### Magnetic inelastic Scattering

Similar, the magnetic inelastic scattering is given by

 (219)

The total magnetic cross section is  barn. In (230) the first term in the bracket corresponds to the total and the second term to the elastic scattering. If we split the index into basis and lattice part and compare equation (203), we see that the scattering function depends on the correlation function between the magnetisation operator , which is the observable in the case of magnetic neutron scattering ( ).

 (220)

is the Debye-Waller factor of the atom number in the magnetic unit cell28. denotes the number of magnetic atoms in the magnetic unit cell. Therefore, if the generalised eigenvalue problem (200) for the dynamical matrix has been solved, the magnetic neutron scattering function can be evaluated with the help of equations (204) and (212):

 (221)

Once the eigenvectors of the system have been determined, this expression can be evaluated. mcdisp evaluates for every mode the expression (232) with exception of the -function and multiplies it by in order to get the nuclear Intensity in barns/meV formula unit. In addition, the components of the magnetic scattering function can be output (to be used to interpret polarised magnetic neutron scattering). then refer to either the xyz coordinate system (, and perpendicular to and ) or the uvw coordinate system ( , perpendicular to the scattering plane (as determined by the cross product of subsequent vectors in the input q-vector list of mcdisp) and perpendicular to and , such that uvw for a righthanded system).

Form factor effects on the scattering intensity are due to the -dependence of the magnetisation operator, which means that the transformation matrices and the eigenvalues are also -dependent. These quantities have to be calculated by evaluating the transition matrix elements29 of for every scattering vector and diagonalising the matrix (208) with . For small this procedure can be simplified by using the dipole approximation, which is described below.

Martin Rotter 2017-01-10