X-ray Resonant Exchange Research Articles

A novel approach for x-ray scattering experiments in magnetic fields utilizing trapped flux in type-II superconductors

We introduce a novel approach to x-ray scattering studies in applied magnetic fields by exploiting vortices in superconductors. This method is based on trapping magnetic flux in a small disk-shaped superconductor (known as a trapped field magnet, TFM) with a single-crystal sample mounted on or at close proximity to its surface. This opens an unrestricted optical access to the sample and allows magnetic fields to be applied precisely along the x-ray momentum transfer, facilitating polarization-sensitive experiments that have been impractical or impossible to perform to date. The TFMs used in our study remain stable and provide practically uniform magnetic fields for days, which are sufficient for comprehensive x-ray diffraction experiments, specifically x-ray resonance exchange scattering (XRES) to study field-induced phenomena at a modern synchrotron source. The TFM instrument has been used in a "proof-of-principle" XRES study of a meta-magnetic phase in a rare-earth compound, TbNi(2)Ge(2), in order to demonstrate its potential.

Strong coupling between the spin polarization of Mn and Tb in multiferroicTbMnO3determined by x-ray resonance exchange scattering

We report on an x-ray resonance exchange scattering (XRES) study of multiferroic $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$. Magnetic scattering is observed close to the $\mathrm{Mn}\phantom{\rule{0.2em}{0ex}}K$ edge and the $\mathrm{Tb}\phantom{\rule{0.2em}{0ex}}{L}_{III}$ and ${L}_{II}$ edges. Surprisingly, Tb shows XRES also in the paraelectric phase, where neutron diffraction results suggested the $4f$ moments to be disordered. The temperature dependence of the XRES intensities shows a distinct kink close to the ferroelectric transition temperature ${T}_{C}$ for all absorption edges. We were able to model the temperature dependence for all edges, assuming a strong coupling of Mn and Tb magnetism via the spin polarized $5d$ conduction band. We argue that the hybridization between Mn and Tb states is a prerequisite for the multiferroic effect in this material.

Magnetic structure ofGdAgSb2determined by x-ray resonant exchange scattering

X-ray resonant exchange-scattering experiments were performed on a single crystal of ${\mathrm{GdAgSb}}_{2}$ to determine the magnetic structure. Long-range antiferromagnetic ordering, characterized by a wave vector of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}=(\frac{1}{2}00),$ develops below the N\'eel temperature ${(T}_{N}=13 \mathrm{K}),$ consistent with the dc susceptibility measurements. For the scattering geometry employed in these measurements, the resonant enhancement at the $(\frac{1}{2}08)$ magnetic peak arises from electric quadrupole transitions only while the resonant enhancement at the $(0\ensuremath{-}\frac{1}{2}8)$ magnetic peak arises from electric dipole transitions. Q-dependent integrated intensity measurements were carried out, along with polarization analysis of the scattered beam, and demonstrated that the moments lie in the tetragonal basal plane and are perpendicular to the magnetic wave vector.

Element-specific magnetic long- and short-range order and competing interactions in Gd x Eu 1 - x S

We report on an investigation of the magnetic properties of Gd x Eu 1 - x S mixed crystals with compositions in the range of 0.6 < x < 1. For the two samples Gd 0.8 Eu 0.2 S and Gd 0.73 Eu 0.27 S a long-range antiferromagnetic order was observed at low temperatures. Element-specific measurements exhibited a different temperature dependence of the reduced sublattice magnetisation of the two magnetic species. A model calculation and Monte Carlo simulations revealed that the different temperature dependence is due to frustration effects. These frustration effects lead to a breakdown of the long-range order for higher europium contents. For the Gd 0.67 Eu 0.33 S-sample we were able to observe a short-range antiferromagnetic order with correlation lengths of a few 10A with X-ray resonance exchange scattering.

Antiferromagnetic order and phase transitions in GdS as studied with X-ray resonance-exchange scattering

We report on X-ray resonance exchange and neutron scattering of metallic GdS. At the LII and L III absorption edges of Gd, resonance enhancements of more than two orders of magnitude over the non-resonant magnetic scattering are observed. Polarisation analysis proves that these enhancements are due to dipolar transitions from the 2p to the 5d states. The branching ratio between the LII and L III edges of 2.5 suggests a polarisation of the 5d electrons in the ground state. The antiferromagnetic order is of type II in the fcc lattice. Single crystal diffraction of hot neutrons suggests that the spin direction lies within the (111) planes with a value for the sublattice magnetisation of 6.51(3) . The critical exponent for the sublattice magnetisation has a value of β = 0.38(2) in agreement with a pure Heisenberg model. Above T N, a sharp component persists in the critical diffuse scattering. Lattice distortions give indications for two additional low-temperature phase transitions at about 49 K and 32 K. We argue that these transitions are not connected to spin reorientations and discuss the possible influence of fourth-order exchange interactions.

Effects of Band Filling on Magnetic Structures: The Case ofRNi2Ge2

We establish that strong Fermi surface nesting drives the N\'eel transition in the $R{\mathrm{Ni}}_{2}{\mathrm{Ge}}_{2}$ compounds. Generalized susceptibility, ${\ensuremath{\chi}}_{0}(\mathbf{q})$, calculations found nesting to be responsible for both incommensurate wave vector, $(000.793)$, in ${\mathrm{GdNi}}_{2}{\mathrm{Ge}}_{2}$, and the commensurate structure, $(001)$, in ${\mathrm{EuNi}}_{2}{\mathrm{Ge}}_{2}$, as revealed by x-ray resonant exchange scattering. A continuous transition from incommensurate to commensurate magnetic structures via band filling is predicted. The surprisingly higher ${T}_{N}$ in ${\mathrm{EuNi}}_{2}{\mathrm{Ge}}_{2}$ than that in ${\mathrm{GdNi}}_{2}{\mathrm{Ge}}_{2}$ is also explained.

Experiments on transuranium compounds with X-ray resonant exchange scattering

Synchrotron radiation experiments are reported on single crystals of NpS and PuSb to examine the magnetic structures by using the technique of X-ray resonance exchange scattering (XRES). In the case of NpS the results augment our knowledge of the magnetic phase transition, and, by measuring the ratio of the intensities at the M 5 and M 4 energies we suggest that the electronic configuration of NpS is trivalent Np 3+. In the case of PuSb our experiments were unable to observe magnetic scattering. Our interpretation is that an absorbing layer of ∼1 μm exists on the surface of the single crystals. No powder diffraction peaks (e.g. from PuO 2 or PuSb) could be detected from this layer, indicating that it is either amorphous or small grain. An EXAFS-type analysis shows that the overlayer consists primarily of plutonium and oxygen. We suggest how this may be caused preferentially in the Pu-containing samples because of the alpha-particle activity present in 239 Pu .

Neutron diffraction and x-ray resonant exchange-scattering studies of the zero-field magnetic structures ofTbNi2Ge2

The zero-field magnetic structures of the rare-earth intermetallic compound ${\mathrm{TbNi}}_{2}{\mathrm{Ge}}_{2}$ have been determined using conventional magnetic neutron diffraction and high-resolution x-ray resonant exchange scattering techniques. There are two distinct magnetic phase transitions in this material: one is from the high-temperature paramagnetic state to a long period antiferromagnetic phase at the N\'eel temperature ${(T}_{N}=16.8 \mathrm{K}),$ and the other is at a lower temperature ${(T}_{t}=9.3 \mathrm{K}),$ where the system locks into a commensurate phase. The structure above ${T}_{t}$ is described by a longitudinal, amplitude modulated, sinusoidal wave with propagation vector ${\mathit{\ensuremath{\tau}}}_{1}\ensuremath{\approx}(000.758\ifmmode\pm\else\textpm\fi{}0.002)$ in reciprocal-lattice units (r.l.u.). As the temperature is lowered below ${T}_{t},$ ${\mathit{\ensuremath{\tau}}}_{1}$ locks at $(0 0 \frac{3}{4})$ and additional magnetic Bragg reflections corresponding to ${\mathit{\ensuremath{\tau}}}_{2}=(\frac{1}{2} \frac{1}{2} 0)$ and ${\mathit{\ensuremath{\tau}}}_{3}=(\frac{1}{2} \frac{1}{2} \frac{1}{2})$ develop. A weak modulation ${\mathit{\ensuremath{\tau}}}_{1}^{\ensuremath{'}}=(0 0 \frac{1}{4}),$ related to ${\mathit{\ensuremath{\tau}}}_{1}$ also appears indicating a squaring-up of the low-temperature structure. In this equal moment structure all Tb moments have the saturation value of ${\ensuremath{\mu}}_{s}=9.0\ifmmode\pm\else\textpm\fi{}0.2{\ensuremath{\mu}}_{\mathrm{B}}.$ Both the phases are uniaxial with Tb moments parallel to the $\mathbf{c}^$ axis of the tetragonal unit cell.

Synchrotron radiation in the study of amorphous materials

The present paper illustrates the use of synchrotron radiation for determining the structure of amorphous systems. Case studies are presented to show some relevant results obtained in the study of disordered materials, using extended X-ray absorption fine structure (EXAFS). Particular emphasis is given to the recent successes of X-ray absorption spectroscopy in obtaining a quantitative determination of the three body correlation function in glasses and liquids. The potential and limitations of anomalous X-ray scattering are described and illustrated with examples. The new possibilities opened up by these techniques as well as by the application of other experimental techniques, like inelastic X-ray scattering, X-ray circular magnetic dichroism and resonant exchange X-ray scattering are described.

Surface contamination of single-crystal PuSb

Pu M-edge X-ray absorption experiments were performed on a single crystal of PuSb in order to understand incongruous X-ray resonant exchange scattering (XRES) results from the same material. Analysis of the extended X-ray absorption fine structure (EXAFS) reveals that there is an amorphous or polycrystalline surface phase on the PuSb. The Pu at the surface of the crystal is coordinated primarily to a first-row main-group element, probably oxygen. In addition, the surface may be slightly deficient in antimony. These EXAFS results are sufficient to explain the absence of an XRES response in this PuSb sample.

Determination of magnetic-moment directions using x-ray resonant exchange scattering

We present determinations of the magnetic structures of ${\mathrm{NdNi}}_{2}$${\mathrm{B}}_{2}$C and ${\mathrm{SmNi}}_{2}$${\mathrm{B}}_{2}$C by means of x-ray resonant exchange scattering (XRES). The integrated intensity of a number of magnetic reflections was measured as a function of the Bragg angle and compared to model calculations for various magnetic structures. The two compounds were found to have the same magnetic modulation wave vector but different moment directions. A resonant feature observed below the Sm ${\mathrm{L}}_{3}$-absorption edge, similar to unexplained effects found in other light rare-earth compounds, is identified as quadrupolar XRES and is used to refine the details of the moment direction.

X-ray Resonant Exchange Scattering: Polariztaion Dependence and Correlation Function

The cross section for X-ray resonant exchange scattering is reformulated in terms of linear polarization states perpendicular and parallel to the scattering plane, a basis particularly well suited to synchrotron X-ray diffraction experiments. The explicit polarization dependence of the terms is calculated for the electric dipole and quadrupole contributions. This expression, in turn, is rewritten in an orthonormal basis to highlight the dependence of the cross section on each component of the magnetic moment. This has the benefit of providing an empirically useful expression for the cross section. Diffraction patterns from a few simple magnetic structures are calculated. Finally, the correlation function measured at each resonant harmonic is derived.

X-ray resonant exchange scattering from 3d transition metal surfaces

The decay of the elastic X-ray intensity peak versus perpendicular transferred momentum is theoretically studied at energies close to the L II edge, for single crystal Fe surfaces and thin Fe films. For the single crystal surface, large intensity changes are observed upon reversal of the direction of the magnetisation. For thin Fe films, which are known to exhibit perpendicular magnetisation, analogous effects are predicted when, by raising the temperature, the magnetisation becomes in-plane. These changes are sensitive to both direction and magnitude of the surface magnetic moments, making this technique a powerful probe for studying the magnetic properties of 3d surfaces and interfaces.

X-ray resonant magnetic scattering from surfaces.

We show that the magnetic structure of surfaces can be successfully investigated by combining x-ray surface diffraction and x-ray resonant exchange scattering. The resonant x-ray surface diffraction spectra of linearly polarized radiation are shown to be sensitive to the magnitude and direction of the surface magnetic moments by explicit calculations for different magnetic structures of the (001) surface of antiferromagnetic UAs and of the (0001) surface of ferromagnetic Gd.

X-ray Resonance Exchange Scattering Study of Nd2Fe14B

The X-ray resonance exchange scattering (XRES) has been measured at the Nd L2,3-edges on the 330, 440 and 550 Bragg reflections in a ferromagnetic Nd2Fe14B single crystal. The XRES results at the L2-edge reflect the spin polarization of unoccupied 5d-bands of Nd due to electric dipole transitions. Those at the L3-edge show the possibility of electric quadrupole transitions to the highly localized 4f-states. The temperature dependence of XRES confirms the sensitivity to the local magnetic moment of specific site. The magnetic moments of Nd 4f and 4g sites rotate from the c-axis with different angles below spin reorientation temperature.

X-Ray Resonance Exchange Scattering at the NdL2,3-Edges in Nd2Fe14B

X-ray resonance exchange scattering has been measured at the Nd L 2,3 absorption edges on the (440) Bragg reflection in a ferromagnetic Nd 2 Fe 14 B single crystal. The magnetic spectrum at the L 2 -edge reflects the spin polarization of unoccupied 5 d -bands of Nd due to electric dipole transitions. The magnetic spectrum at the L 3 -edge shows a more complicated structure than that at the L 2 -edge. The difference in magnetic spectra between the L 2 - and L 3 -edges is discussed from the viewpoints of L S coupling in 5 d -bands and the contributions of electric quadrupole transitions to the highly localized and partially vacant 4 f -states.

Resonant X-ray magnetic scattering in holmium

We review the results of resonant X-ray magnetic scattering experiments on the rare earth metal holmium. When the incident X-ray energy is tuned near the L 111 absorption edge, large resonant enhancements of the magnetic scattering and resonant integer harmonics are observed. These results are analyzed within the theory of X-ray resonance exchange scattering assuming electric dipole (2p → 5d) and quadrupole (2p → 4f) transitions among atomic orbitals.

X-ray resonance exchange scattering in dysprosium.

Resonant enhancement of the scattering intensity of the magnetic satellite resulting from the basal-plane spiral antiferromagnetic structure is observed in dysprosium metal at the ${L}_{\mathrm{III}}$ absorption edge. The polarization dependence and enhancemenet agree with theory and are similar to those observed previously in holmium metal.

X-ray Resonance Exchange Scattering (XRES)

Large resonant magnetization-sensitive X-ray scattering is predicted to occur in the vicinity of the LII, LIII, MII-MV absorption edges in the rare earth and actinide elements, and at the LII, LIII edges in the transition and 4d elements. Additional longer wavelength resonances will occur in the actinides and 4d elements. These “magnetic” resonances result from electric multipole transitions, with the sensivity to the magnetization arising from exchange and spin-orbit correlations. For some transitions, the magnetic scattering will be comparable to the charge scattering.

X-ray resonance exchange scattering in UAs.

Resonant enhancement of the magnetic x-ray scattering cross section in UAs has been investigated by tuning the incident x-ray energy through the uranium ${\mathrm{M}}_{\mathrm{IV}}$ and ${\mathrm{M}}_{\mathrm{V}}$ absorption edges. At the ${\mathrm{M}}_{\mathrm{IV}}$ edge the intensity for the (0,0,(5/2) magnetic reflection is enhanced by ${10}^{7}$ relative to the nonresonant component far above the edge, and is a remarkable 1% of the intensity of the (0,0,2) charge peak. At the ${\mathrm{M}}_{\mathrm{V}}$ edge the enhancement is ${10}^{5}$. The dramatic enhancement at M edges has been predicted by Hannon et al., and arises from strong electric multipole transitions between atomic core states and the exchange-split Fermi edge states.