magnon.build¶

Functions¶

`cell_transformation`(original_cell, new_cell)	Computes the matrix transformation mapping from scaled coordinates in the original cell
`build_primitive_cell`(ase_atoms, interactions[, ...])	From the provided Atoms object, attempts to find a primitive cell and rewrites the interactions for this primitive cell.
`convert_kpts`(kpts, original_cell, new_cell)	Convert k-point(s) from scaled coordinates of one cell to another.

Module Contents¶

magnon.build.cell_transformation(original_cell, new_cell)¶

Computes the matrix transformation mapping from scaled coordinates in the original cell to scaled coordinates in the new cell.

Parameters:

original_cell (numpy.ndarray, dtype float) – The lattice vectors of the original cell with shape (3, 3).
new_cell (numpy.ndarray, dtype float) – The lattice vectors of the new cell with shape (3, 3).

Returns:

transformation_matrix – The matrix transforming a point from the old to the new basis with shape (3, 3).

Return type:

numpy.ndarray, dtype float

See also

magnon.build.build_primitive_cell: Uses to map from conventional to primitive cell.

Notes

\[NTx = Ox\]

for transformation_matrix \(T\), scaled coordinates \(x\), and old and new cell bases \(O,N\) respectively.

magnon.build.build_primitive_cell(ase_atoms, interactions, distance_tol=default_distance_tol, no_idealize=False)¶

From the provided Atoms object, attempts to find a primitive cell and rewrites the interactions for this primitive cell.

Parameters:

ase_atoms (ase.Atoms) – The atoms object from which to build the primitive cell.
interactions (magnon.InteractionsList) – The InteractionList object for the original cell exchange couplings.
distance_tol (float, optional) – The precision to use in determining equivalent positions.
no_idealize (bool) – Whether Spglib should idealize the primitive cell.

Raises:

RuntimeError – If the generated primitive cell includes atom properties not compatible with those of the retained atoms from the original cell.

Returns:

ase_prim_atoms (ase.Atoms object) – The ASE Atoms object for the primitive cell
interactions (magnon.InteractionsList) – The InteractionList object for the primitive cell.
transformation_matrix (numpy.ndarray, dtype float) – The matrix transformation mapping from scaled coordinates with respect to the original cell, with shape (3, 3).

Notes

This ‘idealizes’ the lattice, meaning the primitive cell may be rotated in cartesian space. We do this because otherwise we can end up with strange primitive lattice vectors (e.g. negative or left-handed), which then causes great difficulty in plotting correct k-space paths. We next calculate the transformation matrix between the two cells in the next step which we will need for manipulating the interaction vectors.

The spglib standardize_cell function does not use magnetic information. We cannot use spglib.get_magnetic_symmetry_dataset because this has no way to idealize the cell. This is an issue, for example, with antiferromagnets where often the magnetic cell must be larger than non-magnetic cell. We work around the problem here by assigning all atoms with the same atomic number and same magnetic moment a unique number. Spglib only sees numbers as type labels, not as atomic numbers, so this is fine. To avoid collisions with atomic numbers we add 1000x the magnetic moment index. This also means we can trivially remove the artificial type and restore the atomic numbers for the primitive cell data returned by spglib.

magnon.build.convert_kpts(kpts, original_cell, new_cell)¶

Convert k-point(s) from scaled coordinates of one cell to another.

Parameters:

kpts (numpy.ndarray, dtype float) – The k-point(s) in scaled coordinates of the original_cell as an array of shape (3,) or (\(N_k\), 3)
original_cell (numpy.ndarray, dtype float) – The lattice vectors of the original cell with shape (3,3)
new_cell (numpy.ndarray, dtype float) – The lattice vectors of the new cell with shape (3,3)

Returns:

k_scaled_new_cell – The k-point(s) in scaled coordinates of new_cell with shape (3,) or (\(N_k\), 3)

Return type:

numpy.ndarray, dtype float