Similar, the magnetic inelastic scattering is given by
The total magnetic cross section is
barn.
In (265) 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 (238), 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
(
).
is the Debye-Waller
factor of the atom number
in the magnetic unit cell30.
denotes the number of magnetic
atoms in the magnetic unit cell.
Therefore, if the generalised eigenvalue problem (235) for the dynamical matrix
has been solved, the magnetic neutron scattering function can
be evaluated with the help of equations (239) and (247):
Once the eigenvectors
of the system have been determined, this expression can be
evaluated.
mcdisp evaluates for every mode the expression (267) 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 elements31
of
for every
scattering vector
and diagonalising the matrix (243)
with
.
For small
this procedure can be simplified by using the dipole approximation,
which is described below.