Determination Of Magnetic Structure Research Articles

Magnetic structures and their determination using group theory

The determination of magnetic structures is a special area of condensed matter research. While being fundamental to the understanding of electronic structures and properties, it remains a subject that is treated with difficulty and is full of incorrect solutions. This article is based around two goals: • The explanation of the different possible types of magnetic structure. • The demonstration of how symmetry leads to their proper description, and can aid their solution. In content, the first part of this article is based on the practicalities of what an experimenter should know in order to understand and describe a magnetic structure. In the second part, symmetry arguments will be shown to reduce the otherwise arduous task of determining a magnetic structure, to the investigation of a handful of possible structures.

Magnetic Structure Determinations at NBS/NIST.

Magnetic neutron scattering plays a central role in determining and understanding the microscopic properties of a vast variety of magnetic systems, from the fundamental nature, symmetry, and dynamics of magnetically ordered materials to elucidating the magnetic characteristics essential in technological applications. From the early days of neutron scattering measurements at NBS/NIST, magnetic diffraction studies have been a central theme involving many universities, industrial and government labs from around the United States and worldwide. Such measurements have been used to determine the spatial arrangement and directions of the atomic magnetic moments, the atomic magnetization density of the individual atoms in the material, and the value of the ordered moments as a function of thermodynamic parameters such as temperature, pressure, and applied magnetic field. These types of measurements have been carried out on single crystals, powders, thin films, and artificially grown multilayers, and often the information collected can be obtained by no other experimental technique. This article presents, in an historical perspective, a few examples of work carried out at the NIST Center for Neutron Research (NCNR), and discusses the key role that the Center can expect to play in future magnetism research.

Magnetic Structure Determination from Powder Diffraction Symmetry Analysis and Simulated Annealing

The classical approach for solving magnetic structures is the “trial and error” (TE) method. The reason is that many studies have been performed on relatively simple systems and the fact that the dominant isotropic exchange interactions, in absence of frustration, favour simple collinear structures. The improvement of the resolution of neutron powder diffractometers has allowed handling complex incommensurate magnetic systems. For solving complex magnetic structures the TE method is unable to provide appropriate results and other methods have to be used. In this communication the techniques for magnetic structure determination from neutron powder diffraction (NPD) data are reviewed. In the general case the magnetic moment of an atom in the crystal is given as a Fourier series. The Fourier coefficients, S , are complex vectors constituting the “unknowns” to be determined. These vectors define the magnetic structure and they correspond to the “atom positions” of an unknown crystal structure. The steps for solving magnetic structures from NPD are the following: i) Search for the propagation vector(s) {k}. The set {k} provides the translation symmetry of the spin configuration. ii) Symmetry analysis is needed to find the smallest set of free parameters. In general the vectors S are linear combinations of the basis functions of the irreducible representations of the wave vector group G j k

Determination of magnetic symmetry by optical second-harmonic generation

Optical second-harmonic (SH) spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic X-ray diffraction experiments are overcome. As an example, various antiferromagnetic compounds of the Mn 3+ and Cr 3+ ions are discussed.

Polarisation analysis for the determination of magnetic structures in high magnetic fields

We have upgraded an existing two axis spectrometer for polarisation analysis experiments using supermirror polarisers. The instrument is fully compatible with a complex sample surrounding, including high magnetic fields up to 7 T. The primary use of this spectrometer is the determination of spin directions. The polarisation analysis technique is well suited for problems where only a few magnetic reflections can be investigated for the determination of a structure as it provides selection rules, in addition, to the well-known dipolar selection rule. The instrument has been applied for the investigation of the field dependent phase diagram on K 2IrCl 6. There a multiple q structure is identified in high field which presumably can only be explained by the presence of biquadratic exchange interactions.

Polarised neutrons and complex antiferromagnets: an overview

Determination of magnetic structure from measurement of the intensities of neutrons (or X-rays) scattered by magnetic Bragg reflections is in some ways a more difficult problem than determination of the crystal structure. This is because the magnetic structure factor is a vector quantity so that directional as well as phase information is lost in measuring just the intensity. In this situation, the vector properties of the neutron's polarisation provide a way of recovering some of this lost information. The changes in direction of the neutron spin which take place on scattering by the fourier components of the magnetic induction in a crystal are highly dependent on their relative orientation. These changes can be measured using a neutron polarimeter which can determine the direction of scattered neutron polarisation for any chosen incident polarisation direction. This technique has been named spherical polarimetry. Using spherical polarimetry, it has been possible to solve a number of magnetic structure problems which were intractable by other means. The polarimetric data obtained from just a very few Bragg reflections may impose sufficient constraints on the possible magnetic structures to allow a unique model to be established. The technique has proved particularly valuable in the study of non-collinear magnetic structures where it has already shown that certain previously determined structures were incorrect.

Optical Tomography of a Sunspot. II. Vector Magnetic Field and Temperature Stratification

An observational determination of the three-dimensional magnetic and thermal structure of a sunspot is presented. It has been obtained through the application of the SIR inversion technique (Stokes Inversion based on Response functions) on a low-noise, full Stokes profile two-dimensional map of the sunspot as observed with the Advanced Stokes Polarimeter. As a result of the inversion, maps of the magnetic field strength, B, zenith angle, γ, azimuth, χ, and temperature, T, over 25 layers at given optical depths (i.e., an optical tomography) are obtained, of which those between log τ5 = 0 and log τ5 = -2.8 are considered to provide accurate information on the physical parameters. All over the penumbra γ increases with depth, while B is larger at the bottom layers of the inner penumbra (as in the umbra) but larger at the top layers of the outer penumbra (as in the canopy). The corrugation of the penumbral magnetic field already observed by other authors has been confirmed by our different inversion technique. Such a corrugation is especially evident in the zenith angle maps of the intermediate layers, featuring the presence of the so-called spines that we further characterize: spines are warmer and have a less inclined magnetic field than the spaces between them and tend to have a smaller gradient of γ with optical depth over the entire penumbra, but with a field strength which is locally stronger in the middle penumbra and locally weaker in the outer penumbra and beyond in the canopy. In the lower layers of these external parts of the sunspot, most of the field lines are seen to return to the solar surface, a result that is closely connected with the Evershed effect (e.g., Westendorp et al., the third paper in this series). The Stokes V net area asymmetry map as well as the average B, γ, and T radial distributions (and that of the line-of-sight velocities; see the third paper in this series) show a border between an inner and an outer penumbra with different three-dimensional structure. We suggest that it is in this middle zone where most of a new family of penumbral flux tubes (some of them with Evershed flow) emerge interlaced (both horizontally and vertically) among themselves and with the background magnetic field of the penumbra. The interlacing along the line of sight is witnessed by the indication of many points in the outer penumbra showing rapid transitions with height between two structures, one with very weak and inclined magnetic field at the bottom of the photosphere and the other with a stronger and less inclined magnetic field. Over the whole penumbra, and at all optical layers, a constant but weak deviation from radiality of some 5° is detected for the azimuth of the vector magnetic field, which may be in agreement with former detections but which is not significantly higher than the size of the errors for this parameter.

Study of disorder in a tetragonal tungsten bronze ferroelectric relaxor: a structural approach

Electron diffraction analysis, nuclear magnetic resonance measurements, structure determinations and refinements were performed on two ferroelectric lead-containing ceramics (classical and relaxor), with tetragonal tungsten bronze structure, in order to investigate the origin of the relaxor behaviour in such compounds. In both compounds the lead atoms are found to be off-centred in the CN (coordination number) 15 (A2) site. The main difference between the two compositions is the proportion of lead in this site: in the relaxor composition, theA2 site is at least half occupied by lead atoms. Disorder in the repartition of lead and potassium atoms in theA1 (CN 12) andA2 sites was also studiedviacombinatorial calculations to correlate the evolution of the relaxor behaviour in the Pb5Ta10O30–Li10Ta10O30–K10Ta10O30ternary system with composition. The combinatorial study demonstrated that the relaxor behaviour is enhanced by the disorder in cationic repartition.

Determination of the magnetic symmetry of hexagonal manganites by second harmonic generation

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites RMnO3 ( R = Sc, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.

A new protocol for the determination of magnetic structures using simulated annealing and representational analysis (SARA h)

The determination of magnetic structures from neutron diffraction data is often carried out by trial and error. Much time is wasted in the examination of structures that are in fact symmetry forbidden. The technique of representation analysis (RA) uses simple matrix calculations to provide model magnetic structures that can arise from a second-order phase transition, but has fallen into misuse because of its tedious nature. New Windows-based code performs these calculations automatically. Integration with refinement packages based on simulated annealing (SA) algorithms allows these models to be fitted against diffraction data. Combination of simulated annealing and representation analysis creates a powerful new protocol for the determination of magnetic structures.

Neutron diffraction and mössbauer effect study of quenched 112CdFe 2O 4

Neutron diffraction analysis revealed 5% occupancy of octahedral (B) spinel lattice sites by cadmium in a 112Cd-enriched CdFe 2O 4 sample prepared by the ceramic technique and quenched from 1273 K in water. The very small magnetic contribution to intense Bragg peaks at 1.3 K hampered the magnetic structure determination. ME investigation confirmed the partial disorder of the Fe 3+ magnetic moments on B sites.

Collinear ferromagnetism and spin orientation in the molecule-based magnetsM[N(CN)2]2(M=Co,Ni)

Zero-field unpolarized neutron powder diffraction has been used to study the low-T magnetic structure and {ital T}-dependent crystal structure of M[N(CN){sub 2}]{sub 2} (M=Co,Ni). Both compounds show collinear ferromagnetism with spin orientation along the {ital c} axis. The results provide the determination of a complete magnetic structure in the ordered state for a molecule-based magnet. The {ital c} lattice parameter exhibits negative thermal expansion, explained by a wine-rack-like deformation. {copyright} {ital 1999} {ital The American Physical Society}

The D3C project: improvements and new fields of science

In order to improve the characteristics and extend the fields of science investigated on the present polarised hot-neutron diffractometer D3B of the Institut Laue Langevin (ILL), we propose the project D3C. Taking advantage of the novel 3 He neutron spin filter presently available at the ILL, we can: (1) improve the peak count rates by optimising the monochromator irrespective of the spin selection process; (2) add polarisation analysis of the scattered beam. By featuring the best polarised flux at short wavelength in combination with a 10 T cryomagnet for optimised flipping ratio measurements and uniaxial polarisation analysis, or a dedicated zero-field neutron polarimeter Cryopad for carrying out three-dimensional polarisation analysis experiments, D3C will be the most powerful and flexible neutron machine in the field. Among the new fields of science, there are determination of exotic magnetic structures and the precision measurements of antiferromagnetic form factors in large Q → range.

Neutrons and synchrotron X-rays in materials science

We shall review some results in a few areas of material science in which neutron scattering and X-ray synchrotron scattering have exercised complementary (if not competitive!) roles. Three areas are selected: magnetism and the determination of magnetic structures; crystallography at high pressure; lattice dynamics and the phonon dispersion relations. In each case we compare the information on the same systems as provided by the two source of radiation.

On the determination of the internal magnetic structure by magnetic force microscopy

In this contribution it is proven mathematically that it is in principle impossible to determine the magnetic charge distribution inside a magnetic material by a method which measures the stray field outside the sample, such as magnetic force microscopy (MFM). A general source of stray field, E σ, is defined and it is shown that different solutions can be found for E σ that result in the same stray field. It is also shown how both a perpendicular and a longitudinal medium can be described with the same E σ. Using the equations for stray field, resulting from E σ, it is also proven that performing the same MFM measurement at different scanning heights does not provide any new information on the stray field for sample; from a measurement at one (constant) height, the stray field at all other heights can be calculated. Moreover, the component of the field parallel to the same plane can be obtained from a measurement of the field component perpendicular to the sample plane.

Some Achievements in Neutron Crystallography

In this article, some results are described in a few areas of crystallography in which the methods of neutron scattering have played a major role. Four areas are selected: the determination of magnetic structures, high-resolution powder diffraction, crystallography at high pressure, and the measurement of phonon-dispersion relations. In each case, the results are considered in the context of complementary information provided by synchrotron X-ray studies.

An Investigation of the Magnetic Properties of Sm1−xTiO3forx=0.03, 0.05, and 0.10: Magnetic Structure Determination of Sm0.97TiO3by Short-Wavelength Neutron Diffraction on Single Crystals

Single crystals of Sm0.97TiO3have been prepared and their magnetic properties have been investigated. Dc magnetic susceptibility measurements indicate paramagnetic Curie–Weiss behavior above 100 K whereas two magnetic transitions are observed atTN∼52 K andTN∼40 K. Similar observations for antiferromagnetic behavior have been made for thex=0.05 compound withTN∼40 K whereas for thex=0.10 compound this behavior vanishes. The magnetic structure determination of thex=0.03 compound has been accomplished by using low-temperature single-crystal neutron diffraction. The room temperature crystal structure is a distorted orthorhombic perovskite structure belonging toPnma, which is preserved down to 15 K. The magnetic structure is found to be consistent with aGxGymoment configuration on the Ti(III) sublattice and aCzmoment configuration on the Sm(III) sublattice. The magnetic moments are estimated to be 0.72(1) and 0.43(1)μBon the Ti(III) and Sm(III) sublattices, respectively. The orientations of the moments were found to be 7(3)° to thex-axis for Ti(III) and 2(2)° to thez-axis for Sm(III).

Yb2BaCoO5 magnetic and crystal structure determination from neutron scattering

The magnetic and crystal structure of Yb2BaCoO5 have been studied from powder neutron diffraction. The compound crystallizes in the orthorhombic space group Pnma, with lattice parameters: a=12.1745(2) Å, b=5.6594(1) Å, c=6.9993(1) Å. Bulk magnetic measurements reveal a jump in the temperature dependence of the susceptibility around 10 K, which corresponds to the antiferromagnetic ordering of the Yb3+ and Co2+ sublattices which is fully confirmed with neutron diffraction data. From the later, a magnetic structure with an identical cell to the chemical one (k=0) has been proposed to explain the onset of new reflections due to magnetic scattering that develop below TN≈9.4 K. The spin arrangement is described on the basis of CxAz symmetry modes for all magnetic sublattices.

Preparation and characterization of metal complexes with an extended TTF dithiolato ligand, bis(propylenedithiotetrathiafulvalenedithiolato)-nickelate and -cuprate

Novel monoanionic nickel and dianionic copper complexes with the extended TTF dithiolato ligand, propylenedithiotetrathiafulvalenedithiolate [ptdt2–=(S8C9H6)2– ], have been synthesized. Characterization of monoanionic tetraphenylphosphonium and tetramethylammonium salts of Ni(ptdt)2– and the dianionic tetraphenylphosphonium salt of Cu(ptdt)22– have been performed, using cyclic voltammetry, electrical resistivity measurements, magnetic susceptibility measurements and X-ray crystal structure determination. The geometries around the Ni atoms are almost square planar. In both Ni complexes, one of the extended ligands of Ni(ptdt)2– is overlapping with that of the adjacent anion separated by about half of the unit of the molecule, forming a one-dimensional chain. The adjacent chains are connected by transverse short S‥S contacts. Cu(ptdt)22– has a distorted tetrahedral geometry around the Cu atom and the dihedral angle between the planes of the dithiolato ligand is 54.2 °. The crystal structures of Ni(ptdt)2– and Cu(ptdt)22– complexes show the possibility of novel 2D or 3D intermolecular contacts through ptdt ligands. The complex [Me4N][Ni(ptdt)2 ]·Me2CO is a semiconductor with a room temperature conductivity of 1.4×10–3 S cm–1 and activation energy of 9.9×10–2 eV.

Magnetic Properties and Neutron Diffraction Study of the Chlorofluoride Series Ba2MM′F7Cl (M, M′=Mn, Fe, Co, Ni, Zn)

The magnetic properties of the new chlorofluoride series Ba2MM′F7Cl (M,M′=Mn, Fe, Co, Ni, Zn) have been investigated by susceptibility and magnetization measurements on powder or single-crystal, Mössbauer spectrometry, and neutron diffraction experiments. Our results allow a direct comparison with the magnetic behavior of the well-known series BaMF4(M=Mn, Fe, Co, Ni, Cu, Zn), whose structure is closely related to the chlorofluoride structure. High-temperature series expansion has been used in the case of the manganese and nickel compounds to determine the average magnetic exchange parameter. Mössbauer acquisitions on the Ba2FeMF7Cl series show that, despite the close similarity between the magnetic susceptibilities, hyperfine structure is greatly disturbed by chlorine substitution. The other main difference between both series is the absence of the spin–flop transition observed on the manganese fluoride and in the field-dependent transition observed on the nickel chlorofluoride. Indeed, the field dependence of the magnetization of a Ba2Ni2F7Cl single crystal shows the existence of a magnetic transition when (H) is parallel to (c). The determination of the magnetic structure of Ba2Ni2F7Cl by neutron powder diffraction allows us to propose a qualitative explanation of this transition. We also report the magnetic structure determination in the case of the cobalt compound. In both cases (Ni or Co compounds), the magnetic structures are closely related to those of the corresponding fluorides. The magnetic structure of the mixed compounds Ba2MnNiF7Cl and Ba2FeCoF7Cl are also reported.