Problem: Reflectivity in magnetic materials

Question 1

What will occur in reflectivity from a magnetic material with \(\overline{b}_N = C\overline{M}_{\perp}\)?

Solution

The refractive index for a magnetic material is given by:

\(n_{\pm}^2 = 1-\frac{\lambda^2_0}{\pi}\rho\left(\overline{b}_N \pm C\overline{M}_{\perp}\right)\)

When \(\overline{b}_N = C\overline{M}_{\perp}\), the refractive index for one spin state \({\left(-\right)}\) becomes 1 (the same as the refractive index in a vacuum), and becomes very different to 1 for the other spin state \(\left(+\right)\). The critical edge for total reflection is given by

\(q_c = \sqrt{16\pi\left(\rho_2\overline{b}_2-\rho_1\overline{b}_1\right)}\)

If neutrons in a vacuum (or in air) are incident on this surface (i.e. \(\rho_1\overline{b}_1 = 0\)), the critical edge for the \(\left(+\right)\) spin-state neutrons will be large and the critical edge for the \(\left(-\right)\) spin-state neutrons will be zero. Only \(\left(+\right)\) neutrons would be reflected. The surface could then be used as a neutron polarizer, creating a neutron beam with only \(\left(+\right)\) neutrons.