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Polarisation/Magnetic Scattering

Magnetic scattering is implemented in five (2D) models

  • SphereModel
  • CoreShellModel
  • CoreMultiShellModel
  • CylinderModel
  • ParallelepipedModel

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, Mperp, perpendicular to the scattering vector Q contributes to the the magnetic scattering length.

mag_vector.bmp

The magnetic scattering length density is then

dm_eq.gif

where |gamma| = -1.913 is the gyromagnetic ratio, |mu|B is the Bohr magneton, r0 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 (- +)

M_angles_pic.bmp

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

sld1.gif

when there are no spin-flips, and

sld2.gif

when there are, and

mxp.gif myp.gif mzp.gif mqx.gif mqy.gif

Here, M0x, M0y and M0z are the x, y and z components of the magnetization vector given in the laboratory xyz frame given by

m0x_eq.gif m0y_eq.gif m0z_eq.gif

and the magnetization angles |theta|M and |phi|M are defined in the figure above.

The user input parameters are:

M0_sld = DM M0
Up_theta = |theta|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.

Note

This help document was last changed by Steve King, 02May2015

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