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, $r_0$ 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 $theta_text{up}$, 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.