Crystal structure

Tutorial tasks

• Create a crystal structure for the material of your choice. Create a cell and a set of atoms. For each atom specify all properties mentioned on this page.

• (extra) Visualize created structure using magnopy.PlotlyEngine

• (extra) Compute conventional and primitive cell of your structure (see wulfric.crystal.get_primitive() and wulfric.crystal.get_conventional()). Visualize them. Are they the same? Is it true for all crystals?

Cell and atoms

There is a crystal structure at the heart of every spin Hamiltonian. It defines the unit cell of the lattice and set of magnetic sites.

Unit cell is simply a set of three vectors. Magnopy stores it in the same way as wulfric and many other Python codes do

import magnopy

cell = [
    [1.0, 0.0, 0.0],
    [0.0, 1.0, 0.0],
    [0.0, 0.0, 1.0],
]

To read more about the cell see magnopy's dedicated documentation page.

Magnopy calls magnetic centers "atoms" due to historical reasons, but they are not necessary atoms. We will use the term "atoms" in this tutorial. In all cases "atoms" simply mean an object that has a set of properties

• Name.

  A label of the magnetic center. If magnetic center coincides with an actual atom of the crystal, then it is a good idea to include atom's type in its name (i. e. "Cr1" or "I_000").

• Position.

  Three numbers that define position of the atom in the basis of the unit cell. I. e. relative position (can also be called "fractional").

• Spin.

  Spin value of the magnetic center. Please note that this is a single number.

• g-factor.

  Proportionality coefficient for the Zeeman term.

Magnopy always uses a set of atoms (even if there is only one atom in the set). It stores them as a dictionary, for example

atoms = {
    "names": ["Cr1", "I1", "I2"],
    "positions": [[0.0, 0.0, 0.0], [0.5, 0.0, 0.0], [0.0, 0.5, 0.0]],
    "spins": [1.5, None, None],
    "g_factors": [2, None, None],
}

Read more about atoms on the magnopy's dedicated documentation page.

Visualization

Magnopy relies on wulfric for all manipulations with the crystal. In fact, the visualization engine of magnopy (magnopy.PlotlyEngine) is an extension of wulfric's visualization engine (wulfric.PlotlyEngine). Both operate in the same way, the only difference is that magnopy's engine offers extra methods.

There is a recommended scenario for using this kind of visualization. First, one shall create an instance of visualization backend

pe = magnopy.PlotlyEngine(_sphinx_gallery_fix=True)

Note

Please ignore _sphinx_gallery_fix=True and do not include this argument in you scripts.

Then, plot what you want to plot. See API reference for the list of available plotting methods - magnopy.PlotlyEngine. For example, to display the cell and atoms

pe.plot_cell(cell, legend_label="Unit cell", color="Black")
pe.plot_atoms(cell, atoms, legend_label="Atoms of the unit cell")

Finally, display or save the figure

Hint

Figures are interactive. Try to rotate it. Try to zoom in/out. Try to click on the elements of the legend.

pe.show(axes_visible=False)