source: sasmodels/doc/guide/magnetism/magnetism.rst @ 2c108a3

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 2c108a3 was 2c108a3, checked in by Paul Kienzle <pkienzle@…>, 5 years ago

simplify magnetism code

  • Property mode set to 100644
File size: 2.9 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.

mag_img/mag_vector.png

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

Non spin-flip (+ +) and (- -)

Spin-flip (+ -) and (- +)

mag_img/M_angles_pic.png

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 for non spin-flip states

and

β±∓ =  − DM(My±iMz) for spin-flip states

where

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

Note

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

Docutils System Messages

?
Note: See TracBrowser for help on using the repository browser.