Computer Algebra calculation of XRMS polarisation dependence in the non spherical case

TL;DR

This paper develops analytical formulae and a Mathematica code to relate experimental geometry and sample orientation to XRMS scattering intensity in non-centrosymmetric magnetic systems, aiding experimental design and data analysis.

Contribution

It introduces a concise Mathematica implementation for calculating XRMS polarization dependence in non-spherical, non-centrosymmetric magnetic systems, expanding analytical tools in the field.

Findings

Provides explicit formulae for XRMS polarization dependence.

Offers a Mathematica code for practical calculations.

Demonstrates applications to specific magnetic systems.

Abstract

Simple analytical formulae, directly relating the experimental geometry and sample orientation to the measured R(M)XS scattered intensity are very useful to design experiments and analyse data. Such formulae can be obtained by the contraction of an expression containing the polarisations and crystal field tensors, and where the magnetisation vector acts as a rotation derivative\cite{mirone}. The result of a contraction contains a scalar product of (rotated) polarisation vectors and the crystal field axis. The contraction rules give rise to combinatorial algorithms which can be efficiently treated by computers. In this work we provide and discuss a concise Mathematica code along with a few example applications to non-centrosymmetric magnetic systems.