Polarisation/Magnetic Scattering

Models which define a scattering length density parameter can be evaluated

as magnetic models. 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 $mathbf{M_perp}$ perpendicular to the scattering vector $mathbf{Q}$ contributes to 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 $theta_{up}$, respectively, then, depending on the spin state of the neutrons, the scattering length densities, including the nuclear scattering length density ($beta{_N}$) are

and

where

Here, $M_{0x}$, $M_{0x}$, $M_{0z}$ 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:

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