magneticScattering 0.1.0

Simulates x-ray magnetic scattering

Magnetic Diffraction

Simple code for computing the magnetic diffraction pattern of a magnetic structure.

To use: Define the structure, beam and geometry of the experiment, then compute scattering by calling the Scatter class. The magnetic structure is defined using the Sample class, the incident beam is defined using the Beam class and the geometry is defined using the Geometry class.

Sample

The Sample is initialized with the following parameters:

Sample(sample_length, scattering_factors, magnetic_configuration)

sample_length: real size of the sample in meters. Scalar if x, y dimensions are equal or vector otherwise.

scattering_factors: scattering factors list with [f0, f1, f2] representing charge, XMCD and XMLD respectively.

structure: the magnetic configuration for scattering (see section below).

Beam

The Beam is initialized with the following parameters:

Beam(wavelength, beam_fwhm, polarization)

wavelength: wavelength of incident radiation in meters.

beam_fwhm: size of beam or full width at half maximum of the beam. Can be a scalar or a 2 component vector.

polarization: 4 component polarization in the form of a Stokes vector (see section below).

Geometry

The Geometry is initialized with the following parameters:

Geometry(angle, detector_distance)

angle: The angle between the beam and the sample plane in degrees.

detector_distance: The distance between the sample and the detector in meters.

Scatter

To compute the scattering pattern call the Scatter class with the following parameters:

Scatter(Sample, Beam, Geometry)

The intensity of the scattering can be obtained from Scatter.intensity or plotted directly using functions in the plotting.py folder, some examples are:

plotting.plot_structure(Sample, quiver=True)        # plot the components magnetic structure
plotting.plot_intensity(Scatter, log=True)          # plot the intensity of the scattering
plotting.plot_diff(Scatter_a, Scatter_b, log=True)  # plot the difference between two scattering patterns

Stokes Parameters

The Stokes parameters are four components that define the polarization state of light. For convenience they are combined to form a vector; it is actually a pseudovector and does not have any physical interpretation. They are defined as follows:

S_0: Intensity of the light.

S_1: Component of intensity of light that is linearly polarized. Positive values for horizontal polarization, negative values for vertical polarization.

S_2: Component of intensity of light that is linearly polarized along the diagonals. Positive values for +45 degree polarization, negative values for -45 degree polarization.

S_3: Component of intensity of light that is circularly polarized. Positive values for right-handed polarization, negative values for left-handed polarization.

Structure

The magnetic vector field is a two-dimensional field, with three components. It is therefore defined as a numpy array of shape (3, nx, ny). To create this array from its scalar components, (mx, my, mz) one can use:

structure = np.array([mx, my, mz])

mx, my, mz must all be of the same size and should be two dimensional, of size (nx, ny), same as the pixel_size.

Structures can be made or imported using the structures header. Some examples are:

strucutres.vortex(nx, ny) and structures.skyrmion(nx, ny).

Geometry

The geometry here is such that the beam travels in the positive z dimension when angle_d = 0 and along the negative y dimension when angle_d = 90.

The sample plane is the x-y plane, thus the mx and my components are in-plane and mz is out of plane.

Theory of Magnetic Diffraction

Theory from "Soft X-ray resonant magnetic scattering of magnetic nanostructures" , https://doi.org/10.1016/j.crhy.2007.06.004