# ================================== LICENSE ===================================
# Magnopy - Python package for magnons.
# Copyright (C) 2023-2025 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
# Save local scope at this moment
old_dir = set(dir())
old_dir.add("old_dir")
[docs]
def to_iso(parameter, matrix_form=False):
r"""
Extracts isotropic part of the full matrix parameter.
.. math::
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}
\boldsymbol{S}_{\nu}
=
C_{2,2}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_S
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{D}
\cdot
\left(
\boldsymbol{S}_{\mu}
\times
\boldsymbol{S}_{\nu}
\right)
where :math:`J_{iso}` is defined as
.. math::
J_{iso} = \dfrac{tr(\boldsymbol{J})}{3}
This term can be written in the matrix form as
.. math::
C_{2,2}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\nu}
&=
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_{iso}
\boldsymbol{S}_{\nu}
\\
\boldsymbol{J}_{iso}
&=
\begin{pmatrix}
J_{iso} & 0 & 0 \\
0 & J_{iso} & 0 \\
0 & 0 & J_{iso} \\
\end{pmatrix}
Parameters
----------
parameter : (3, 3) |array-like|_
Full matrix of the exchange parameter (:math:`\boldsymbol{J}`).
matrix_form : bool, default False
Whether to return isotropic part of the matrix instead of isotropic parameter.
Returns
-------
iso : float or (3, 3) :numpy:`ndarray`
Isotropic parameter.
* If ``matrix_form == False``, then returns a number :math:`J_{iso}`.
* If ``matrix_form == True``, then returns a matrix :math:`\boldsymbol{J}_{iso}`.
See Also
--------
from_iso
to_dmi
to_symm_anisotropy
Examples
--------
.. doctest::
>>> from magnopy import converter22
>>> matrix = [[1, 3, 4], [-1, -2, 3], [4, 0, 10]]
>>> converter22.to_iso(matrix)
3.0
>>> converter22.to_iso(matrix, matrix_form=True)
array([[3., 0., 0.],
[0., 3., 0.],
[0., 0., 3.]])
"""
iso = (parameter[0][0] + parameter[1][1] + parameter[2][2]) / 3
if matrix_form:
return iso * np.eye(3, dtype=float)
return float(iso)
[docs]
def to_symm_anisotropy(parameter):
r"""
Extracts traceless, symmetric anisotropic part of the full matrix parameter.
.. math::
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}
\boldsymbol{S}_{\nu}
=
C_{2,2}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_S
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{D}
\cdot
\left(
\boldsymbol{S}_{\mu}
\times
\boldsymbol{S}_{\nu}
\right)
where matrix :math:`\boldsymbol{J}_S` is defined as
.. math::
\boldsymbol{J}_S
=
\dfrac{\boldsymbol{J}
+
\boldsymbol{J}^T}{2}
Parameters
----------
parameter : (3, 3) |array-like|_
Full matrix of the exchange parameter (:math:`\boldsymbol{J}`).
Returns
-------
aniso : float or (3, 3) :numpy:`ndarray`
Matrix of a traceless, symmetric anisotropy.
See Also
--------
to_iso
to_dmi
Examples
--------
.. doctest::
>>> import magnopy
>>> matrix = [[1, 3, 4], [-1, -2, 0], [4, 0, 10]]
>>> magnopy.converter22.to_symm_anisotropy(matrix)
array([[-2., 1., 4.],
[ 1., -5., 0.],
[ 4., 0., 7.]])
"""
parameter = np.array(parameter)
return (parameter + parameter.T) / 2 - to_iso(parameter=parameter, matrix_form=True)
[docs]
def to_dmi(parameter, matrix_form=False):
r"""
Extracts antisymmetric part (DMI) of the full matrix parameter.
.. math::
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}
\boldsymbol{S}_{\nu}
=
C_{2,2}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_S
\boldsymbol{S}_{\nu}
+
C_{2,2}
\boldsymbol{D}
\cdot
\left(
\boldsymbol{S}_{\mu}
\times
\boldsymbol{S}_{\nu}
\right)
where vector :math:`\boldsymbol{D}` is defined as
.. math::
\begin{pmatrix}
0 & D^z & -D^y \\
-D^z & 0 & D^x \\
D^y & -D^x & 0 \\
\end{pmatrix}
=
\dfrac{\boldsymbol{J}
-
\boldsymbol{J}^T}{2}
=
\boldsymbol{J}_A
Parameters
----------
parameter : (3, 3) |array-like|_
Full matrix of the exchange parameter (:math:`\boldsymbol{J}`).
matrix_form : bool, default False
Whether to return dmi in a matrix form instead of a vector.
Returns
-------
dmi : (3,) or (3, 3) :numpy:`ndarray`
Antisymmetric exchange (DMI).
* If ``matrix_form == False``, then returns a vector :math:`\boldsymbol{D}`.
* If ``matrix_form == True``, then returns a matrix :math:`\boldsymbol{J}_A`.
See Also
--------
from_dmi
to_iso
to_symm_anisotropy
Examples
--------
.. doctest::
>>> from magnopy import converter22
>>> parameter = [[1, 3, 0], [-1, -2, 3], [0, 3, 9]]
>>> converter22.to_dmi(parameter)
array([0., 0., 2.])
>>> converter22.to_dmi(parameter, matrix_form = True)
array([[ 0., 2., 0.],
[-2., 0., 0.],
[ 0., 0., 0.]])
"""
parameter = np.array(parameter)
asymm_matrix = (parameter - parameter.T) / 2
if matrix_form:
return asymm_matrix
return np.array(
[asymm_matrix[1][2], asymm_matrix[2][0], asymm_matrix[0][1]],
dtype=float,
)
[docs]
def from_iso(iso):
r"""
Computes matrix form of the isotropic exchange parameter.
.. math::
C_{2,2}
J_{iso}
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\nu}
=
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_{iso}
\boldsymbol{S}_{\nu}
where matrix :math:`\boldsymbol{J}_{iso}` is defined as
.. math::
\boldsymbol{J}_{iso}
=
\begin{pmatrix}
J_{iso} & 0 & 0 \\
0 & J_{iso} & 0 \\
0 & 0 & J_{iso} \\
\end{pmatrix}
Parameters
----------
iso : int or float
Isotropic exchange parameter.
Returns
-------
parameter : (3, 3) :numpy:`ndarray`
Matrix form of the isotropic exchange parameter (:math:`\boldsymbol{J}_{iso}`).
See Also
--------
to_iso
from_dmi
Examples
--------
.. doctest::
>>> from magnopy import converter22
>>> converter22.from_iso(iso=1)
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
"""
return iso * np.eye(3, dtype=float)
[docs]
def from_dmi(dmi):
r"""
Computes matrix form of the Dzyaloshinsky-Moriya interaction parameter.
.. math::
C_{2,2}
\boldsymbol{D}
\cdot
\left(
\boldsymbol{S}_{\mu}
\times
\boldsymbol{S}_{\nu}
\right)
=
C_{2,2}
\boldsymbol{S}_{\mu}
\boldsymbol{J}_A
\boldsymbol{S}_{\nu}
where matrix :math:`\boldsymbol{J}_A` is defined as
.. math::
\boldsymbol{J}_A
=
\begin{pmatrix}
0 & D^z & -D^y \\
-D^z & 0 & D^x \\
D^y & -D^x & 0 \\
\end{pmatrix}
Parameters
----------
dmi : (3,) |array-like|_
Vector of Dzyaloshinsky-Moriya interaction parameter :math:`(D_x, D_y, D_z)`.
Returns
-------
parameter : (3, 3) :numpy:`ndarray`
Matrix form of the Dzyaloshinsky-Moriya interaction parameter
(:math:`\boldsymbol{J}_A`).
See Also
--------
to_dmi
from_iso
Examples
--------
.. doctest::
>>> from magnopy import converter22
>>> converter22.from_dmi(dmi = (1, 2, 0))
array([[ 0., 0., -2.],
[ 0., 0., 1.],
[ 2., -1., 0.]])
"""
return np.array(
[
[0, dmi[2], -dmi[1]],
[-dmi[2], 0, dmi[0]],
[dmi[1], -dmi[0], 0],
],
dtype=float,
)
# 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