Magnetic Space Group Research Articles

A study of magnetic ordering in multiferroic hexagonal Ho1-xDyxMnO3

This paper investigates the magnetic properties of Ho1-xDyxMnO3 by considering the inter-planar Mn3+-O-O-Mn3+ interaction. The theoretical analysis shows that the asymmetric in-plane exchange interaction couples the in-plane and inter-planar Mn3+ spin structures via asymmetry parameter δ. This leads to the existence of both the in-plane and inter-planar ordering, which in turn restricted the allowed magnetic space groups to Γ1 and Γ4. The experimental studies confirmed the concomitant nature of the in-plane and the inter-planar ordering at TN, TSR, and T2. It also showed that the magnetic phase diagram is dominated by the allowed magnetic structures Γ1 and Γ4. Furthermore, an effort is made to resolve the inconsistency regarding the TSR (32 or 40 K). The studies revealed that the antiferromagnetic inter-planar interaction is switched to the ferromagnetic interaction (40 K) upon cooling, which in turn drives the spin reorientation at 32 K. The Mn3+ spin structure is seen to be coupled to rare earth sub-lattice through the modulation of the inter-planar interaction.

Crystallography and Magnetic Phenomena

This essay describes the development of groups used for the specification of symmetries from ordinary and magnetic point groups to Fedorov and magnetic space groups, as well as other varieties of groups useful in the study of symmetric objects. In particular, we consider the problem of some incorrectness in Vol. A of the International Tables for Crystallography. Some results of tensor calculus are presented in connection with magnetoelectric phenomena, where we demonstrate the use of Ascher’s trinities and Opechowski’s magic relations and their connection. Specific tensor decomposition calculations on the grounds of Clebsch Gordan products are illustrated.

Magnetic order and crystal structure study of YNi4Si-type NdNi4Si

Magnetic measurements and neutron powder diffraction investigation of the magnetic structure of the orthorhombic YNi4Si-type (space group Cmmm) NdNi4Si compound are presented. The magnetocaloric effect of NdNi4Si is calculated in terms of the isothermal magnetic entropy change and it reaches the maximum value of –3.3J/kgK for a field change of 50kOe near TC=12K. Below ~12K, NdNi4Si exhibits a commensurate b-axis collinear ferromagnetic ordering with the Cmm′m magnetic space group in a zero magnetic field. At 1.5K, the neodymium atoms have the magnetic moment of 2.37(5)μB. The orthorhombic crystal structure and its thermal evolution are discussed in comparison with the CaCu5-type compound.

Full propagation-vector star antiferromagnetic order in quantum spin trimer system Ca3CuNi2(PO4)4

We show that the antiferromagnetic structure in the quantum spin trimer system Ca3CuNi2(PO4)4 is based on both arms of propagation vector k star of the paramagnetic space group C2/c. The structure is generated by a symmetric direction of the order parameter of two-dimensional irreducible representation of C2/c with one active magnetic mode and corresponds to the Shubnikov magnetic space group Ca2/c. We reveal the relation between representation analysis in the propagation vector formalism and Shubnikov symmetry. These types of multi-k structures are extremely rarely observed experimentally. To further prove the specific magnetic structure we have performed the calculations of the spin expectation values in the isolated Ni2+–Cu2+–Ni2+ trimer with realistic Hamiltonian. The calculated spin values 〈SNi〉 = 0.9 and 〈SCu〉 = 0.3 are within 10% accuracy in agreement with the experiment, providing a strong complementary argument in favor of a multi-arm magnetic structure.

Multipole order and global/site symmetry in the hidden-order phase ofURu2Si2

On the basis of group theory and the first-principles calculations, we investigate high-rank multipole orderings in URu2Si2, which have been proposed as a genuine primary order parameter in the hidden order phase below 17.5K. We apply Shubnikov group theory to the multipole ordered states characterized by the wave vector Q = (0, 0, 1) and specify the global/site symmetry and the secondary order parameters, such as induced dipole moments and change in charge distribution. We find that such antiferroic magnetic multipole orderings have particularly advantageous to conceal the primary order parameter due to preserving high symmetry in charge distribution. Experimental observations of the inherent low-rank multipoles, which are explicitly classified in this paper, will be key pieces to understand the puzzling hidden order phase.

Comment on “Canonical magnetic insulators with isotropic magnetoelectric coupling”

Coh et al. presented in [Phys. Rev. B 88, 121106(R) (2013)] a systematic search of the simplest so-called ``canonical'' structures allowing isotropic magnetoelectric response, and reported a total of 30 such magnetic configurations. Using magnetic symmetry we show in this Comment that this listing is severely incomplete, and 14 additional distinct cases satisfying the same conditions should be added. The complete list of these elementary magnetic arrangements is then presented in a short and efficient form as distinct Wyckoff positions of some cubic magnetic space groups.

Electronic properties of a distorted kagome lattice antiferromagnetDy3Ru4Al12

Electronic properties of ${\mathrm{Dy}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$ (hexagonal crystal structure, Dy atoms form distorted kagome nets) are studied on a single crystal by means of magnetization, neutron diffraction, specific heat, and resistivity measurements. The onset of a long-range magnetic order of Dy moments occurs at 7 K through a first-order phase transition. The compound has a noncollinear antiferromagnetic structure with a propagation vector (1/2 0 1/2). The configuration of the Dy moments is consistent with the monoclinic Shubnikov group ${C}_{c}2/c$. The \ensuremath{\gamma} coefficient in the temperature linear term of the specific heat is strongly enhanced to 500 mJ ${\mathrm{mol}}^{\ensuremath{-}1}$ ${\mathrm{K}}^{\ensuremath{-}2}$ taking into account the localized nature of Dy magnetism. An additional contribution originates from spin fluctuations induced in the $4d$ subsystem of Ru by the exchange field acting from the Dy $4f$ moments. In an applied magnetic field ${\mathrm{Dy}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$ displays magnetization jumps along all crystallographic directions. All the metamagnetic transitions are accompanied by large positive magnetoresistance. The maximum effect (125%--140%) is attained for current along the [100] axis and field along the [120] or [001] axes. The large positive effect is explained by changes in the conduction electron spectra through the jumps as the conduction electrons interact with localized magnetic moments.

Phase-transition studies at the Bilbao Crystallographic Server

The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with crystallographic databases and programs. The server is built on a core of databases that contain crystallographic data of space groups, magnetic space groups, subperiodic groups and their symmetry relations. Parallel to the crystallographic software we have developed specialized tools for the analysis of complex solid-state physics and structural chemistry problems. The aim of this contribution is to report on databases and computer programs of the server that facilitate complete and thorough phase-transition studies. Starting from the experimental structures of the high- and low-symmetry phases the program STRUCTURE RELATIONS studies the crystal-structure relationship between two phases. It is characterized by a global distortion that, in general, can be decomposed into homogeneous strain and atomic displacement field. The program AMPLIMODES [2] performs the decomposition of the global distortion into symmetry-mode contributions, and the determination of the corresponding polarization vectors. This type of analysis separates the correlated atomic displacements that are fundamental for the phase stability, the so-called primary modes, from the weaker distortions of limited relevance for the transition mechanism. The server also offers online tools for the evaluation of the pseudosymmetry of a given structure with respect to a supergroup of its space group [3]. The detection of structural pseudosymmetry as the consequence of a small distortion of a higher symmetry is a powerful method for the prediction of new ferroic materials. Recently, computer databases and tools for the analysis of magnetic phase transitions have been implemented. Case studies will accompany the presentation of the programs offered by the Bilbao Crystallographic Server and will illustrate their capacities and efficiency in phase-transition studies.

Double antisymmetry in magnetic structures

This work follows from the recent introduction of the rotation-reversal operation intended to be analogous to the time-reversal operation used to describe the symmetry of magnetic structures. As a second independent antisymmetry operation, this operation "doubles" the antisymmetry of the magnetic space groups, hence the term double antisymmetry. Supposing the consideration of both rotation-reversal and time-reversal symmetry, it was found that there are 17,803 types of symmetry that a crystal could exhibit; the 1,651 magnetic space group types being a subset of these, just as the 230 crystallographic space group types are a subset of the magnetic space group types. In addition to discussing the methods applied to determine these types, describing their properties, and listing their symmetry diagrams (available online), the implications for symmetry constraints in magnetic structure determination will be explored.

Multi-k magnetic order in Ca3CuNi2(PO4)4: irrep approach and Shubnikov symmetry

The multi-k magnetic structures with propagation vectors k being the arms of the propagation vector star rarely can be justified experimentally. We show that the antiferromagnetic structure in the low dimensional quantum spin trimer system Ca3CuNi2(PO4)4 is based on the full star of propagation vector k=[1/2,1/2,0] of the paramagnetic space group C2/c. The relation between representation analysis in the propagation vector formalism and Shubnikov magnetic space group (MSG) symmetry is examined in details. A symmetry restrictive MSG that excellently fits the experimental data can be constructed only with the use of the full star. The magnetic structure is further supported by the calculations of the spin expectation values of the isolated Ni-Cu-Ni trimer with realistic Hamiltonian.

Open Meeting of the Commission on International Tables for Crystallography

The development of the seriesInternational Tables for Crystallographysince the 2011 Congress in Madrid will be discussed. The series includes eight published volumes with a ninth expected before the end of 2014 and definite plans for a tenth. A new edition of Volume A (Space-group symmetry, Editor Mois Aroyo) is nearly ready. A great deal of work has been done on the associated onlineSymmetry Database. Volume A1 (Symmetry relations between space groups, 2011, editors Hans Wondratschek and Ulrich Müller) is the companion volume. Work on a revision of theBrief Teaching Editionwill begin once the new Volume A is finished. Volume B (Reciprocal space, 2010; Editor Gervais Chapuis, who succeeded Uri Shmueli in 2011) and Volume C (Mathematical, physical and chemical tables, 2006, Editor Richard Welberry) are undergoing revisions, which will be major. The volumes will be reorganized with those topics connected to reciprocal space in B and those connected to direct space in C. A new edition of Volume D (Physical properties of crystals, Editor André Authier) was completed in 2013. A new edition of Volume F (Crystallography of biological macromolecules, Editors Eddy Arnold, Daniel Himmel, and Michael Rossmann) appeared in 2012. A new Volume H onPowder diffraction(Editors Chris Gilmore, Jim Kaduk, and Henk Schenk) is nearing completion. A new Volume I onXAFS(Editors Chris Chantler, Federico Boscherini, and Bruce Bunker) is in the planning stage. The Commission on Magnetic Structures is developing plans for a volume. In the meantime Danny Litvin's compilation of 1-, 2-, and 3-dimensional magnetic subperiodic groups and space groups was published as an e-book by the IUCr in 2013. Ideas for future developments will be welcome.

Symmetry constraints in frustrated magnets with strong magnetoelastic coupling

Geometrical frustration, related to the specific topology of certain crystal structures, plays a crucial role in forming exotic magnetic ground states. The presence of frustrated spins often leads to the suppression of long-range magnetic ordering and promotes short-range correlations due to fluctuations between nearly or totally degenerate ground states. The well-known structural topologies causing the presence of geometrical frustration are the three-dimensional pyrohlore and two-dimensional Kagome lattices. Compounds whose structural motif embraces these lattices are of great interest as model systems and have been the focus of numerous studies. In some cases, frustration is partially or entirely released by structural distortions through a strong magnetoelastic coupling and long-range magnetic order is established at a finite temperature. In the resulting distorted phases, complex noncollinear or partially disordered spin configurations can be observed. The phase transitions to the ordered state are quite often first order and may involve several irreducible representations of the paramagnetic space group and sometimes, like in the case of ZnCr2O4, even several propagation vectors which do not belong to the same star. The approach to determine magnetic structures in these systems, based on representation theory, should take into account the coupling free-energy invariants relating the magnetic and structural order parameters. Application of magnetic space groups and superspace groups is especially useful and can be efficiently combined with the representation theory. Based on specific examples, I will demonstrate how both approaches can be combined to provide symmetry constraints sufficient to solve complex magnetic structures in some geometrically frustrated systems.

Sixty Five Years of Magnetic Structures. Present and Future of Magnetic Crystallography

Magnetic Crystallography is a sub-field of Crystallography concerned with the description and determination of the magnetisation density in solids. A magnetic structure corresponds to a particular spatial arrangement of magnetic moments that sets up below the ordering temperature. The determination of magnetic structures is mainly done using neutron diffraction (powder and single crystals) and in special cases the use of polarized neutrons is necessary to solve ambiguities found in the interpretation of magnetic neutron diffraction data. We can consider that Magnetic Crystallography starts with the seminal paper by C.G. Shull and S. Smart on the magnetic structure of MnO published the 29 August 1949 in the Physical Review 76, 1256. The symmetry properties of periodic arrangement of atoms are well described by the 230 space group types in three dimensions, however more complex spatial arrangements of atoms may need to be described by periodicity in higher dimensions. Incommensurate, composite and quasi-crystal structures represent a relatively small part of the huge amount of materials that can be described by conventional Crystallography, however many magnetic structures are non-commensurate: the periodicity of the orientation of the magnetic moments is not commensurate with the underlying crystal structure. The symmetry properties of magnetic structures are traditionally described using two different approaches: the magnetic Shubnikov groups [1] and the group representation analysis [2-3]. In this talk we shall describe how these approaches have been established historically and the advantages of the new trend towards the use of magnetic superspace groups. A review of the most important papers and milestones in magnetic neutron scattering as well as in the symmetry concepts will be presented. The current analytical tools and methods for determining magnetic structures and their symmetry will briefly be described.

Monoclinic deformation of the crystal lattice of hematite α-Fe2O3

Lineshape analysis of high resolution synchrotron radiation diffraction patterns of polycrystalline α-Fe2O3 powders show distortions from trigonal (space group R-3c) symmetry. The symmetry lowering is observed for α-Fe2O3 polycrystalline powders from several commercial vendors. The experimental observations can be explained by assuming a monoclinic symmetry (space group C2/c). The relative differences between the monoclinic and the hexagonal lattice constants are of the order of 10−4. The monoclinic symmetry of the crystal structure of α-Fe2O3 (C2/c) is in agreement with magnetic space group analysis [American Mineralogist 95 (2010) 974].

Magnetic order of YNi4Si-type TbNi4Si

Magnetic measurements and neutron powder diffraction investigation of the magnetic structure of the YNi4Si-type TbNi4Si compound are presented. The magnetocaloric effect of TbNi4Si is calculated in terms of the isothermal magnetic entropy change and it reaches the maximum value of –6.3J/kgK for a field change of 0–50kOe near TC of ~37K.Below ~37K and in a zero applied magnetic field, TbNi4Si exhibits a commensurate b-axis collinear ferromagnetic ordering with the Cmm′m magnetic space group. At 1.5K, the terbium magnetic moment reaches the value of 8.66(6)μB.

Magnetic order of the La3NiGe2-type Ho3NiGe2

Magnetic measurements and neutron powder diffraction investigation of the magnetic structure of the La3NiGe2-type Ho3NiGe2 compound are presented. It is found that below TC=43K Ho3NiGe2 exhibits a commensurate ac-plane mixed antiferromagnetic–ferromagnetic ordering with Pn׳ma magnetic space group. At 1.5K the holmium magnetic moment reaches the value of 9.1(2)μB.

Evolution of two-dimensional antiferromagnetism with temperature and magnetic field in multiferroicBa2CoGe2O7

We report on spherical neutron polarimetry and unpolarized neutron diffraction in zero magnetic field as well as flipping ratio and static magnetization measurements in high magnetic fields on the multiferroic square lattice antiferromagnet ${\text{Ba}}_{2}{\text{CoGe}}_{2}{\text{O}}_{7}$. We found that in zero magnetic field the magnetic space group is $C{m}^{\ensuremath{'}}m{2}^{\ensuremath{'}}$ with sublattice magnetization parallel to the [100] axis of this orthorhombic setting. The spin canting has been found to be smaller than $0.{2}^{\ensuremath{\circ}}$ in the ground state. This assignment is in agreement with the field-induced changes of the magnetic domain structure below 40 mT as resolved by spherical neutron polarimetry. The magnitude of the ordered moment has been precisely determined. Above the magnetic ordering temperature short-range magnetic fluctuations are observed. Based on the high-field magnetization data, we refined the parameters of the recently proposed microscopic spin model describing the multiferroic phase of ${\text{Ba}}_{2}{\text{CoGe}}_{2}{\text{O}}_{7}$.

Multiferroic (ferroelastic/ferromagnetic/ferrimagnetic) aspects of phase transitions in RCo2 Laves phases

Magnetic phase transitions in RCo2 Laves phases with R as a rare earth element are accompanied by changes in crystallographic space group. For purely structural transitions they would be described as improper ferroelastic and therefore fulfil the condition for multiferroic phase transitions in combining two out of three properties, ferro/antiferromagnetism, ferroelectricity and ferroelasticity. Here lattice parameter data from the literature and new measurements of elastic and anelastic properties, by resonant ultrasound spectroscopy, for NdCo2 and ErCo2 have been analysed from this perspective. The temperature dependence of symmetry-breaking shear strains is consistent with the cubic ↔ tetragonal transition in NdCo2 being close to tricritical in character and the cubic ↔ rhombohedral transition in ErCo2 being first order. Elastic softening and acoustic loss within the stability ranges of the ferroelastic phases can be understood in terms of a combination of intrinsic softening due to strain/order parameter coupling and ferroelastic twin-wall motion. Softening ahead of the transitions does not fit with standard macroscopic descriptions of dynamic effects from other systems but, rather, in the case of NdCo2, might be attributed to the involvement of a second zone centre order parameter related to a separate instability driven by cooperative Jahn–Teller distortions. In ErCo2, acoustic loss in the temperature interval above the transition point is discussed in terms of a possible tweed microstructure associated with strain coupling to local magnetic ordering. The overall multiferroic behaviour can be understood in terms of a single magnetic order parameter (irrep of magnetic space group ) which couples with a structural order parameter (irrep or ). The coupling is linear/quadratic which, in the case of two separate instabilities, causes them to combine in a single multiferroic phase transition.

Symmetry-protected hidden order and magnetic neutron Bragg diffraction by URu2Si2

We investigate how the order parameter of a continuous phase transition can be protected from view by symmetry in a magnetic crystal. The symmetry in question forbids atomic displacements and formation of magnetic dipoles, rendering the order parameter invisible in standard x-ray and magnetic neutron Bragg diffraction. Analysis of the allowed magnetic space-groups reveals exact properties of the hidden order parameter. We demonstrate that Bragg spots forbidden by the chemical structure can unveil magnetic hidden order. The method is applied to URu2Si2, which has been thoroughly investigated in the past few decades using all manner of experimental techniques. Starting from the established chemical structure of URu2Si2, we have performed a critical analysis of available data for magnetic neutron Bragg diffraction.

Magnetic structure in the spin liquid Tb2Ti2O7induced by a [111] magnetic field: Search for a magnetization plateau

We have studied the field-induced magnetic structures of Tb${}_{2}$Ti${}_{2}$O${}_{7}$ pyrochlore by single-crystal neutron diffraction under a field applied along the [111] axis, up to $H=12$ T and down to $T=40$ mK. We refined the magnetic structures with $\mathbit{k}=\mathbf{0}$ propagation vector by performing a symmetry analysis in the space group $R\overline{3}m$, reducing the number of free parameters to three only. The Tb moments gradually reorient towards the field direction, keeping close to a ``3-in, 1-out / 1-in, 3-out'' spin structure (magnetic space group $R\overline{3}{m}^{\ensuremath{'}}$) in the whole measured field range 0.05--12 T. Our results rule out the ``all-in/all-out'' structure previously proposed and do not support the existence of a magnetization plateau. We perform a quantitative comparison with mean-field calculations and we propose the presence of a low-temperature dynamic symmetry breaking of the local trigonal symmetry, akin to a dynamic Jahn-Teller effect, i.e., preserving the overall cubic symmetry. We discuss the possible origin of this off-diagonal mixing term in the crystal field Hamiltonian in terms of quadrupole-quadrupole interaction or magnetoelastic effects.