Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 5 / a / Solution

Choose the four basis-spin signs as $(+,-,-,+)$ in the order of positions listed in the source; reversing all signs changes no diffraction intensity. Apart from the common magnetic form factor and perpendicular-moment factor, the magnetic structure factor isThe first factor is nonzero exactly when $h$ and $k$ have opposite parity, and the second exactly when $l$ is odd. Thus the magnetic Bragg peaks requireWhen both conditions hold, $|F_M|=4|m|$ before geometric and magnetic-form-factor weights. These are magnetic selection rules for the antiferromagnetic component, not conditions forbidding all nuclear diffraction at other indices.