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. The proposed classification of superspace groups is tested on experimental studies of type‐II multiferroics published in the literature.
A classification of the symmetry of magnetic modulations is presented. Helical magnetic ordering is possible only in magnetic superspace groups with proper rotations only, i.e. from classes 1, 2, 222, 4, 422, 3, 32, 6 and 622. Cycloidal modulations are possible in groups from crystal classes 1, 2, m and mm2.
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. (2021), A77, 327–338 is extended to a classification of electric and toroidal (anapole) modes in crystals. These three classifications are based on magnetic point groups, which are used in two contexts: (i) the magnetic point group of the magnetic crystal class and (ii) the magnetic site‐symmetry point group of the Wyckoff position of interest. The classifications for magnetic, electric and toroidal modes are based on the properties of the three generalized inversions: space inversion 1, time inversion 1′ and the space‐and‐time inversion 1′. It is emphasized that none of these three inversions is more important than the other two. A new notation for symmetry operation symbols and magnetic point group symbols is proposed; each operation is presented as a product of one proper rotation and one generalized inversion. For magnetic, electric and toroidal orderings there are 64 modes: three pure ferro(magnetic/electric/toroidal) modes, 13 mixed ferro(magnetic/electric/toroidal) and antiferro(magnetic/electric/toroidal) modes, and 48 pure antiferro(magnetic/electric/toroidal) modes. The proposed classification of modes leads to useful observations: the electric and toroidal modes have many symmetry limitations similar to those already known for the magnetic modes, e.g. a continuous reorientation of the magnetic or electric or toroidal moments is possible only in triclinic or monoclinic symmetry. An antiferro(magnetic/electric/toroidal) ordering with a weak perpendicular ferro(magnetic/electric/toroidal) component is possible only in monoclinic or orthorhombic symmetry. The general classifications of magnetic, electric and toroidal modes are presented for the case of NdFeO3.
A classification of the modes for magnetic, electric and toroidal polarization in crystals is proposed. The classification relies on magnetic point groups. A new notation of magnetic point groups based on the decomposition on proper rotation and generalized inversions is used.
The layered oxide chalcogenides Ba3-xSrxFe2O5Cu2Ch2 (x = 0, 1, 2; Ch = S, Se) and BaCa2Fe2O5Cu2S2 are reported here for the first time. They are isostructural with the previously reported ...Sr3Fe2O5Cu2Ch2, crystallising in the I4/mmm space group. This structure is related to the n = 2 Ruddlesden-Popper type structure which is common for oxides and contains Sr3Fe2O5 perovskite-related slabs intergrown with Cu2Ch2 layers which resemble fragments of the antifluorite structure. In the oxide slabs, a double layer of FeO5 pyramids is formed by the sharing of apical oxide ions. Structural analysis shows a clear partial ordering of the alkaline earth cations of different sizes over the available 12 and 8-coordinate sites which correlates with the size variation of the alkaline earth cations. Long range magnetic ordering on a √2a × √2a × c expansion of the nuclear cell reveals nearest neighbour Fe3+ moments coupling antiferromagnetically via all the Fe–O–Fe linkages. In Ba3Fe2O5Cu2Se2, the moments are oriented in the ab-plane, whereas in Ba3-xSrxFe2O5Cu2Ch2 (x = 2; Ch = S, Se), the Fe3+ moments are tilted towards the c-axis, reflecting that high spin d5 ions with no orbital angular momentum have only a weak preference for a particular spin direction.
Cation site preferences determine alkaline earth ion ordering in layered oxide chalcogenides and long range ordered Fe3+ moments are controlled by the degree of covalency. Display omitted
•Novel iron oxide chalcogenides with Ba2+/Sr2+/Ca2+ ordering synthesised.•Ordered moment correlates inversely with Fe ion bond valence sum.•Long range antiferromagnetic ordering persists well above room temperature.•Magnetic ordering model depends on whether there is a single alkaline earth ion present, or a mixture.
In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this ...result, some equivalent characterizations of stochastic comparisons of sample ranges with respect to various stochastic orders are established. In this process, two open problems mentioned in Mao and Hu (2010) 16 are solved. The main results established here extend and strengthen several known results in the literature including those of Khaledi and Kochar (2000) 8, Zhao and Li (2009) 22 and Genest et al. (2009) 7.
In this paper, we investigate some multivariate integral stochastic orderings of skew-normal random vectors. We derive the results of the sufficient and/or necessary conditions by applying an ...identity for $ Ef({\mathbf Y})-Ef({\mathbf X}) $, where $ {\mathbf X} $ and $ {\mathbf Y} $ are multivariate skew-normal random vectors, $ f $ satisfies some weak regularity condition. The integral orders considered here are the componentwise convex, copositive, completely-positive orderings and their corresponding increasing ones as well as linear forms of stochastic orderings, which play a vital role in transforming the unmanageable multivariate components into an easy-to-handle univariate variable.
In this paper we revisit the borate systems, Sr4-xBaxNa(BO3)3 and illustrate their structural relationship with the perovskite structure. In these phases, the Na and B can be considered as forming an ...ordered arrangement on the perovskite small cation site, with the orientation of the oxygen atoms on the borate group such that the Na is octahedrally coordinated to O. In addition, we report the preparation of a new related solid solution series, Sr4-xBaxNa1-yLiy(BO3)3, showing a complete Sr/Ba solid solution series for y = 0.5. Through further investigation into Ca doping into Sr4Li(BO3)3, we have identified a new A site (Ca/Sr) ordered variant of this structure with structure refinement indicating a composition, Sr2·2Ca1·8Li(BO3)3. Thus, these borate systems represent interesting perovskite-type variants, with large oxygen deficiencies compared to a traditional perovskite brought about by ordered oxygen vacancies, and whose existence is dependent on cation ordering features.
•Synthesis of solid solutions series Sr4-xBaxNa0.5Li0·5(BO3)3.•Synthesis and structure determination of new ordered Sr2·2Ca1·8Li(BO3)3 system.•Relatable to oxygen vacancy ordered perovskite structures.
•Fe100-xPtx alloy films are prepared by ion beam sputtering technique.•Composition was tuned by precise control of exposed area of Fe and Pt to ion beam.•Chemical composition films are confirmed ...via × ray fluorescence and reflectivity.•Degree and type of chemical ordering is revealed via grazing incidence XRD.
Fe100-xPtx alloy films are fabricated by controlled ion beam sputtering. Composition of the films was tuned by varying the relative atomic percentage of iron and platinum via controlling the area exposed to the ion beam. Structural and magnetic properties of films are studied using x-ray reflectivity, x- ray fluorescence, x-ray diffraction and Magneto Optic Kerr Effect. Isochronal annealing of films was done at 500 °C for 1 hour. Evolution of L10 ordering upon thermal annealing is investigated and correlation with the relative atomic percentage has been observed and explained. The finding of the work is useful for the fabricating the future recording media material.
Effect of high‐energy mechanical milling on glassy AsxSe100 − x (5 ≤ x ≤ 75) is recognized with X‐ray powder diffraction analysis applied to their diffuse halos ascribed to intermediate—and ...extended‐range structural ordering, which are revealed respectively in the first sharp diffraction peak (FSDP) and principal diffraction peak (PDP). Straightforward interpretation of the results is developed within modified microcrystalline approach, treating diffuse halos as superposition of broadened Bragg‐diffraction reflexes from remnants of inter‐planar correlations, supplemented by inter‐atomic Ehrenfest‐diffraction reflexes from most prominent inter‐atomic and inter‐molecular correlations between cage‐like molecules (such As4Se4 and/or As4Se3). Milling is shown to be ineffective in glassy arsenoselenides near Se (x < 20), while causing increase in the FSDP width for glasses with 20 ≤ x ≤ 40 due to destroyed inter‐planar ordering. Remnants of cage‐like molecules in over‐stoichiometric As‐rich AsxSe100 − x glasses (40 ≤ x ≤ 75) disappear under milling, promoting formation of higher polymerized structural network. This milling‐driven reamorphization results in a drastic increase in the FSDP position and fragmentation impact on the correlation length of the FSDP‐responsible entities. Breakdown in intermediate‐range ordering in these glasses is accompanied by changes in their extended‐range ordering revealed in high‐angular shift and broadening of the PDP. This effect is concomitant with the disappearance of distant inter‐atomic correlations between quasi‐crystalline planes in the milled arsenoselenide glasses at a cost of prolonged correlations dominating in their extended‐range ordering.
The microstructure evolution and tensile properties of a newly designed Fe-21Mn-10Al-1C-5Ni (wt.%) lightweight steel subjected to two annealing conditions (inducing partial recrystallization and full ...recrystallization) and subsequent aging treatment have been investigated. In the as-annealed condition, the microstructure of the steel consists of polygonal B2 particles along grain boundaries of recrystallized austenite grains and plate-shape B2 particles within unrecrystallized austenite grains, with no B2 bands. In addition, there is a formation of nano-sized κ-carbide and D03 particles within austenite grains and B2 particles, respectively. Subsequent aging promotes the formation of intragranular κ-carbide and D03 nanoparticles within austenite grains and B2 particles, respectively. As a result, the present steel shows an ultrahigh yield strength of 1.6 GPa after aging, which is mainly due to the presence of fine B2 particles within austenite grains and along grain boundaries as well as the additional strengthening effect of nano-sized κ-carbide and D03 particles present in austenite grains and B2 particles, respectively. The steel possesses good ductility (total elongation of 20%) even at such an ultrahigh strength level in the as-aged condition, surpassing the tensile properties of other B2 and κ-carbide strengthened lightweight steels.
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To achieve a large terahertz (THz) amplitude from a spintronic THz emitter (STE), materials with 100% spin polarisation such as Co‐based Heusler compounds as ferromagnetic layer are required. ...However, these compounds are known to loose their half‐metallicity in the ultrathin film regime, as it is difficult to achieve L21 ordering, which has become a bottleneck for the film growth. Here, the successful deposition using room temperature DC sputtering of the L21 and B2 ordered phases of the Co2FeAl full Heusler compound is reported. Co2FeAl is used as ferromagnetic layer together with highly orientated Pt as nonferromagnetic layer in the Co2FeAl/Pt STE, where an MgO (10 nm) seed layer plays an important role to achieve the L21 and B2 ordering of Co2FeAl. The THz generation in the Co2FeAl/Pt STE is presented, which has a bandwidth of 0.2–4 THz. The THz electric field amplitude is optimized with respect to thickness, orientation, and growth parameters using a thickness dependent model considering the optically induced spin current, superdiffusive spin current, inverse spin Hall effect, and the THz attenuation in the layers. This study, based on the full Heusler Co2FeAl compound opens up a plethora of possibilities in STE research involving full Heusler compounds.
The ultrathin L21 and B2 ordered Co2FeAl Heusler compounds are utilized as spintronic terahertz emitter (STE), grown on MgO‐ and Si‐substrates using room temperature sputtering. The terahertz electric field amplitude of Co2FeAl/Pt STE is similar to conventional Fe/Pt (referred as green‐color in the image). This study, based on the Co2FeAl compound opens up plethora of possibilities in STE research involving Heusler compounds.
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