Problem: Magnetic reflectivity

Question 1

Unlike neutron diffraction, magnetic reflectivity does not have a form factor. Why not?

Solution

The form factors arise because a wave scatters from an object that is of a comparable size to the wavelength. In the case of the magnetic form factor, the neutron scatters from the spatial density of unpaired electrons in an atom. This density is about the size of an atom, which is comparable to the wavelength of thermal neutrons. Mathematically, the magnetic form factor can be derived by taking the Fourier transform of the unpaired electron density around the atom. This is then multiplied by the Fourier transform of the spatial distribution of the magnetic atoms when calculating the expected neutron scattering.

The influence of the magnetic form factor only becomes important at larger scattering vectors, \(q\), where the length scales probed correspond to interatomic distances. The reflectivity regime is at very small \(q\), where the scattering length densities are probed rather than coherent scattering from individual atoms. The magnetic form factor barely changes over the reflectivity regime and can be safely ignored.

Furthermore, a magnetic medium is regarded as a homogeneous block when calculating the expected neutron reflectivity. The subsequent mathematics already account for the size and shape of this block, both in the first Born approximation and in the rigorous dynamical treatment discussed above.

The net result is that a magnetic form factor is unnecessary to describe neutron reflectivity from magnetic media.