Polarisation/Magnetic Scattering

Magnetic scattering is implemented in five (2D) models

• sphere
• core_shell_sphere
• core_multi_shell
• cylinder
• parallelepiped

In general, the scattering length density (SLD, = |beta|) in each region where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised neutrons, also depends on the spin states of the neutrons.

For magnetic scattering, only the magnetization component, M_perp, perpendicular to the scattering vector Q contributes to the the magnetic scattering length.

The magnetic scattering length density is then

where |gamma| = -1.913 is the gyromagnetic ratio, |mu|_B is the Bohr magneton, r₀ is the classical radius of electron, and |sigma| is the Pauli spin.

Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) to the x' axis, the possible spin states after the sample are then

No spin-flips (+ +) and (- -)

Spin-flips (+ -) and (- +)

If the angles of the Q vector and the spin-axis (x') to the x-axis are |phi| and |theta|_up, respectively, then, depending on the spin state of the neutrons, the scattering length densities, including the nuclear scattering length density (|beta|_N) are

when there are no spin-flips, and

when there are, and

Here, M_0x, M_0y and M_0z are the x, y and z components of the magnetization vector given in the laboratory xyz frame given by

and the magnetization angles |theta|_M and |phi|_M are defined in the figure above.

The user input parameters are:

Note: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1.