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sasmodels/doc/guide/magnetism/magnetism.rst
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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 $( +)$
Each measurement is an incoherent mixture of these spin states based on the fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, with weighting:
Ideally the experiment would measure the pure spin states independently and perform a simultaneous analysis of the four states, tying all the model parameters together except $u_i$ and $u_f$.
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  $D_M M_0$ 
mtheta:sld  $theta_M$ 
mphi:sld  $phi_M$ 
up:angle  $theta_mathrm{up}$ 
up:frac_i  $u_i$ = (spin up)/(spin up + spin down) before the sample 
up:frac_f  $u_f$ = (spin up)/(spin up + spin down) 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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