 Solution

Measure several allowed magnetic reflections from an oriented single crystal by magnetic neutron diffraction, preferably with polarization analysis. A neutron couples to the component of the ordered magnetic moment perpendicular to the scattering vector $\mathbf{Q}$. For a collinear arrangement, the geometric intensity factor isCompare reflections whose $\mathbf{Q}$ point in different crystal directions, correcting for the magnetic form factor and known experimental geometry. Their relative intensities distinguish candidate spin directions; a moment parallel to $\mathbf{Q}$ gives no magnetic signal from that component. Polarized neutrons help separate nuclear and magnetic contributions. Observing only peak positions establishes periodicity, not the spin direction.