Magnetic Domains

Whenever the magnetic symmetry of a structure is less than the symmetry of the nuclear structure magnetic domains can occur. Different parts of the crystal conform to one or other of the possible domains. The different types that occur are: configuration domains, 180^o domains, orientation domains and chirality domains.

Configuration domains occur when the propagation vector is not invariant under one or more of the symmetry operations of the space group. Magnetic structure factors are calculated for the configuration domain whose propagation vector is given on the Q PROP card. If magnetic atoms which were equivalent under the full symmetry, are found to be inequivalent with the reduced configuration symmetry CCSL will raise an error. In this case the symmetry cards and atomic positions must be adjusted to conform to the configuration symmetry.

180^o domains occur for all structures for which $\kv =0$; the magnetic structure factors for pairs of 180^o domains are reversed in direction.

Orientation domains occur whenever the magnetic group has symmetry lower than the configurational symmetry i.e. when there are one or more Q NSYM cards.

The subroutines FMCALC and LMCALC calculate magnetic interaction vectors for all the orientation domains and store them in COMMON/QCAL/. They also calculate the mean squared interaction vector averaged over all such orientation domains assuming equal populations. This is the quantity used in the MAGLSQ magnetic structure refinement and printed out as $F_m^2$ by the magnetic structure factor program GETMSF.

A further type of orientation domain occurs when the magnetic structure cannot be described using all the operators of the parent space-group even using NSYM operations. This happens when one or more of the symmetry operators of the space group operates differently on the magnetic moments of different magnetic atoms. In this case the magnetic structure factors must be calculated using the sub-group which omits these operators. The associated domains can be described as magnetic twin domains related by twin matrices corresponding to the rotational parts of the missing operators.

In magnetic structure calculations the contributions from different twin domains can be included by using twin matrices given on R TMAT cards.

In cases where chirality domains occur their interaction vectors complex conjugate to one another; they are not now (Mark 4.4) included separately in /QCAL/.

Numbering of magnetic domains

The $N_m$ orientation domains generated by NSYM operations are numbered by $n_m$ in the order in which the operators appear in the magnetic symmetry table. Then if there are $N_t$ twin matrices given on $N_t$ R TMAT cards numbered $n_t$ with ($1 <=n_t<=N_t$) and $N_c$ chirality domains ($N_c= 1$ or 2) numbered $n_c$. Then the number given to the domain $n_t,n_m,n_c$ is

$$N_d(n_t,n_m,n_c)=N_mN_c(n_t-1) + N_c(n_m-1)+n_c$$

If 180^o domains can be distinguished the numbers given to a pair of such domains differ by $N_tN_mN_c$.