source:
sasmodels/doc/guide/magnetism/magnetism.rst
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2c108a3
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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 antiparallel () to the $x'$ axis, the possible spin states after the sample are then
Non spinflip (+ +) and ( )
Spinflip (+ ) and ( +)
If the angles of the $Q$ vector and the spinaxis $x'$ 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:
M0_sld  = $D_M M_0$ 
Up_theta  = $theta_mathrm{up}$ 
M_theta  = $theta_M$ 
M_phi  = $phi_M$ 
Up_frac_i  = (spin up)/(spin up + spin down) neutrons before the sample 
Up_frac_f  = (spin up)/(spin up + spin down) neutrons after the sample 
Note
The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1.
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