A common optical algorithm for the evaluation of specular spin polarized neutron and Mössbauer reflectivities

Abstract

Using the general approach of Lax for multiple scattering of waves a 2 × 2 covariant expression for the reflectivity of polarized slow neutrons of a magnetic layer structure of arbitrary complexity is given including polarization effects of the external magnetic field. The present formalism is identical to the earlier published one for the (nuclear) resonant x-ray (Mössbauer) reflectivity and properly takes the effect of the external magnetic field of arbitrary direction on the neutron beam into account. The form of the reflectivity matrix allows for an efficient numerical calculation.

Stroboscopic detection of nuclear resonance in an arbitrary scattering channel

“…Mössbauer nuclei (Deák et al, 2001;Hannon et al, 1985b;Deák et al, 1996). Like in the forward case, this scattering is independent of the atomic positions in the reflecting medium, such that the scattering is described by its index of refraction n (E) (Deák et al, 1996;Lax, 1951).…”

“…The index of refraction is related to the susceptibility matrix χ (Deák et al, 2001;Deák et al, 1996) through…”

“…This takes into account the interferences of the reflected radiation from the surfaces and interfaces between the layers with different refraction index. The methods of calculating the reflectivity matrix can be found in the literature (Röhlsberger et al, 2003;Deák et al, 2001;Deák et al, 1996). Accordingly, the total scattering matrix of the specimen and the reference from Eq.…”

“…Grazing-incident NRS of SR, often called Synchrotron Mössbauer Reflectometry (SMR) (Gerdau & DeWaard, 1999;Deák et al, 2001;Deák et al, 2002), has been established in both time and angular regime (Chumakov et al, 1999;Deák et al, 2002;Nagy et al, 1999), as time differential (TD) and time integral (TI) SMR, respectively.…”

“…In the grazing incidence limit, an optical model was derived from the dynamical theory (Hannon & Trammell, 1969;Hannon et al, 1985b), which has been implemented in numerical calculations (Röhlsberger et al, 2003). The reflectivity formulae given by Deák et al (1996) and Deák et al (2001) are suitable for fast numerical calculations in order to actually fit the experimental data (Spiering et al, 2000) and, as has been shown , this optical method is equivalent to that of the other approaches in the literature (Röhlsberger et al, 2003;Hannon et al, 1985b).…”