Polarisation/Magnetic Scattering

Magnetic scattering is implemented in five (2D) models

• SphereModel
• CoreShellModel
• CoreMultiShellModel
• CylinderModel
• ParallelepipedModel

In general, the scattering length density (SLD) in each regions where the SLD (=/beta/) is uniform, is a combination of the nuclear and magnetic SLDs and depends on the spin states of the neutrons as follows. For magnetic scattering, only the magnetization component, M*perp, perpendicular to the scattering vector *Q contributes to the the magnetic scattering length.

The magnetic scattering length density is then

where /gamma/ = -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0 is the classical radius of electron, and /sigma/ is the Pauli spin. For polarised neutron, the magnetic scattering is depending on the spin states.

Let's consider that the incident neutrons are polarized parallel (+)/ anti-parallel (-) to the x' axis (See both Figures above). The possible out-coming states then are + and - states for both incident states

Non-spin flips: (+ +) and (- -) Spin flips: (+ -) and (- +)

Now, let's assume that the angles of the Q vector and the spin-axis (x') against x-axis are /phi/ and /theta/up, respectively (See Figure above). Then, depending upon the polarisation (spin) state of neutrons, the scattering length densities, including the nuclear scattering length density (/beta/N) are given as, for non-spin-flips

for spin-flips

where

Here, the M0x, M0y and M0z are the x, y and z components of the magnetization vector given in the xyz lab frame. The angles of the magnetization, /theta/M and /phi/M as defined in the Figure (above)

The user input parameters are M0_sld = DMM0, Up_theta = /theta/up, M_theta = /theta/M, and M_phi = /phi/M. The 'Up_frac_i' and 'Up_frac_f' are the ratio

(spin up)/(spin up + spin down)

neutrons before the sample and at the analyzer, respectively.

Note: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range between 0 and 1.