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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.

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.

Below the ordering temperature, coherent spin correlations produce magnetic Bragg intensity. Depending on the magnetic propagation vector, this can appear as additional peaks or as added intensity at positions already occupied by nuclear reflections. A magnetic unit cell larger than the chemical one gives extra reciprocal-space positions; a zero-propagation-vector canted structure need not do so.

Magnetic intensity generally decreases at large scattering vector through the magnetic form factor and depends on moment components perpendicular to the scattering vector. Above the transition the long-range magnetic Bragg contribution disappears, though short-range correlations can leave diffuse scattering. The nuclear pattern remains approximately unchanged unless magnetic ordering also drives a structural distortion.

For type I, a magnetic unit cell uses the magnetic Bravais translations $(0,a,a)$, $(a,0,a)$ and $(a,a,0)$. They form an FCC lattice with conventional cubic parameter $2a$. A two-spin basis is an up spin at $(0,0,0)$ and a down spin at $(a,0,0)$, or fractional conventional coordinates $(0,0,0)$ and $(1/2,0,0)$. Every translation preserves the parity of $n_x+n_y+n_z$.

At $\mathbf{Q}=(2\pi /a)(h,k,l)$, the FCC translation sum allows $h,k,l$ all integers or all half-odd-integers. The spin basis contributes $S[1-e^{2\pi ih}]$, which removes the integer set and leavesEquivalently the spin field is $S(-1{)}^{n_x+n_y+n_z}$, so magnetic Bragg peaks are nuclear reciprocal vectors shifted by $(1/2,1/2,1/2)$.

For type II with parallel spins along $z$, use $(a,a,0)$, $(-a,a,0)$ and $(0,0,a)$ as magnetic translations: a primitive tetragonal cell with side lengths $\sqrt{2}a,\sqrt{2}a,a$, containing an up spin at zero and a down spin at $(a,0,0)$. The reciprocal translations have $h,k$ both integers or both half-odd-integers, with $l$ integer. The same basis factor removes the integer-$h$ set:This also follows from $S(-1{)}^{n_x+n_y}$. Other domains permute the three coordinate directions. A magnetic neutron cross section further multiplies these lattice conditions by the magnetic form factor and by the component of ordered moment perpendicular to $\mathbf{Q}$; that polarization factor can suppress an otherwise allowed peak.

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.

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.