6. 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:
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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