极化中子衍射及在电子自旋密度研究中的应用

极化中子衍射方法常用于研究含未配对电子化合物中电子自旋密度的分布．分子中电子自旋密度分布从一个独特的角度反映化合物的磁性质．本文介绍极化中子衍射方法的背景知识和基本原理．包括中子源、中子和X射线衍射、极化中子衍射,以及一些常用的实验数据处理方法．选用几个实例总结了用极化中子衍射方法得到的电子自旋密度分布在无机和有机化学中的应用．通过单分子磁体[Fe8O2（OH）12（tacn）6]^8＋和氰基桥联化合物K2[Mn（H2O）2]3[Mo（CN）7]2·6H2O,说明如何用该方法研究金属原子间的磁相互作用;并通过Ru（acac）3这个只含一个未配对电子的化合物来说明如何获得化合物中金属和配体上小的自旋密度;最后介绍了该方法在nitronylnitroxide自由基研究中的应用．     

Spin-dependent electron momentum densities in Co2FeGa studied by Compton scattering

The spin density of Heusler alloy Co₂FeGa, has been studied using the Compton scattering technique with 274 keV circularly polarized synchrotron radiation in the high energy inelastic scattering beamline (BL08W), at SPring-8, Japan. The magnetic Compton profiles along the two principal directions [1 1 0] and [1 1 1] were measured. The spin profiles shows a good agreement with our FLAPW-GGA results, where the theoretical results were based on the ferromagnetic ground state. The 3d spin moment at the Co and the Fe site was found to be in excellent agreement with the earlier reported neutron diffraction measurements.     

Contributions of the electronic spin and orbital current to the CoCl(4) (2-) magnetic field probed in polarised neutron diffraction experiments

Polarised neutron diffraction experiments conducted at 4.2 K on Cs(3)CoCl(5) crystals have been analysed by using a four-dimensional model Hilbert space made of ab initio n-electron wave functions of the CoCl(4) (2-) molecular ion. Two spin-orbit mixing coefficients and several configuration interaction coefficients have been optimized by fitting calculated magnetic structure factors to experimental ones, to obtain the best ensemble density operator that is representable in the model space. A goodness of fit, χ(2), less then 1 has been obtained for the first time for the two experimental data sets available. In the present article, the optimized density operators are used to calculate the magnetic field densities that are the genuine observables probed in neutron diffraction experiments. Density maps of such observables are presented for the first time and numerical details are provided. The respective contributions of spin density and orbital current to the magnetic field density are analyzed.     

Effective potential energy curves of H2 molecule evolving in a strong time‐dependent magnetic field

Evolution of hydrogen molecule, starting initially from its field‐free ground state, in a time‐dependent (TD) magnetic field of order 10¹¹ G is presented in a parallel internuclear axis and magnetic field‐axis configuration. Effective potential energy curves (EPECs), in terms of exchange and correlation energy, of the hydrogen molecule as a function of TD magnetic‐field strength, are analyzed through TD density functional computations based on a quantum fluid dynamics approach. The numerical computations are performed for internuclear separation R ranging from 0.1 to 14.0 a.u. The EPECs exhibit field‐dependent significant potential‐well minima both at large internuclear separations and at short internuclear separations with a considerable increase in the exchange and correlation energy of the hydrogen molecule. The results, when compared with the time‐independent (TI) studies involving static TI magnetic fields, reveal TD behavior of field‐dependent crossovers between different spin‐states of hydrogen molecule as indicated by the TI investigations in static magnetic fields. Besides this, present work reveals interesting dynamics in the TD total‐electronic charge‐density distribution of the hydrogen molecule. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Neutron diffraction and theoretical DFT studies of two dimensional molecular-based magnet K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O

Exchange mechanisms and magnetic structure in the two-dimensional cyano-bridged molecule-based magnet K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O have been investigated by a combination of neutron diffraction studies on both single crystal and powder samples and theoretical DFT calculations. The experimental spin density has been deduced from a new refinement of previously obtained polarized neutron diffraction (PND) data which was collected in the ordered magnetic state at 4 K under a saturation field of 3 T performed in the C2/c space group, determined by an accurate re-evaluation of the X-ray structure. Positive spin populations were observed on the two manganese sites, and negative spin populations were observed on the molybdenum site, which provides evidence of antiferromagnetic Mo3+-Mn2+ exchange interactions through the cyano bridge. The experimental data have been compared to the results of DFT calculations. Moreover, theoretical studies reveal the predominance of the spin polarization mechanism in the Mo-C-N-Mn sequence, with the antiferromagnetic nature of the interaction being due to the overlap between the magnetic orbitals relative to manganese and molybdenum in the cyano bridging region. The magnetic structure of K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O has been solved at low temperature in zero field by powder neutron diffraction measurements. The structure was found to be ferrimagnetic where the manganese and molybdenum spins are aligned along the axis in opposite directions.     

Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels

Low-energy excitation energies of a magnetic solid with localized spins are probed by magnetic susceptibility, neutron scattering and Raman scattering measurements, and are analyzed using a spin Hamiltonian with a set of spin exchange parameters. The nature and values of the spin exchange parameters deduced from this analysis depend on what spin exchange paths one includes in the spin Hamiltonian. In this article, we review how spin exchange interactions of magnetic solids with localized spins are described on formal, quantitative and qualitative theoretical levels, investigate antisymmetric and anisotropic interactions for general spin dimers, and discuss the spin exchange interactions and magnetic structures of various extended magnetic solids on the basis of spin dimer analysis. Strongly interacting spin exchange paths of a magnetic solid are determined by the overlap between its magnetic orbitals, so that the strongly interacting spin unit of a magnetic solid does not necessarily have the same geometrical feature as does the arrangement of its magnetic ions or spin-carrying molecules. Therefore, in interpreting results of magnetic susceptibility, inelastic neutron scattering or Raman scattering measurements, it is essential to employ a set of spin exchange parameters chosen on the basis of proper electronic structure considerations. Spin dimer analyses based on extended Hückel tight binding calculations provide a reliable and expedient means to study the relative strengths of superexchange and super-superexchange spin exchange interactions.     

Noncollinear spin density functional theory for spin‐frustrated and spin‐degenerate systems

We have implemented ab initio linear combinations of Gaussian‐type orbital calculations with generalized localized spin density approximation (GLSDA) for a dimer of equilateral H₃ as a model of the noncollinear magnetic clusters. It has been found that the GLSDA solution with the three‐dimensional noncollinear spin structure is, contrary to prior band calculations by other groups, the ground state near the O_h conformation. Further computational results are compared to that of ab initio generalized Hartree–Fock. The difference between them and the influence of the correlation correction were discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

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

This article details the local spin density determination in the cyano-bridged, two-dimensional, molecular based magnet K₂Mn₃(H₂O)₆[Mo(CN)₇]₂·6 H₂O (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 d⁵ 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.     

Density functional study of the structural,electronic, and magnetic properties of neutral and charged rhodium clusters up to tetramer

Model core potential computations were performed for Rh₂, Rh₃, and Rh₄ clusters and their respective cations and anions using the linear combination of Gaussian‐type orbital, nonlocal spin density method. The optimized geometries, electronic and magnetic structures, binding and fragmentation energies, adiabatic ionization potentials, and electron affinities were determined. Results show that the ionization potentials, electron affinities, binding energies, and magnetic moments decrease with the cluster size. For Rh₂ and Rh₃ the most stable structures exhibit ferromagnetic properties, while Rh₄ in its ground state is found to be paramagnetic. The structures of minimum energy for the charged species often differs from the corresponding neutral one. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Isotropic hyperfine interaction and spin-lattice relaxation for radicals in the solid state. Part 4

Spin-lattice relaxation is discussed for radicals in a solid with isotropic hyperfine interaction; various models are used for the interaction between the vibrations in the radical and the lattice vibrations. The formulas relate the relaxation time to temperature, magnetic field, and the parameters of the spin hamiltonian.     

Structure and magnetic properties of nitroxide molecular crystals by density functional calculations employing periodic boundary conditions.

The structure and magnetic properties of one-dimensional chains of representative nitroxides have been studied by a density functional model employing periodic boundary conditions. The optimized geometries are in better agreement with experiments than those obtained from optimizations of model dimeric systems. The spin populations and isotropic hyperfine couplings compare well with the values measured by polarized neutron and electron spin resonance experiments. Magnetic couplings computed by the broken symmetry approach reproduce the ferro- or antiferromagnetic behavior of different nitroxides derived from experiments. These results point out the reliability of the computational model and the significant tuning of all the magnetic properties by intermolecular hydrogen bridges.     

Spin-free quantum chemistry. XV Spin-only neutron diffraction

The cross section for elastic neutron diffraction is analyzed for the spin-only case, in which the orbital contributions to the magnetic moment density are negligible. For systems specified by spin-free Hamiltonians, we show that the magnetic moment density is calculated from the unpaired electron density, a spin-free quantity, which is equivalent to the spin density. The computation of the unpaired electron density is outlined and examples are discussed. The scattering cross section for an infinite interaction range Heisenberg model exhibits a temperature dependence which parallels that of the spontaneous magnetization. With a knowledge of the unpaired electron density one may determine the magnetic space group symmetry.     

Synthesis,crystal structure,magnetic properties and spin glass behaviour of the new ternary compound Cr4TiSe8

The new ternary selenide Cr₄TiSe₈ crystallises in the V₅S₈ type structure. The determination of the metal atom distribution over the three crystallographically independent sites using neutron scattering experiments reveals that the Ti atoms exclusively occupy the sites within the full metal atom layers with a pronounced preference for one of the two possible sites. The magnetic properties in the high temperature region exhibit Curie–Weiss behaviour with a paramagnetic Curie temperature θ of −300(5) K indicating strong antiferromagnetic exchange interactions. Between about 100 and 300 K the susceptibility data pass a very broad maximum and a qualitatively explanation is presented that base on antiferromagnetic exchange interactions between Cr atoms forming linear trimers, dimers, or Cr atoms being isolated. Below about 50 K the zero field cooled and field cooled susceptibility curves diverge suggesting spin glass behaviour. In the low temperature neutron diffraction patterns no additional peaks are observed which gives further evidence for the occurrence of a spin glass. Below 120 K the background of the diffraction patterns becomes modulated due to the short range magnetic interactions with sizes of the domains ranging from about 15 to 38 Å. Low temperature single crystal X-ray investigations show a remarkable change of the contraction of the lattice parameters below about 220 K that may be due to the onset of the strong magnetic exchange interactions.     

Effects of Neutron Irradiation on Superconducting Properties of GdBa2Cu3O7-δ Single Domain Superconductor

The effects of neutron irradiation with a fluence of 1015 n/cm2 on the superconducting properties of GdBa2Cu3O7-δsingle domain sample were studied. The point and cascade defects produced by the neutron irradiation were observed by high-resolution transmission electron microscopy. The cascade defects were found to have the sizes of about 4-7 nm which is comparable to the coherence lengths of high temperature superconductors. The point defects disappear while the cascades still exist through thermal annealing. The temperature dependence of magnetization for the magnetic field parallel to the crystallographic c axis shows that the neutron irradiation leads to a dramatic degradation of uperconductivity for the as-irradiated sample, a decrease of critical current density (Jc), and the weakening of the fishtail effect in the Jc versus magnetic induction B curve. However, for the as-irradiated sample annealed in the flowing oxygen atmosphere, it shows that Jc under high magnetic fields is greatly enhanced, the fishtail shifts towards higher magnetic fields, and its superconductivity is partially recovered as well due to the remaining effecive pinning centers of the cascades. These results suggest a prospective application for such a treated GdBa2Cu3O7-δsuperconductor.     

A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields

We present a novel NMR approach to the determination of crosslink densities in rubber materials. The method is based on the dipolar correlation effect (DCE) on the stimulated echo examined in a series of rubber samples and linear polyisoprene. The parameter evaluated from the echo attenuation curves is the mean‐squared dipolar fluctuation associated with anisotropic reorientations of macromolecular backbones. The contributions to the DCE of the constraints due to excluded volume effects and chemical crosslinks are estimated. A strong dependence of the mean‐squared dipolar fluctuation on the crosslink density of rubber combined with the simplicity of performing the measurements with inexpensive low‐field instruments suggests that the DCE is a useful tool for routine applications. The potential and problems of performing DCE measurements in low‐magnetic‐field conditions are discussed in detail. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2207–2216, 2001     

Ferromagnetic interaction in an asymmetric end-to-end azido double-bridged copper(II) dinuclear complex: a combined structure, magnetic, polarized neutron diffraction and theoretical study

A new end-to-end azido double-bridged copper(II) complex [Cu(2)L(2)(N(3))2] (1) was synthesized and characterized (L=1,1,1-trifluoro-7-(dimethylamino)-4-methyl-5-aza-3-hepten-2-onato). Despite the rather long Cu-Cu distance (5.105(1) A), the magnetic interaction is ferromagnetic with J= +16 cm(-1) (H=-JS(1)S(2)), a value that has been confirmed by DFT and high-level correlated ab initio calculations. The spin distribution was studied by using the results from polarized neutron diffraction. This is the first such study on an end-to-end system. The experimental spin density was found to be localized mainly on the copper(II) ions, with a small degree of delocalization on the ligand (L) and terminal azido nitrogens. There was zero delocalization on the central nitrogen, in agreement with DFT calculations. Such a picture corresponds to an important contribution of the d(x2-y2) orbital and a small population of the d(z2) orbital, in agreement with our calculations. Based on a correlated wavefunction analysis, the ferromagnetic behavior results from a dominant double spin polarization contribution and vanishingly small ionic forms.     

Intriguing electric field effect on magnetic spin couplings in dielectron clathrate hydrates

Clathrate hydrates have appeared as promising icy materials as the radical, high-spin molecule, and even electron clathrate hydrates are found. In particular, dielectron clathrate hydrates are expected to develop as structural units for a novel class of icy magnetic materials because of not only possible spin coupling interaction, but also very sensitive response to electric field of the loosely bound electrons. However, electric field responses concerning the magnetic properties of such hydrates have not been reported so far. In this work, three representative dielectron clathrate hydrate model clusters (e₂@4⁶6⁸BB, e₂@5¹²6²BB, and e₂@4⁶6⁸AB) were considered for the exploration of their magnetic spin coupling properties, electron distributions, and energy responses to applied electric field. The results calculated at the density functional theory level show that the energies and electron spin coupling properties of these dielectron clathrate hydrate clusters are quite sensitive to applied electric field, presenting intriguing variations. Most importantly, applied electric field can regulate the strength of spin coupling between two trapped electrons, and even could realize the magnetic interconversion of such dielectron cluster structures between antiferromagnetic and paramagnetic or diamagnetic characteristics. Clearly, the intriguing variations should be attributed to the diffuse character, special mobility and polarizable properties of such trapped electrons, and especially the susceptible redistributions of two electrons (including the electron cloud shape and distance between two electron centers) to the electric field. This work opens up the possibility of designing novel icy magnetic materials with sensitive electric field responses of the magnetic properties.     

Synthesis and Characterization of the Crystal Structure and Magnetic Properties of the New Fluorophosphate LiNaCo[PO(4)]F

The new compound LiNaCo[PO(4)]F was synthesized by a solid state reaction route, and its crystal structure was determined by single-crystal X-ray diffraction measurements. The magnetic properties of LiNaCo[PO(4)]F were characterized by magnetic susceptibility, specific heat, and neutron powder diffraction measurements and also by density functional calculations. LiNaCo[PO(4)]F crystallizes with orthorhombic symmetry, space group Pnma, with a = 10.9334(6), b = 6.2934(11), c = 11.3556(10) ?, and Z = 8. The structure consists of edge-sharing CoO(4)F(2) octahedra forming CoFO(3) chains running along the b axis. These chains are interlinked by PO(4) tetrahedra forming a three-dimensional framework with the tunnels and the cavities filled by the well-ordered sodium and lithium atoms, respectively. The magnetic susceptibility follows the Curie-Weiss behavior above 60 K with θ = -21 K. The specific heat and magnetization measurements show that LiNaCo[PO(4)]F undergoes a three-dimensional magnetic ordering at T(mag) = 10.2(5) K. The neutron powder diffraction measurements at 3 K show that the spins in each CoFO(3) chain along the b-direction are ferromagnetically coupled, while these FM chains are antiferromagnetically coupled along the a-direction but have a noncollinear arrangement along the c-direction. The noncollinear spin arrangement implies the presence of spin conflict along the c-direction. The observed magnetic structures are well explained by the spin exchange constants determined from density functional calculations.