source: sasmodels/doc/guide/magnetism/magnetism.rst @ 1f058ea

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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

βM = (γr0)/(2μB)σM = DMσM

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

β±± = βNDMMx when there are no spin-flips


β±∓ =  − DM(My±iMz) when there are


Mx = M0qxcos(θup) + M0qysin(θup) My = M0qycos(θup) − M0qxsin(θup) Mz = M0z M0qx = (M0xcosφ − M0ysinφ)cosφ M0qy = (M0ysinφ − M0xcosφ)sinφ

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

M0x = M0cosθMcosφM M0y = M0sinθM M0z =  − M0cosθMsinφM

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


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

Document History

2015-05-02 Steve King
2017-05-08 Paul Kienzle

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