Space-time characteristics of nuclear resonant excitation during Bragg reflection from multilayers

Mössbauer experiments using synchrotron radiation have opened up a new method for investigating nuclear-resonance scattering — in the time domain. It is shown that the field distribution in a multilayer structure, including periodic interlayers of a resonant isotope, under Bragg reflection conditions is substantially different in the energy and time differential regimes of investigation. For separate delay times the field does not decay into the medium, but rather it undergoes complicated dynamic beats. The positions of the antinodes of the “ energy” and “temporal” standing waves are also different. In consequence the energy (Mö ssbauer) and temporal spectra of nuclear resonant reflection contain substantially different information about the structure of the films.     

Enhancement and speedup in nuclear resonant diffraction

The interaction of Mössbauer radiation with the nuclei in a single crystal provides the unique possibility to enhance the coherent channel in nuclear resonance scattering by means of a properly phased excitation of the scattering centers. When a primary beam is incident in the exact Bragg direction, all nuclei are excited in phase. The resonance parameters of such a collective nuclear excitation of a perfect single crystal (γ-exciton) are entirely different from those of an individual nuclear excitation. In Bragg geometry diffraction, the resonance lines are shifted and broadened (enhancement effect), the lifetime of the collective excited state is shortened (speedup effect) and the reflectivity becomes total (suppression effect). Recent experiments arc reviewed, where these effects were studied in the resonant diffraction of Mössbauer and of synchrotron radiation.

     

Standing Wave Effects in Nuclear Resonance Bragg Reflectivity: Comparison of the Energy and Time Scales and First Experimental Results

The applicability of the concept of standing wave for the nuclear resonance Bragg reflectivity of synchrotron radiation has been tested for a microcrystalline (Fe/Cr)₂₆ multilayer. In the time domain the depth selectivity is strongly enhanced. A “scan” of hyperfine field distribution over bilayer depth was performed by a variation of the angle near the Bragg peak. In particular we observed that Fe/Cr and Cr/Fe interfaces are quite different and that the magnetic field orientation is different in the interfaces and in the central part of Fe layers. This revised version was published online in September 2006 with corrections to the Cover Date.     

Dependence of nuclear diffraction on the azimuthal angle: (002)- and (0010)-reflections of YIG

Nuclear diffraction of synchrotron radiation has been investigated using YIG single crystals in different scattering geometries. Time resolved quantum beat spectra of pure nuclear (002) and (0010) Bragg reflections were observed in a set-up where the hyperfine interaction was kept constant, while the azimuthal angle in the (001) surface between the [100] axis and the scattering plane (k _in,k _out) was varied. The time spectra were analyzed by means of the dynamical theory for coherent nuclear scattering. The results revealed the high sensitivity of this experimental technique on the complete set of hyperfine interaction parameters and on the specific geometrical conditions for nuclear diffraction of polarized γ-rays.     

Nuclear resonant scattering of synchrotron radiation by multilayer structures

Multilayer structures form a particular class of samples employed in nuclear resonant scattering of synchrotron radiation. Their specific properties lead to unusual energy and time characteristics of nuclear resonant scattering, which differ much from those of single crystals. The analysis of these distinctions is presented. Several approaches to achieve pure nuclear reflections with multilayers are discussed. Finally, we review the studies of multilayer structures with nuclear resonant scattering of synchrotron radiation.

     

Studies of nuclear resonant scattering at TRISTAN-AR

Studies of nuclear resonant scattering of synchrotron radiation undertaken with the X-ray undulator installed in the TRISTAN Accumulation Ring at the National Laboratory for High Energy Physics, KEK, are reported. These studies have evaluated the effect of fast magnetic switching on the nuclear collective decay in an FeBO₃ crystal, the change in the polarization state of nuclear Bragg scattering by fast magnetic switching, and the influence of this switching on the time evolution of the nuclear forward scattering. The phenomenon of interferometric nuclear forward scattering has also been studied.     

Electric quadrupole interactions and the γ–α phase transition in Ce: the role of conduction electrons

We present a theoretical model of the “isostructural" - phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. The latter are treated in tight-binding approximation. The - transition is described as an orientational ordering of quadrupolar electronic densities in a structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the - transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the structure. Received 21 September 1999 and Received in final form 2 May 2000     

Developments in time domain Mössbauer spectroscopy

Time differential measurements of nuclear resonance scattering using synchrotron radiation have been performed with the low energy Mössbauer transitions of⁵⁷Fe,¹¹⁹Sn, and¹⁶⁹Tm since 1984. Various methods of filtering the nuclear energy band from the incident synchrotron radiation are now available. The possibilities of applying these methods to transition energies above 30 keV are discussed. A new technique is proposed, which is especially effective for the high energy Mössbauer transitions. It takes advantage of the different dependence of the electronic Debye-Waller factor and the Mössbauer-Lamb factor on the scattering angle.     

Grazing‐incidence synchrotron‐radiation 57Fe‐Mössbauer spectroscopy using a nuclear Bragg monochromator and its application to the study of magnetic thin films

Energy‐domain grazing‐incidence ⁵⁷Fe‐Mössbauer spectroscopy (E‐GIMS) with synchrotron radiation (SR) has been developed to study surface and interface structures of thin films. Highly brilliant ⁵⁷Fe‐Mössbauer radiation, filtered from SR by a ⁵⁷FeBO₃ single‐crystal nuclear Bragg monochromator, allows conventional Mössbauer spectroscopy to be performed for dilute ⁵⁷Fe in a mirror‐like film in any bunch‐mode operation of SR. A theoretical and experimental study of the specular reflections from isotope‐enriched (⁵⁷Fe: 95%) and natural‐abundance (⁵⁷Fe: ～2%) iron thin films has been carried out to clarify the basic features of the coherent interference between electronic and nuclear resonant scattering of ⁵⁷Fe‐Mössbauer radiation in thin films. Moreover, a new surface‐ and interface‐sensitive method has been developed by the combination of SR‐based E‐GIMS and the ⁵⁷Fe‐probe layer technique, which enables us to probe interfacial complex magnetic structures in thin films with atomic‐scale depth resolution.     

Application of a pnCCD in X‐ray diffraction: a three‐dimensional X‐ray detector

The first application of a pnCCD detector for X‐ray scattering experiments using white synchrotron radiation at BESSY II is presented. A Cd arachidate multilayer was investigated in reflection geometry within the energy range 7 keV < E < 35 keV. At fixed angle of incidence the two‐dimensional diffraction pattern containing several multilayer Bragg peaks and respective diffuse‐resonant Bragg sheets were observed. Since every pixel of the detector is able to determine the energy of every incoming photon with a resolution ΔE/E? 10^?2, a three‐dimensional dataset is finally obtained. In order to achieve this energy resolution the detector was operated in the so‐called single‐photon‐counting mode. A full dataset was evaluated taking into account all photons recorded within 10⁵ detector frames at a readout rate of 200 Hz. By representing the data in reciprocal‐space coordinates, it becomes obvious that this experiment with the pnCCD detector provides the same information as that obtained by combining a large number of monochromatic scattering experiments using conventional area detectors.     

Nuclear resonance scattering of synchrotron radiation by two non-equivalent crystal sublattices in57Fe3BO6

Pure nuclear Bragg reflections off a single crystal of⁵⁷Fe₃BO₆ consisting of two antiferromagnetic sublattices were studied using Mössbauer and synchrotron radiation. Energy and time spectra were measured of different reflections (h00), when either only one sublattice was reflecting, (300), or both sublattices at comparable strength either in antiphase, (500), or in phase, (700). Characteristic line shapes and quantum beat modulations revealed the interference of the scattering by the two sublattices.     

High-pressure Mössbauer spectroscopy with nuclear forward scattering of synchrotron radiation

Abstract

Using a diamond anvil cell, high-pressure ⁵⁷Fe Mössbauer spectroscopy has been performed with the nuclear forward scattering of synchrotron radiation. A pressure-induced magnetic hyperfine interaction at ⁵⁷Fe in SrFeO_{2, 97} has been detected at 44 GPa and 300 K for a first time by a quantum-beat modulation of the decay rate after collective nuclear excitation by the synchrotron pulse. The basic concept and method used to detect nuclear forward scattering with synchrotron radiation are discussed.     

Dielectric loss measurements on silver halide sheet crystals

Abstract

A series of studies on the partial X-ray diffuse scattering intensities from ternary alloys analysed through synchrotron radiation experiments has been reviewed. An intensity expression for the short-range order diffuse scattering has been developed, which is necessary in understanding the separation method of an observed X-ray diffuse intensity into partial intensities contributed from different origins. Techniques have been described in detail mainly concerning the Cu₂NiZn alloy, which have shown the benefits of the anomalous scattering effect of synchrotron radiation. The negative partial intensity maximum for the Cu-Ni pair found in the Cu-Ni-Zn alloy has been discussed from the viewpoints of crystallography and thermodynamics. In addition, at the end of the paper, local atomic arrangements causing the diffuse scatterings have been discussed.     

Synchrotron Mössbauer reflectometry using stroboscopic detection

The concept of the heterodyne/stroboscopic detection of nuclear resonance scattering of synchrotron radiation is extended to the grazing incidence geometry. Model calculations for an antiferromagnetic [⁵⁷Fe/Cr]₂₀ multilayer are shown and discussed. Principles and methodological aspects of stroboscopic synchrotron Mössbauer reflectometry are briefly reviewed.     

Bragg scattering of light in vacuum structured by strong periodic fields

Elastic scattering of laser radiation due to vacuum polarization by spatially modulated strong electromagnetic fields is considered. The Bragg interference arising at a specific impinging direction of the probe wave concentrates the scattered light in specular directions. The interference maxima are enhanced with respect to the usual vacuum polarization effect proportional to the square of the number of modulation periods within the interaction region. The Bragg scattering can be employed to detect the vacuum polarization effect in a setup of multiple crossed superstrong laser beams with parameters envisaged in the future Extreme Light Infrastructure.     

How to do resonant nuclear experiments with synchrotron radiation

Summary The use of synchrotron radiation to excite low-lying nuclear resonances is a rapidly developing field showing great promise for hyperfine spectroscopy, phonon spectroscopy and kinetic studies, crystallography, and fundamental physics experiments. Recent technical advances in synchrotron sources, optics, and fast detectors have drastically increased signal rates and expanded the range of samples that can be studied. A typical experiment today uses a high-brightness synchrotron source having X-ray pulses well-separated in time, a meV-bandpass monochromator using perfect crystals of silicon or germanium, a sample containing resonant nuclei, and an avalanche photodiode timing detector. Both coherent and incoherent scattering can be observed; the coherent scattering is used for hyperfine spectroscopy and studies of diffraction interference phenomena, and the incoherent-scattering signal promises to be very useful for phonon spectroscopy and other studies of excitations in condensed systems. At this point seven nuclear isotopes have been used to resonantly scatter synchrotron radiation, but the number is rapidly increasing. Paper presented at the ICAME-95, Rimini 10–16 September 1995.     

Basic features of coherent nuclear resonant scattering of synchrotron radiation

The time dependences of spatially coherent nuclear resonant scattering of synchrotron radiation show a wealth of characteristic features which originate from the interference of several radiation components and from dynamical nuclear scattering. These effects will be of importance for the future fields of time domain Mössbauer spectroscopy and of nuclear resonant -ray optics. The basic features are discussed and experimental evidence is reviewed.     

Nongyrotropic magneto-optical effects in metal-insulator magnetic multilayer thin films

Nongyrotropic magneto-optical effects are investigated in metal-insulator magnetic multilayer thin films. These effects manifest themselves in changes in the coefficients of transmission and reflection of electromagnetic radiation from the surface of a multilayer film due to the crossover of the magnetic structure from an antiferromagnetic configuration to a ferromagnetic configuration. The nongyrotropic magneto-optical effect observed in reflected light is analyzed theoretically. It is assumed that the multilayer structure is exposed to radiation of a monochromatic plane wave polarized along the direction of magnetization of the film. The magneto-optical effect is described in terms of the permittivity tensor of the multilayer medium, which depends only on the light frequency. The Boltzmann kinetic equation is treated with allowance made for spin-dependent electron scattering both inside conducting layers and at rough interfaces. Using an Fe/C multilayer as an example, it is demonstrated that the nongyrotropic magneto-optical effect is equal in order of magnitude to the equatorial Kerr effect or other strong magneto-optical effects.     

Angular dependence of electronically allowed nuclear bragg reflection of Mössbauer radiation

A typical angular integrated Mössbauer reflection spectrum of an electronically allowed nuclear Bragg reflection was analysed. Mössbauer reflection spectra were measured with high angular resolution. They reveal almost pure nuclear scattering far off Bragg and strong nuclear-electronic interference in the scattering near and at Bragg. The spectra show a pronounced asymmetry with respect to the Bragg position, which is caused by refraction and by interference of nuclear and electronic scattering.     

Nuclear resonant scattering using synchrotron radiation

A one-dimensional quantum model for nuclear resonant scattering using synchrotron radiation has been developed. This model gives a clear physical interpretation of the most prominent features of the coherent forward scattering process namely, the “speed-up” and “dynamical beat” effects. The form of the solution, for the time-dependent forward scattered intensity of the resonant radiation from the resonant medium after synchrotron radiation excitation, is a finite series. This unique solution can be interpreted in terms of a summation over all multiple forward scattering paths the radiation takes in reaching the detector. The resonant medium is represented by a linear chain of N effective resonant nuclei. The analysis starts from a coupled set of quantum mechanical equations for the relevant amplitudes in frequency space. Transformation to the time domain gives an analytical expression for the forward scattered intensity. The contribution of every order of the multiple scattering processes from the N effective nuclei appears naturally. The expression gives a clear physical understanding of all relevant aspects of resonant forward nuclear scattering. Furthermore, the present formalism allows the consideration of incoherent processes. This permits the study of processes in which there is gamma emission with recoil or emission of internal-conversion electrons. This revised version was published online in August 2006 with corrections to the Cover Date.