Atoms/Sites#

Note

Historically, we called the collection of positions in the real space with a number of properties defined for each position as "atoms".

In the paper about Magnopy we do not use the term "atoms", but rather talk about "magnetic sites". However, not every atom of the crystal would be a magnetic site in general. Moreover, a cluster of several atoms can form a single magnetic site in some models.

Altogether, the situation is a bit confusing.

We continue to call a position in the real space with a number of properties (such as name, spin value, g-factor, etc.) an "atom" in the documentation and code of Magnopy. Still we want to stress that this is just a historical name. It is for the user to decide how to interpret an "atom" in their particular model.

Atoms are stored as a plain python dictionary. Keys of the atoms are plural and describe what kind of information is stored in the corresponding value. Values are lists of the same length \(M^{\prime}\).

Here is an example of the atoms dictionary with six atoms in it

>>> atoms = {
...     "names": ["Cr1", "Br1", "S1", "Cr2", "Br2", "S2"],
...     "positions": [
...         [0.5, 0.0, 0.882382],
...         [0.0, 0.0, 0.677322],
...         [0.5, 0.5, 0.935321],
...         [0.0, 0.5, 0.117618],
...         [0.5, 0.5, 0.322678],
...         [0.0, 0.0, 0.064679],
...     ],
...     "spins" : [3/2, None, None, 3/2, None, None],
...     "g_factors" : [2.0, None, None, 2.0, None, None],
...     "spglib_types": [1, 2, 3, 1, 2, 3],
... }

>>> f"{len(atoms['names'])} atoms"
'6 atoms'

>>> for name, position, spin, g_factor, spglib_type in zip(*atoms.values()):
...     print(f'Atom "{name}"')
...     print(f"  position is {position}")
...     print(f"  S = {spin}")
...     print(f"  g = {g_factor}")
...     print(f"  spglib type is {spglib_type}")
Atom "Cr1"
  position is [0.5, 0.0, 0.882382]
  S = 1.5
  g = 2.0
  spglib type is 1
Atom "Br1"
  position is [0.0, 0.0, 0.677322]
  S = None
  g = None
  spglib type is 2
Atom "S1"
  position is [0.5, 0.5, 0.935321]
  S = None
  g = None
  spglib type is 3
Atom "Cr2"
  position is [0.0, 0.5, 0.117618]
  S = 1.5
  g = 2.0
  spglib type is 1
Atom "Br2"
  position is [0.5, 0.5, 0.322678]
  S = None
  g = None
  spglib type is 2
Atom "S2"
  position is [0.0, 0.0, 0.064679]
  S = None
  g = None
  spglib type is 3

atoms is one of the three objects that are required for the creation of an instance of the SpinHamiltonian class. It is then stored as an immutable attribute SpinHamiltonian.atoms.

We specify keys of the atoms dictionary that are expected by Magnopy in the docstrings of the relevant functions and classes.

Hint

the atoms dictionary is defined in the same way as in Wulfric. Magnopy does not define any helper functions to manipulate with the atoms, as it is out of the scope of this package. Instead we depend on Wulfric for all manipulations with atoms.

Expected keys#

"names" : Inherited from Wulfric. Arbitrary labels of atoms. Each element is a string.
"positions" : Relative coordinates of atoms. Inherited from Wulfric. Each element is an array-like of length \(3\).
"spins" : Spin values for each atom. Each element is a float or int.
"g_factors" : g-factors for each atom. Used in the definition of the Zeeman term. Each element is a float or int.
"spglib_types" : Inherited from Wulfric. Atomic types as defined in spglib. Used in the symmetry analysis (via Wulfric and spglib). See wulfric.get_spglib_data() and wulfric.get_spglib_types() for details. Each element is an int (\(\ge 1\)).

Hint

The dictionary structure of atoms allows to add any other property simply by adding a new key and a corresponding list of values to the atoms dictionary. This addition would not break anything in Magnopy.

Magnetic vs non-magnetic atoms#

By itself the dictionary atoms does not differentiate between magnetic and non-magnetic atoms. The concept of magnetic and non-magnetic appear only when atoms are used to create a SpinHamiltonian object. The magnetic atoms are defined as atoms that have at least one interaction parameter associated with them (even if the value of the interaction parameter is zero).

More details are given in the Magnetic vs non-magnetic atoms page.

Note

In the example above one might be tempted to say that "Cr1" and "Cr2" are magnetic atoms, while "Br1", "Br2", "S1", and "S2" are non-magnetic based on the values of the "spins" key. However, this is not how the magnetic atoms are defined in Magnopy.