Getting Started#

Installation#

To use magpack, first install it using pip:

(.venv) $ pip install magneticScattering

Magnetic Diffraction#

This package can be used to simulate scattering from a magnetic structure. To to this, three classes describing the experimental setup must first be specified:

  1. Sample

  2. Beam

  3. Geometry

These classes are then passed to the Scatter class in order to calculate the resulting scattering pattern. In the following sections, these parameters are described in more detail and examples are provided.

Sample#

The Sample is initialized with the following parameters:

Sample(sample_length, scattering_factors, magnetic_configuration)

  • sample_length: size of the sample in meters as a scalar or a two-component vector in meters

  • scattering_factors: scattering factors list [f0, f1, f2]. These are the complex pre-factors corresponding to the charge, magnetic circular and magnetic linear scattering. The real part is the refractive index (or phase) and the imaginary part is the dissipation (absorption).

  • structure: the magnetic configuration of the sample as a numpy array with shape (3, nx, ny) (charge component will be inferred) or (4, nx, ny) with the charge component at index 0 (see Structure.)

Beam#

The Beam is initialized with the following parameters:

Beam(wavelength, beam_fwhm, polarization)

  • wavelength: wavelength of incident radiation in meters.

  • beam_fwhm: full width at half maximum of the beam as a scalar or a two-component vector in meters.

  • polarization: four-component polarization in the form of a Stokes vector (see Stokes Parameters.).

Geometry#

The Geometry is initialized with the following parameters:

Geometry(angle, detector_distance)

  • angle: The angle of incidence between the beam and the sample in degrees.

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

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

The sample plane is the x-y plane, such that the \(m_x\) and \(m_y\) components are in-plane, and \(m_z\) is out of plane.

Scatter#

To compute the scattering pattern, call the Scatter class with the three classes from before:

Scatter(Sample, Beam, Geometry)

The intensity of the scattering can be obtained from Scatter.intensity or plotted directly using functions in the plot submodule. Some examples are:

plot.structure(Sample)                          # plot the components of the magnetic structure
plot.intensity(Scatter, log=True)               # plot the intensity of the scattering
plot.difference(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 \((S_0,S_1,S_2,S_3)\) defined as follows:

  • \(S_0\): Intensity of the light, conventionally normalized to unity.

  • \(S_1\): Component of light that is linearly polarized. \(+1\) corresponds to purely linear horizontal polarization and \(-1\) to purely linear vertical.

  • \(S_2\): Component of light that is linearly polarized along the diagonals. \(+1\) corresponds to purely \(+45^\circ\) polarization, \(-1\) to purely \(-45^\circ\) polarization.

  • \(S_3\): Component of light that is circularly polarized. \(+1\) corresponds to purely right-handed circular polarization, \(-1\) to purely left-handed circular polarization.

Structure#

The magnetic vector field has three components, \((m_x,m_y,m_z)\) and extends is two-dimensional in space. Therefore, it is represented here as a numpy array of shape (3, nx, ny). The charge component can also be specified using a (4, nx, ny) shaped numpy array, where the index 0 corresponds to the electron density of the sample.

To create such an array this array given its individual, 2D scalar components, \(m_x,\, m_y,\, m_z\), one can use:

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

\(m_x,\, m_y,\, m_z\) must all be the same size and should be two-dimensional, e.g. (nx, ny) and should have the same physical properties (e.g., lateral dimension)

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

when the beam is perpendicular to the sample (angle = 0) the magnetization components \(m_x,\,m_y\) are in the plane of the sample, while the magnetization component \(m_z\) is out of the plane (and parallel to the beam).

References#

van der Laan, G., “Theory from Soft X-ray resonant magnetic scattering of magnetic nano structures,” https://doi.org/10.1016/j.crhy.2007.06.004