Polarized Neutron Diffraction Data Research Articles

Spin-resolved atomic orbital model refinement for combined charge and spin density analysis: application to the YTiO3 perovskite.

A new crystallographic method is proposed in order to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data. This atomic orbital model is applied to the YTiO3 perovskite crystal, where orbital ordering has previously been observed by several techniques: X-ray diffraction, polarized neutron diffraction and nuclear magnetic resonance. This method gives the radial extension, orientation and population of outer atomic orbitals for each atom. The interaction term between Ti3+, Y3+ cations and O2- ligands has been estimated. The refinement statistics obtained by means of the orbital method are compared with those obtained by the multipole model previously published.

Spin-resolved atomic orbital model refinement for combined charge and spin density analysis: application to the perovskite

A new crystallographic method is proposed in order to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data. This atomic orbital model is applied to the YTiO3 perovskite crystal, where orbital ordering has previously been observed by several techniques: X-ray diffraction, polarized neutron diffraction and nuclear magnetic resonance. This method gives the radial extension, orientation and population of outer atomic orbitals for each atom. The interaction term between Ti3+, Y3+ cations and O2− ligands has been estimated. The refinement statistics obtained by means of the orbital method are compared with those obtained by the multipole model previously published.

A new mathematical approach to finding global solutions of the magnetic structure determination problem

Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensed-matter physics and chemistry to advanced manufacturing. It is typically performed using a neutron diffraction technique; however, finding global solutions of the magnetic structure optimization problem represents a significant challenge. Generally, it is not possible to mathematically prove that the obtained magnetic structure is a truly global solution and that no solution exists when no acceptable structure is found. In this study, the global optimization technique called semidefinite relaxation of quadratic optimization, which has attracted much interest in the field of applied mathematics, is proposed to use as a new analytical method for the determination of magnetic structure, followed by the application of polarized neutron diffraction data. This mathematical approach allows avoiding spurious local solutions, decreasing the amount of time required to find a tentative solution and finding multiple solutions when they exist.

Spin density in YTiO3 : I. Joint refinement of polarized neutron diffraction and magnetic x-ray diffraction data leading to insights into orbital ordering

Orbital ordering below 30 K was previously observed in the ferromagnetic ${\text{YTiO}}_{3}$ compound both by polarized neutron diffraction (PND) and x-ray magnetic diffraction (XMD). In this paper we report a procedure for the joint refinement of a unique spin-density model based on both PND and XMD data. The distribution of the unpaired $3d$ electron of titanium is clearly seen on the magnetization density reconstructed by the maximum entropy method from the PND data collection at 5 K. The ${\text{Ti}}^{3+}$ $3d$ orbital populations obtained by joint model refinement are discussed in terms of the orbital ordering scheme. Small but significant magnetic moments on apical oxygen ${\text{O}}_{1}$ and yttrium atoms are found. The agreement between experimental and theoretical spin densities obtained using density functional theory is discussed.

When combined X-ray and polarized neutron diffraction data challenge high-level calculations: spin-resolved electron density of an organic radical.

Joint refinement of X-ray and polarized neutron diffraction data has been carried out in order to determine charge and spin density distributions simultaneously in the nitronyl nitroxide (NN) free radical Nit(SMe)Ph. For comparison purposes, density functional theory (DFT) and complete active-space self-consistent field (CASSCF) theoretical calculations were also performed. Experimentally derived charge and spin densities show significant differences between the two NO groups of the NN function that are not observed from DFT theoretical calculations. On the contrary, CASSCF calculations exhibit the same fine details as observed in spin-resolved joint refinement and a clear asymmetry between the two NO groups.

Insights on spin delocalization and spin polarization mechanisms in crystals of azido copper(II) dinuclear complexes through the electron spin density Source Function.

The Source Function (SF) tool was applied to the analysis of the theoretical spin density in azido CuII dinuclear complexes, where the azido group, acting as a coupler between the CuII cations, is linked to the metal centres either in an end-on or in an end-end fashion. Results for only the former structural arrangement are reported in the present paper. The SF highlights to which extent the magnetic centres contribute to determine the local spin delocalization and polarization at any point in the dimetallic complex and whether an atom or group of atoms of the ligands act in favour or against a given local spin delocalization/polarization. Ball-and-stick atomic SF percentage representations allow for a visualization of the magnetic pathways and of the specific role played by each atom along these paths, at given reference points. Decomposition of SF contributions in terms of a magnetic and of a relaxation component provides further insight. Reconstruction of partial spin densities by means of the Source Function has for the first time been introduced. At variance with the standard SF percentage representations, such reconstructions offer a simultaneous view of the sources originating from specific subsets of contributing atoms, in a selected molecular plane or in the whole space, and are therefore particularly informative. The SF tool is also used to evaluate the accuracy of the analysed spin densities. It is found that those obtained at the unrestricted B3LYP DFT level, relative to those computed at the CASSCF(6,6) level, greatly overestimate spin delocalization to the ligands, but comparatively underestimate magnetic connection (spin transmission) among atoms, along the magnetic pathways. As a consequence of its excessive spin delocalization, the UB3LYP method also overestimates spin polarization mechanisms between the paramagnetic centres and the ligands. Spin delocalization measures derived from the refinement of Polarized Neutron Diffraction data seem in general superior to those obtained through the DFT UB3LYP approach and closer to the far more accurate CASSCF results. It is also shown that a visual agreement on the spin-resolved electron densities ρα and ρβ derived from different approaches does not warrant a corresponding agreement between their associated spin densities.

An unique model for joint refinement of (polarised) neutron and X-ray data

A new charge and spin density model and the corresponding refinement software were recently developed to combine X-ray and polarised neutron diffraction experiments [1,2]. This joint refinement procedure allows for an access to both the charge and spin densities but also to spin up ( ) and spin down ( ) electron distributions. These two quantities ( and ) were thus separately modelled and for the first time it was possible to compare them with theoretical results. The first part of the presentation will introduce the refinement procedure and describe its application to the case of an end-to-end azido double bridged copper(II) complex[3]. The results of this joint refinement of X-ray and polarized neutron diffraction data will be compared to theoretical calculations. The second part will be devoted to recent applications to other materials including a purely organic radical.

First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments.

Since the 1980s it has been possible to probe crystallized matter, thanks to X-ray or neutron scattering techniques, to obtain an accurate charge density or spin distribution at the atomic scale. Despite the description of the same physical quantity (electron density) and tremendous development of sources, detectors, data treatment software etc., these different techniques evolved separately with one model per experiment. However, a breakthrough was recently made by the development of a common model in order to combine information coming from all these different experiments. Here we report the first experimental determination of spin-resolved electron density obtained by a combined treatment of X-ray, neutron and polarized neutron diffraction data. These experimental spin up and spin down densities compare very well with density functional theory (DFT) calculations and also confirm a theoretical prediction made in 1985 which claims that majority spin electrons should have a more contracted distribution around the nucleus than minority spin electrons. Topological analysis of the resulting experimental spin-resolved electron density is also briefly discussed.

Joint Refinement of Charge and Spin Densities

A new charge and spin density model and the corresponding refinement software were recently developed to combine X- ray and polarized neutron diffraction experiments [1] . This joint refinement procedure allows getting access to both charge and spin densitiy distributions by refining both spin up and down parameters for magnetic atoms. The paper is focused on the refinement procedure and its application to the case of an end-to-end azido double bridged copper(II) complex. The results of this joint refinement of X-ray and polarized neutron diffraction data are presented.

Experimental determination of spin-dependent electron density by joint refinement of X-ray and polarized neutron diffraction data

New crystallographic tools were developed to access a more precise description of the spin-dependent electron density of magnetic crystals. The method combines experimental information coming from high-resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) in a unified model. A new algorithm that allows for a simultaneous refinement of the charge- and spin-density parameters against XRD and PND data is described. The resulting software MOLLYNX is based on the well known Hansen-Coppens multipolar model, and makes it possible to differentiate the electron spins. This algorithm is validated and demonstrated with a molecular crystal formed by a bimetallic chain, MnCu(pba)(H(2)O)(3)·2H(2)O, for which XRD and PND data are available. The joint refinement provides a more detailed description of the spin density than the refinement from PND data alone.

Determination of atomic site susceptibility tensors from polarized neutrondiffraction data

Polarized neutron diffraction provides information about themagnetization density of each individual crystallographic site. In thepresent paper the role of the atomic site susceptibility tensor χijaccounting for the magnetic response of individual atoms to an external magneticfield is discussed. The symmetry of this tensor is very similar to that of the tensoruijdescribing the thermal motion of atoms. By analogy with the atomicdisplacement parameters (ADPs), atomic susceptibility parameters (ASPs) can beintroduced. The six independent ASPs can be determined from polarizedneutron flipping ratio measurements and visualized as magnetic ellipsoidswhich are analogous to the thermal ellipsoids obtained from ADPs. If thelocal anisotropy is small, these magnetic ellipsoids approximate to sphereswith diameters proportional to the induced magnetization. In other cases,anomalous (elongated or flattened) ellipsoids will occur. The ASPs have beendetermined for the compound Nd3−xS4 which has the Th3P4 structure.They correspond to strongly oblate magnetic ellipsoids; in contrast, in theisomorphous compound Sm3Te4 the magnetic ellipsoids are found to be prolate.

Multiple scattering correction of polarized neutron diffraction data

In this article a simple-to-use analytic procedure for the correction of multiple scattering effects in polarized neutron diffraction experiments is presented. It is demonstrated that assuming (i) same scattering probabilities for multiple scattering of different order (>1) and (ii) isotropic multiple scattering the correction reduces to a linear transform of the differential cross-section in single-scattering approximation. The correction is fully determined by a single parameter. This parameter is not the sample transmission but can be related to it approximately. The relation also involves details of the sample shape. The correction itself is shown to be accurate in the treatment of simulated as well as experimental data. Only for high coherent scattering (deuterated samples with low transmission) deviations due to double-Bragg scattering become obvious.

13C NMR evidence for Fermi-contact interaction and spin delocalization on the ligands in the nanomagnet MN 12O 12-acetate

13C NMR measurements have been carried out on 13CH 3-labeled Mn 12O 12-acetate in both powder and magnetically aligned samples at an applied magnetic field of 8.5 T. The four observed peaks are assignable to the four distinct 13CH 3 moieties. The spectra were measured as a function of the orientation of the Zeeman field with respect to the easy axis in an aligned powder sample. The line positions were fitted to the dipolar plus isotropic interactions and the Fermi-contact parts, and unpaired electron spin density was calculated for each site. The results demonstrate significant spin density delocalization onto the acetate fragments and complement recent proton NMR and polarized neutron diffraction data on this system.

Determination of the nuclear structure and spin density distribution in the cyano-bridged molecular based magnet K2Mn3(H2O)6[Mo(CN)7]2·6 H2O

Abstract This article details the local spin density determination in the cyano-bridged, two-dimensional, molecular based magnet K 2 Mn 3 (H 2 O) 6 [Mo(CN) 7 ] 2 ·6 H 2 O ( T c = 39 K). The crystal structure, determined at room temperature by X-ray diffraction, was redetermined at 50 K using unpolarised neutron diffraction. The importance of intermolecular hydrogen-bonding interactions is clearly demonstrated in this study, previously characterised with X-rays. The local spin density was determined from polarised neutron diffraction data at 4 K with an applied field of 3 T. Positive spin densities were observed on the manganese sites, consistent with high-spin d 5 ions in octahedral fields, whilst a negative spin density was found on the molybdenum sites, signifying delocalisation onto the cyano ligands. The alternating sign of the spin populations on the metal sites, suggests that the primary Mo III –Mn II interactions are antiferromagnetic in nature and the delocalisation onto the cyano-bridges clearly demonstrates the role of the ligand bridges in the magnetic exchange pathway.

Structure, covalence and spin polarisation in tris(acetylacetonato)ruthenium(III) studied by X-ray and polarised neutron diffraction †

A polarised neutron diffraction (PND) experiment on [Ru(acac)3] at 4.18 K and 5 T along the b and c axes yielded 28 and 17 flipping ratios respectively. Single-crystal X-ray structure determinations at 293, 92 and 10.5 K, together with powder neutron diffraction experiments, provided auxiliary data allowing magnetic structure factors to be deduced from the PND experiment. The structure is disordered at all temperatures. There are ordered stacks of molecules along b, which stacks are arranged in the ac plane in two sites of relative displacement 0.4 Å along b. The molecular geometries at the sites are similar and approximately D3 in symmetry, but the magnetisation data indicate C2 symmetry. The PND data showed significant spin delocalisation by covalence onto the acetylacetonato rings, dominated by spin-polarisation effects, and of C2 symmetry. However the two data sets differed, with the field along b indicating a 2A and that along c a 2B dominated state. This cannot be explained in the ligand-field model which fits the magnetic susceptibility data, indicating that vibronic effects must be explicitly considered. Good-quality ab-initio local density calculations reproduced the molecular geometry but grossly underestimated the spin correlation between metal and rings.

A General Maximum-Entropy Method for Model-Free Reconstructions of Magnetization Densities from Polarized Neutron Diffraction Data

A general method for the model-free reconstruction of magnetization densities is presented. The technique is based upon the maximum-entropy principle and is valid for systems with any space-group symmetry, any physically reasonable ordered moment and allows for the incorporation of relevant corrections such as extinction. Thus, it is possible, for the first time, to reconstruct the real-space magnetization densities in essentially any physical system exhibiting a ferromagnetic spin alignment (either natural or induced) from polarized neutron diffraction experiments. The technique is illustrated for the purely organic ferromagnet, β-4,4,5,5-tetramethyl-2-p-(nitrophenyl)-3-oxido-4,5-dihydroimidazolium 1-oxyl.

Spin Density Maps for the Ferrimagnetic Chain Compound MnCu(pba)(H2O)3·2H2O (pba = 1,2-Propylenebis(oxamato)): Polarized Neutron Diffraction and Theoretical Studies

This paper is devoted to the determination of the spin density in the ferrimagnetic ground state of the bimetallic chain compound MnCu(pba)(H2O)(3) . 2H(2)O, with pba = 1,3-propylenebis(oxamato). The crystal structure, previously determined at room temperature through X-ray diffraction, was redetermined at 10 K through unpolarized neutron diffraction (orthorhombic system, space group Pnma, a = 12.727(11) Angstrom, b = 21.352(19) Angstrom, c = 5.153(3) Angstrom, Z = 4). The experimental spin density has been deduced from polarized neutron diffraction data recorded at 10 K under 50 kOe. Positive spin densities were observed on the manganese side and negative spin densities on the copper side. The delocalization of the spin density from the metal centers toward the oxamato bridging ligand was found to be more pronounced on the copper side than on the manganese side, so that the nodal surface (of zero spin density) is closer to manganese than to copper. The experimental spin distribution has been compared to the theoretical distributions deduced from density functional theory (DFT) calculations, using both DGauss and DMol programs. The experimental results for the title chain compound have also been compared to the spin distribution for the binuclear compound [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, and oxpn = N,N'-bis(3-aminopropyl)oxamido, recently reported. The most striking difference between pair and chain compounds concerns the positive P+ and negative P- spin populations carried by the manganese and copper sides, respectively. For the pair compound P+ was found as 4.67(8) mu(B), and P- as -0.67(8) mu(B) while for the chain compound these values are 5.05(7) mu(B) and -1.05(10) mu(B), respectively. The spin distribution for the ferrimagnetic chain compound is very close to a Neel state (P+ = 5 mu(B) and P- = -1 mu(B)).

Progress in magnetization density reconstructions using maximum entropy

Polarized neutron diffraction provides information on the Fourier components of magnetization density distributions in crystals. To obtain the densities themselves, one has to solve the inverse Fourier problem. This problem is complicated by the pres

Retrieval of spin densities from polarized neutron diffraction data using maximum entropy

Retrieval of spin densities from polarized neutron diffraction data using maximum entropy

A non-uniform reference model for maximum-entropy density reconstructions from diffraction data

Diffraction experiments provide information on the Fourier components of microscopic density distributions in crystals. To obtain the spatial densities themselves, an inverse Fourier problem has to be solved. The procedure is complicated by the presence of noise and incompleteness of the data. The application of the maximum-entropy (MaxEnt) principle was a breakthrough in density reconstruction, allowing high-quality density maps to be obtained without involving any a priori information concerning what the reconstructed density should look like. In this work, a procedure is proposed that incorporates a priori (e.g. theoretical) information into MaxEnt reconstructions of spin density distributions. It allows, on the one hand, the evaluation of the existing density models and, on the other, the precise investigation of what new information the experiment brings. Unlike traditional parameter-refinement techniques, the new method does not impose any strict constraints on the density to be reconstructed and is thus much more flexible. At the same time, it suppresses artifacts and yields high-quality density maps. The advantages of the new methods are illustrated by an example of spin density reconstruction based on real polarized neutron diffraction data.