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Description of a Magnetic Structure
In CCSL magnetic structures are described using a propagation vector to define
the periodicity, and a magnetic space group to define the relative
orientations of spins on different sub-lattices within the non-magnetic
unit cell. This approach has the advantage that only the minimum
information need be given and multiple unit cells are not required.
The propagation vector
is defined so that
the ordered moment
on a magnetic sublattice is related to that
in
another unit cell at vector distance l (a lattice vector) from it by
where
is a periodic function of
such that
for
all integer
.
The magnetic space group must be congruent with the crystallographic space
group or one of its sub-groups.
Each of the elements of the magnetic group acts on the magnetic moment with
the rotation and translation appropriate to the corresponding element in the
crystallographic group.
This may be followed by the operation of time
inversion in which case the element is primed ;
otherwise it is unprimed .
If
and
are the rotation and translation operators
associated with one of the elements in the magnetic group and
the corresponding time reversal operator (1 or
1 depending on whether
time-reversal is invoked) then
magnetic moment
at vector distance r from the origin of the unit
cell implies magnetic moment
There is one such relationship for each of the elements in the magnetic
group. One must
remember that magnetic moment is an axial vector so that improper
rotations introduce an additional inversion.
The information needed to describe a magnetic structure is given on
Q cards
which are fully described in chapter 3.
Next: Types of Magnetic Order
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P.J. Brown - Institut Laue Langevin, Grenoble, FRANCE. e-mail brown@ill.fr