect is negligible for single crystals but may be significant for polycrystalline or powder samples.

Verification of the de Wolff hypothesis concerning the symmetry of β-MnO.

The symmetry lowering from tetragonal to orthorhombic is demonstrated using high-resolution diffraction and also justified by using the magnetic superspace groups formalism for the rutile-type compound β-MnO. The (lower) orthorhombic symmetry is observed at temperatures both below and above the Néel temperature. The magnetic ordering of β-MnO is of spin density type and not screw-type helical.

Crystal symmetry aspects of materials with magnetic spin reorientation.

The symmetry of materials which undergo a continuous spin reorientation has been analysed. It is shown that continuous spin reorientation is possible only in materials with triclinic or monoclinic crystal structure symmetry, i.e.

Lack of a threefold rotation axis in α-Fe₂O₃ and α-Cr₂O₃ crystals.

The crystal structure of α-Fe2O3 and α-Cr2O3 is usually described with the corundum-type trigonal crystal structure based on the space group R3¯c. There are, however, some observations of the magnetic ordering of both α-Fe2O3 and α-Cr2O3 that are incompatible with the trigonal symmetry. We show experimental evidence based on X-ray powder diffraction and supported by transmission electron microscopy that the symmetry of the crystal structure of both α-Fe2O3 and α-Cr2O3 is monoclinic and it is described with the space group C2/c (derived from R3¯c by removing the threefold rotation axis).

Crystal and magnetic structure in co-substituted BiFeO3.

Ultra-high-resolution neutron diffraction studies of BiFe(0.8)Co(0.2)O3 show a transition from a cycloidal space modulated spin structure at T = 10 K to a collinear G-type antiferromagnetic structure at T = 120 K.

Hierarchically structured scleractinian coral biocrystals.

Microscopic (AFM and FESEM) observations show that scleractinian coral biomineral fibers in extant Desmophyllum and Favia, and fossil Jurassic Isastrea are composed of nanocrystalline grains of about 30-100 nm in size. In contrast to these findings, SR diffraction data on the same coral materials exhibit narrow Bragg peaks suggesting much larger crystallite size. These seemingly contradicting results of microscopic and diffraction studies are reconciled within a new, minute-scale model of scleractinian biomineral fibers.

A Cretaceous scleractinian coral with a calcitic skeleton.

It has been generally thought that scleractinian corals form purely aragonitic skeletons. We show that a well-preserved fossil coral, Coelosmilia sp. from the Upper Cretaceous (about 70 million years ago), has preserved skeletal structural features identical to those observed in present-day scleractinians.