The resonant magnetic scattering intensity is calculated as outlined for example in [25] for the magnetic electric dipole scattering according to the squared absolute value of the scattering amplitude given for the ion in the lattice as

(22) | |||

Here, dropping the site index , is the Bragg scattering angle and and aree components of the magnetization vector with respect to the coordinate system . The scattering plane, defined by the direction of the incident and final wave vectors and , contains lying perpendicular and in the sense of and parallel to the scattering vector . The scattering channels for and terms are considered separately and no interference is considered.

To determine the azimuthal dependence the are expanded in terms of the components and of the magnetic moment along the orthogonal crystallographic unit cell vectors , and (for non orthogonal crystal lattices currently magnetic xray scattering intensities cannot be calculated):

(23) |

with angles and , where and is the projection of onto the plane perpendicular to . In the chosen experimental geometry when points to the x-ray source.

Martin Rotter 2017-01-10