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

Theoretical description of off-specular grazing-incidence nuclear resonant scattering of synchrotron radiation (synchrotron Mössbauer reflectometry, SMR) is presented. The recently developed SMR, similar 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 formulas of a rather general multilayer with different domains, based on a distorted incident-wave approximation (DIWA), are presented. The distorted-wave Born approximation results are given in an appendix. Physical and numerical implications, of 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. Experimental “ω−2θ” SMR map of a periodic [Fe∕Cr]₂₀ multilayer is presented and compared with simulations by the present theory.