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 $\Sv$ on a magnetic sublattice is related to that ${\Sv}_l$ in another unit cell at vector distance l (a lattice vector) from it by

$${\Sv}_l= {\Sv} \mbox{\rm fn}(\kv\cdot\mathbf{l})$$

where $\mbox{\rm fn}(x)$ is a periodic function of $x$ such that $\mbox{\rm fn}(x)=\mbox{\rm fn}(n+x)$ for all integer $n$.

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 $\tilde R_s$ and ${\bf t}_s$ are the rotation and translation operators associated with one of the elements in the magnetic group and $\tilde T_s$ 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

$${\Sv}_s=\tilde T_s\tilde R_s{\Sv}\quad\mbox{at}\quad \tilde R_s{\bf r}+{\bf t}_s$$

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.