Perturbative theory of grazing-incidence diffuse nuclear resonant scattering of synchrotron radiation

Abstract

Theoretical description of off-specular grazing-incidence nuclear resonant scattering of synchrotron radiation (Synchrotron Mössbauer Reflectometry, SMR) is presented. The recently developed SMR, similarly to polarized neutron reflectometry (PNR), is an analytical tool for the determination of isotopic and magnetic structure of thin films and multilayers. It combines the sensitivity of Mössbauer spectroscopy to hyperfine interactions and the depth selectivity of x-ray reflectometry. Specular reflection provides information on the depth profile, while off-specular scattering on the lateral structure of scattering layers. Off-specular SMR and PNR intensity formulae of a rather general multilayer with different domains, based on a Distorted Incident-Wave Approximation (DIWA) are presented. The Distorted-Wave Born Approximation (DWBA) results are given in an Appendix. Physical and numerical implications, why using DIWA, are explained.The temporal character of SMR imposes specific differences between SMR and PNR. In order to reveal the limits of DIWA and to compare the two analytical methods, two-dimensional diffuse SMR and PNR maps of an antiferromagnetic multilayer are calculated and critically compared.

Field-induced spin reorientation in[Fe/Cr]nmultilayers studied by nuclear resonance reflectivity

“…in the odd and even 57 Fe layers) collinear alignment in each of two magnetic sublevels takes place.…”

“…The antiferromagnetic interlayer coupling of 57 Fe layers was evidently detected by the occurrence of the half order Bragg peaks (Fig. 5) on the delayed reflectivity curves measured at the SPring-8.…”

“…We expected that when the external field is absent the hyperfine fields, antiferromagnetically coupled between adjacent 57 Fe layers, has no any preferable azimuth direction in the surface plane. Even if there is some uniaxial anisotropy in the multilayer due to internal stresses generated during deposition (like it was observed in [59] for finemet ferromagnetic alloy) we can not exclude transverse coherence length for ESRF source has been measured as ~ 3 μm in [52] (notice that it depends of the slit sizes), at grazing angle ~ 10 mrad the lateral coherence length is t ξ ~ 300 μm, so domains D ~ 400 μm looks as a quite true result.…”

“…(1) Here we suppose that the incident SR field is σ -polarized, but the Mössbauer transition in 57 Fe is of the magnetic dipole M1 type, so we follow the magnetic field of the radiation with the nuclei, which is π -polarized. Hyperfine interactions reveal themselves in the time spectra of reflectivity by the quantum beats well described for the nuclear resonance forward scattering, but the data interpretation is complicated by the dynamical beats and other effects specific for coherent decay of the excited nuclear system [21].…”

“…We have used the basic advantage of NRR experiments supplying the possibility to measure the time spectra of reflectivity at selected angles of incidence in addition to the NRR angular reflectivity curve. In such a way we got the combination of the spectroscopic and diffraction information in one experiment that supplies us with depth-profile information about hyperfine interactions in 57 Fe layers and their magnetization direction. The joint fit of the angular curve and the time spectra of reflectivity, measured at several grazing angles, adds the reliability to the obtained magnetization depth-profiles.…”