 Magnetic neutron diffraction

ID: magnetic-neutron-diffraction

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Magnetic neutron diffraction by

Codex  0 2026-10-18

Magnetic neutron diffraction uses scattering of neutrons by ordered magnetic moments to infer magnetic order. Neutrons also scatter from atomic nuclei, so a pattern can contain nuclear and magnetic contributions. A Bragg scattering peak encodes periodicity; it is not a photograph of an individual spin.

A minimal original calculation makes the extra periodicity visible. Consider identical nuclear scatterers at positions

x_{n} = na

, with equal neighboring separation

a

, and ordered magnetic moments alternating between

+ m_{A}

and

- m_{B}

. A two-site repeating block of length

2 a

has nuclear and magnetic scattering amplitudes, apart from common geometric factors,

F_{N} (q) = b (1 + e^{i q a}), F_{M} (q) = m_{A} - m_{B} e^{i q a}, q = \frac{πh}{a}, h \in Z .

Here

b

is the common nuclear scattering coefficient and

q

the component of the scattering wave vector along the row. The magnetic expression assumes equally scattering point magnetic moments perpendicular to the scattering wave vector; real magnetic scattering measures the perpendicular component and has a momentum-dependent amplitude. This one-dimensional calculation is a periodicity illustration, not a finite-temperature solution for a chain.

For even

h

,

F_{N} = 2 b

and

F_{M} = m_{A} - m_{B}

. For odd

h

,

F_{N} = 0

and

F_{M} = m_{A} + m_{B}

. Thus equivalent opposing magnetic sublattices,

m_{A} = m_{B}

, cancel in forward scattering but reinforce at the odd positions of the doubled period. The intensity is proportional to the squared magnitude of the scattering amplitude, so changing an amplitude's sign does not make a negative intensity.

Figure 1.
An alternating magnetic moment pattern creates extra reciprocal lattice peaks
. Original exact two-site crystal basis structure factor illustration, not historical measurements or a simulation of MnO. Nuclear strengths use $b = 1$ . Ordered magnetic strengths use $(m_{A}, m_{B}) = (1, 1)$ or $(2, 1)$ ; each channel is in its own arbitrary units, so their absolute heights cannot be compared. Thin solid nuclear sticks and dashed magnetic sticks coincide at even $h$ in the ferrimagnetic case. The top panel stipulates loss of long-range magnetic order while retaining nuclear periodicity; diffuse magnetic scattering is omitted, rather than asserted absent. Only positive nonzero $q$ is shown. Details.

This calculation also exposes a useful difference between antiferromagnetism and ferrimagnetism: with

m_{A} = 2

and

m_{B} = 1

, magnetic squared amplitudes are

1

at even

h

and

9

at odd

h

. Extra magnetic peaks can therefore occur in a ferrimagnet too. Identifying a real magnetic structure needs the full crystal basis structure factor, multiple reflections, and the allowed moment orientations, rather than a single extra peak.

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