source:
sasmodels/doc/guide/magnetism/magnetism.rst
@
d682f66
Last change on this file since d682f66 was befe905, checked in by awashington, 7 years ago | |
---|---|
|
|
File size: 3.4 KB |
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:
- Non spin-flip $(+ +)$ and $(- -)$
- Spin-flip $(+ -)$ 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 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 | $D_M M_0$ |
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.
Document History