Magnetic structure factor (${\mathbf{F}}_M(\mathbf{Q})={\sum }_j{f}_j(Q){\mathbf{m}}_{j,\perp }{e}^{i\mathbf{Q}\cdot {\mathbf{r}}_j}$)

The structure factor for magnetic neutron diffraction sums the magnetic form factor and the magnetic moment component perpendicular to the scattering vector over the magnetic atomic basis. For unpolarized neutrons, the magnetic contribution to the coherent diffraction wave intensity is proportional to $|{\mathbf{F}}_M{|}^2$. A periodic change of sign of magnetic moments can shift its allowed peaks away from the nuclear reciprocal lattice vectors without changing nuclear positions.

A magnetic Bragg peak is an elastic diffraction peak from periodic ordered magnetic moments. A single ordering wavevector $\mathbf{q}$ shifts chemical reciprocal vectors to $\mathbf{G}\pm \mathbf{q}$; the basis structure factor, magnetic form factor and moment component perpendicular to the neutron momentum transfer can impose additional extinctions. An allowed translation condition alone does not guarantee visible intensity.