Measurements Of Magnetic Form Factors Research Articles

Ground-state wave function of plutonium in PuSb as determined via x-ray magnetic circular dichroism

Measurements of x-ray magnetic circular dichroism (XMCD) and x-ray absorption near-edge structure (XANES) spectroscopy at the Pu ${M}_{4,5}$ edges of the ferromagnet PuSb are reported. Using bulk magnetization measurements and a sum rule analysis of the XMCD spectra, we determine the individual orbital [${\ensuremath{\mu}}_{\mathrm{L}}=2.8(1){\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Pu}$] and spin moments [${\ensuremath{\mu}}_{\mathrm{S}}=\ensuremath{-}2.0(1){\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Pu}$] of the Pu $5f$ electrons. Atomic multiplet calculations of the XMCD and XANES spectra reproduce well the experimental data and are consistent with the experimental value of the spin moment. These measurements of $\ensuremath{\langle}{L}_{z}\ensuremath{\rangle}$ and $\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}$ are in excellent agreement with the values that have been extracted from neutron magnetic form factor measurements, and confirm the local character of the $5f$ electrons in PuSb. Finally, we demonstrate that a split ${M}_{5}$ as well as a narrow ${M}_{4}$ XMCD signal may serve as a signature of $5f$ electron localization in actinide compounds.

Radial integrals for the magnetic form factor of 5dtransition elements

The radial integrals, <linear span>j(L)<linear span>, where L = 0, 2, 4, for several electronic configurations in the 5d electrons of transition metal atoms and ions are calculated using radial wavefunctions from the pseudo-relativistic Hartree-Fock method in the Cowan program. The resultant values are fitted to Gaussian analytical expressions with four exponential terms, and the fitted coefficients are tabulated. This table can be used to interpret the magnetic form factor measurements for 5d transition metals.

Experimental system for X-ray magnetic diffraction under extreme conditions

An experimental system for X-ray magnetic diffraction (XMD) under extreme conditions was constructed on the beamline BL39XU at SPring-8. This system aims at studying magnetic properties of ferromagnets through the measurements of magnetic form factors under the conditions of low temperature (5 K), high magnetic field (6 T) and high pressure (10 GPa). This system consists of a superconducting magnet (SCM), a diamond anvil cell (DAC), a two-axis manipulator for the DAC, a five-axis goniometer for the SCM, and an X-ray polarizer with a phase plate. Details of this system are presented. Experimental results on uranium telluride are shown as a performance test with this instrumentation.

Electron density distribution in paramagnetic and antiferromagnetic CoO: A γ-ray diffraction study

Highly accurate single-crystal structure factors, complete up to $\mathrm{sin}\ensuremath{\theta}/\ensuremath{\lambda}=1.6{\AA{}}^{\ensuremath{-}1},$ have been measured from CoO at 305 K and in the antiferromagnetic state at 10 K using 316.5 keV \ensuremath{\gamma} radiation. Moderate uniaxial pressure was applied in the low-temperature phase to force a single-T-domain sample. A detailed description of the electron-density distribution is presented. The occupancies of the $3d$ shell are computed from multipole refinement parameters, showing significant differences between the two magnetic phases. The spin and orbital contributions to the total magnetic moment of Co are derived from the experimentally determined number of unpaired electrons. Results are compared with ab initio calculations as well as with magnetic form factor measurements. A careful analysis of electronic properties in the internuclear regions reveals the Co-O interaction to be purely ionic. Its physical significance on the antiferromagnetism is discussed.

Magnetic scattering experiments

We discuss the relative use of neutrons and X-rays as scattering tools to probe the magnetic properties of materials. Neutron diffraction experiments continue to be the most appropriate tool to determine the magnetic structure of bulk solids. Synchrotron X-ray experiments are and will be used to investigate selectively the magnetic behaviour of different chemical species and/or electronic shells in magnetic systems. There exist some grey areas where the two probes can be used depending on the scientific problem under investigation. In particular, neutrons allow very accurate measurements of magnetic form factors, but X-rays provide a separation of the orbital momentum contribution to magnetisation. Comparisons between X-rays and neutrons studies of magnetism at surfaces are presented. Finally, one can anticipate that only inelastic neutron scattering experiments will allow the observation of magnetic excitations across the whole Brillouin zone.

Magnetic-Form Factor Measurements by Polarised Neutron Scattering: Application to Heavy Fermion Superconductors

The experimental technique of spin polarised neutron scattering as used in magnetic form factor measurements is presented. An introduction to the interpretation and the calculation of magnetic form factors and magneti- zation densities is given. The experimental technique of neutron scattering theory as applied to elastic spin polarised scattering experiments is briefly introduced. The calculation of the magnetic form factor and the magnetiza- tion densities are considered for simple model systems such as a collection of localised magnetic moments or an itinerant electron system. The discussion is illustrated by an experimental investigation of the magnetic form factor in the heavy fermion superconductors UBe13 and UPt3. Magnetization density maps and magnetic form factors are presented, and their implications for other physical quantities are briefly discussed. PACS numbers: 75.25.+z, 71.28.+d

Coherence effects and 5d contribution to the magnetism of Ce in CeSn 3

From magnetic susceptibility and magnetic form factor measurements on stoichiometric and non-stoichiometric CeSn 3 single crystals, it has been shown that the 5d contribution to Ce magnetism which appears at low temperatures exists only in the stoichiometric sample and is destroyed by the presence of defects.

Magnetic form factor and spin-density asphericity of Ni-Cu.

Magnetic form-factor measurements were made on single crystals of a Ni-Cu alloy containing 47.6 at.% Cu. The results give a magnetic moment of 0.088 ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$/atom at $T=4.2$ K and $H=40$ kOe in excellent agreement with bulk magnetization data. Despite this order of magnitude decrease in moment relative to Ni, the form factor is the same in both the radial distribution and the asphericity as that previously observed for pure Ni. This result is in strong contrast with an early coherent potential approximation calculation which yields a continuous variation of $\ensuremath{\gamma}$, the fractional ${E}_{g}$ population, with Cu content. It is suggested that some of this discrepancy may be attributed to the neglect of local environment effects, which are known to be importnat for the magnetism of Ni-Cu alloys.

MAGNETIC FORM FACTORS

Polarized neutron diffraction has been an extremely valuable technique for studying outer electron distributions in magnetic materials through measurements of magnetic form factors. Representative results are presented on the following classes of elemental materials : 3d ferromagnetic metals, paramagnetic metals, rare-earth metals, and diamagnetic materials. In each case a comparison with the best available theoretical result is given. It is concluded that more theoretical effort is needed on the orbital moment in transition metals, particularly for the paramagnetic metals, in order to have a meaningful confrontation between theory and experiment.

Polarized neutron study of CeSn3 (invited)

Over the past several years there has been considerable interest in materials exhibiting a nonintegral valence. As a result the properties of cerium metal and its compounds have been the subject of many theoretical and experimental investigations. In the present experiment polarized neutron scattering techniques have been used to study the spatial distribution and temperature dependence of the magnetization induced in a single crystal of CeSn3 by a magnetic field of 42.5 kG. In the 40–300 K temperature range the measured magnetic form factor is in good agreement with the 4f magnetic form factor of Ce3+. Below 40 K, on the other hand, the magnetic form factor measurements suggest that the induced magnetization contains a large component of 5d electronic character of eg symmetry, which can account, at least partly, for the increase in the magnetic susceptibility of CeSn3 at low temperatures. The results will be discussed in terms of a model in which the 4f level is positioned slightly above the Fermi energy and is hybridized with the conduction band. Band theoretical calculations have been performed to determine the nature of the electronic wavefunctions at the Fermi level.

Dirac-Fock studies of some electronic properties of rare-earth ions

This paper reports results of accurate fully relativistic Dirac-Fock studies of some electronic properties of rare-earth ions. We present, in addition to eigenvalue information including spin-orbit splittings (useful for interpreting ESCA experiments), 〈 r n 〉 values (for n = -3, 2, 4, 6) for the 4f electrons and Slater F k and G k integrals (of interest for hyperfine interaction and crystal field descriptions), values of the Mössbauer isomer shift electronic densities and the 〈 j i 〉 integrals useful for interpreting neutron magnetic form factor measurements.

Magnetic form factor measurements by inelastic neutron scattering

The thermal neutron cross section for scattering by crystalline-electric field (CEF) levels is d2 σ/dΩdω = A x f2 (Q), where A includes physical and instrumental parameters, and f(Q) is the magnetic from factor of the ion being measured. The intensity of a neutron energy transfer peak resulting from a CEF level, measured at any Q value, is proportionl to f2 (Q) when all quantities in A are kept constant. The Q dependence of the form factor can therefore be derived from an energy analysis of the neutrons scattered from a powder sample, at several Q values. This method is suitable for paramagnetic ions having defined CEF levels (especially the rare earth ions). The method was utilizedby the authors for measuring the form factor of Pr3+ in PrF3, Ho3+ in HoCrO3 and U4+ in UPd3. The measurements were carried out on the triple axis neutron spectrometer KANDI III at the NRCN. The results agree with those found in the literature.

Effect of Crystalline Fields on Charge Densities and Magnetic Form Factors

The effects of crystalline fields on $3d$ charge densities and magnetic form factors for transition metal ions are discussed on the basis of recent theoretical investigations augmented by an analysis of optical absorption data. It is shown that the crystalline field has two effects on the free ion $3d$ wave functions and hence on their form factors as well: (1) a differentiation or "splitting" of the two types of cubic $3d$ functions by an expansion of the ${t}_{2g}({e}_{g})$ orbitals and a contraction of the ${e}_{g}({t}_{2g})$ orbitals resulting in two different radial charge densities, and (2) a net expansion of the charge distribution from the free ion value. The magnetic form factors due to this "splitting" effect when calculated according to the methods of Weiss and Freeman show measurable deviations from the free atom results. A form factor for ${\mathrm{Mn}}^{+2}$ based on optical absorption data shows a large expansion of the $3d$ charge density, in agreement with the magnetic form factor measurements of Hastings, Elliott, and Corliss. This agreement, based on the use of theoretical ${F}^{k}(3d, 3d)$ integrals, indicates that the well-known discrepancy between theoretical and experimental values of these integrals arises from the fact that the quantities obtained experimentally are not true ${F}^{k}(3d, 3d)$ integrals. The crystalline potential due to an array of negative ion charge densities has been employed to discuss these various effects and their meaning with respect to a proper (essentially molecular) treatment.