# ================================== LICENSE ===================================
# Magnopy - Python package for magnons.
# Copyright (C) 2023-2026 Magnopy Team
#
# e-mail: anry@uv.es, web: magnopy.org
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
# ================================ END LICENSE =================================
import numpy as np
from magnopy._parameters._p22 import from_iso
from magnopy._spinham._convention import Convention
from magnopy._spinham._hamiltonian import SpinHamiltonian
# Save local scope at this moment
old_dir = set(dir())
old_dir.add("old_dir")
[docs]
def cubic_ferro_nn(
a: float = 1,
J_iso: float = 1,
J_21=(0, 0, 0),
S: float = 0.5,
dimensions: int = 3,
) -> SpinHamiltonian:
r"""
Prepares ferromagnetic Hamiltonian on the cubic lattice with one atom per unit cell.
Only nearest-neighbor isotropic exchange interactions and on-site quadratic
anisotropy are populated. The Hamiltonian has the form
.. math::
\mathcal{H}
=
\dfrac{1}{2}
\sum_{\mu, \nu}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\mu+\nu}
+
\sum_{\mu}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_{21}
\boldsymbol{S}_{\mu}
where
* :math:`\nu \in {(1,0,0), (-1,0,0)}` if ``dimensions == 1``.
* :math:`\nu \in {(1,0,0), (-1,0,0), (0,1,0), (0,-1,0)}` if ``dimensions == 2``.
* :math:`\nu \in {(1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1)}` if
``dimensions == 3``.
Parameters
----------
a : float, default 1.0
Lattice parameter of the cubic lattice.
The unit cell of the Hamiltonian is defined as
.. code-block:: python
[[a, 0, 0], [0, a, 0], [0, 0, a]]
J_iso : float, default 1.0
Isotropic exchange parameter for the pairs of the nearest-neighbor magnetic
sites, given in energy units. Only magnitude is important, sign is ignored.
J_21 : (3, 3) or (3, ) |array-like|_, default (0, 0, 0)
On-site quadratic anisotropy.
S : float, default 0.5
Spin value of the magnetic site.
dimensions : int, default 3
Either 1, 2 or 3. Dimensionality of the spin Hamiltonian.
Returns
-------
spinham : :py:class:`.SpinHamiltonian`
Spin Hamiltonian.
Examples
--------
To get an example with the default values use
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn()
>>> spinham.cell
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
>>> spinham.atoms.names
['X']
>>> spinham.atoms.spins
[0.5]
>>> spinham.atoms.positions
[[0, 0, 0]]
>>> for alpha, parameter in spinham.p21:
... print(alpha, parameter, sep="\n")
0
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
>>> for alpha, beta, nu, parameter in spinham.p22:
... print(alpha, beta, nu)
... print(parameter)
0 0 (0, 0, 1)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (0, 1, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (0, 0, -1)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (0, -1, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (-1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
With this function one can customize a few things of the Hamiltonian:
* Lattice parameter
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn(a=2)
>>> spinham.cell
array([[2., 0., 0.],
[0., 2., 0.],
[0., 0., 2.]])
* Spin values
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn(S=1.5)
>>> spinham.atoms.spins
[1.5]
* Value of the isotropic exchange
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn(J_iso=2)
>>> for alpha, beta, nu, parameter in spinham.p22:
... print(alpha, beta, nu)
... print(parameter)
0 0 (0, 0, 1)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
0 0 (0, 1, 0)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
0 0 (1, 0, 0)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
0 0 (0, 0, -1)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
0 0 (0, -1, 0)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
0 0 (-1, 0, 0)
[[-2. -0. -0.]
[-0. -2. -0.]
[-0. -0. -2.]]
* Diagonal of the on-site quadratic anisotropy
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn(J_21=(1, 2, -1))
>>> for alpha, parameter in spinham.p21:
... print(alpha, parameter, sep="\n")
0
[[ 1. 0. 0.]
[ 0. 2. 0.]
[ 0. 0. -1.]]
* Dimensionality of the nearest neighbors
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn(dimensions=1)
>>> for alpha, beta, nu, parameter in spinham.p22:
... print(alpha, beta, nu)
... print(parameter)
0 0 (1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (-1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
>>> spinham = magnopy.examples.cubic_ferro_nn(dimensions=2)
>>> for alpha, beta, nu, parameter in spinham.p22:
... print(alpha, beta, nu)
... print(parameter)
0 0 (0, 1, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (0, -1, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
0 0 (-1, 0, 0)
[[-1. -0. -0.]
[-0. -1. -0.]
[-0. -0. -1.]]
"""
cell = a * np.eye(3, dtype=float)
atoms = dict(
names=["X"],
species=["X"],
spins=[S],
g_factors=[2],
positions=[[0, 0, 0]],
)
convention = Convention(
spin_normalized=False,
multiple_counting=True,
c21=1,
c22=0.5,
)
spinham = SpinHamiltonian(cell=cell, atoms=atoms, convention=convention)
J_21 = np.array(J_21, dtype=float)
if J_21.shape == (3,):
J_21 = np.diag(J_21)
spinham.add_21(alpha=0, parameter=J_21)
J_iso = -from_iso(iso=abs(J_iso))
spinham.add_22(alpha=0, beta=0, nu=(1, 0, 0), parameter=J_iso)
if dimensions >= 2:
spinham.add_22(alpha=0, beta=0, nu=(0, 1, 0), parameter=J_iso)
if dimensions >= 3:
spinham.add_22(alpha=0, beta=0, nu=(0, 0, 1), parameter=J_iso)
return spinham
# Populate __all__ with objects defined in this file
__all__ = list(set(dir()) - old_dir)
# Remove all semi-private objects
__all__ = [i for i in __all__ if not i.startswith("_")]
del old_dir
