## MGENPOS - General Positions for Magnetic Space Groups

### Online Help

This program permits the access to the generators and the general positions for a given magnetic space group. The space groups are specified by their label as given in the original listings made by Opechowski-Guccione (1) and Belov-Neronova-Smirnova (2). You can give this number if you know it, or you can choose it using the tables with the space group and magnetic space groups labels and symbols if you click on the button [**choose it**].

If you want to see the generators or the general positions on a non conventional setting, click on [**Non conventional setting**]. This will show a form where you should give the transformation matrix relating the conventional setting of the group you have chosen with the non conventional one you are interested in. Only change of basis matrix with determinant equal to one are accepted.

If you need one of the two conventional settings currently in use, just click on [**Conventional setting**].

**Important:** *A list with all the elements of the traslation lattice and the black-and-white lattice inside the corresponding unit cell is provided for completeness and to compare with other listings.*

References:

1. Opechowski and Guccione (1965). Magnetism, edited by G. T. Rado and H. Suhl, Vol. II, Part A, pp. 105-165. New York: Academic Press

2. Belov et al. (1957). Sov. Phys. Crystallogr. 2, 311-322

### k-vector

This vector defines the black&white lattice of the group according to the following rule: the translations **T** of the lattice generated by the OG unit cell that fullfill exp[i**k**·**T**] = -1 are antitranslations: {1'|**T**}, while the rest, which, will necessarily fulfill exp[i**k**·**T**] = 1, are ordinary lattice translations: {1|**T**}.

The k-vector is given here in the reciprocal basis of the OG lattice unit cell. If the lattice given by the OG unit cell is the one observed in the paramagnetic phase, this k-vector (or any equivalent) coincides with the propagation vector to be observed for this magnetic space group.