.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "master-tutorial/1_python-library/plot_8_lswt.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_master-tutorial_1_python-library_plot_8_lswt.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_master-tutorial_1_python-library_plot_8_lswt.py:


Linear Spin Wave theory
***********************

.. include:: ../../exercises/8.inc

All methods for linear spin-wave theory are grouped in the :py:class:`magnopy.LSWT` class.

To create it we require two things

* Spin Hamiltonian
* Directions of spins in the ground state

.. GENERATED FROM PYTHON SOURCE LINES 14-18

.. code-block:: Python


    import numpy as np
    import magnopy








.. GENERATED FROM PYTHON SOURCE LINES 19-21

An example of the cubic ferromagnet with nearest-neighbor interactions and easy
magnetic axis along :math:`\mathbf{z}`.

.. GENERATED FROM PYTHON SOURCE LINES 22-28

.. code-block:: Python


    spinham = magnopy.examples.cubic_ferro_nn(S=1, J_21=(0, 0, -0.5))

    # Get the LSWT object from it
    lswt = magnopy.LSWT(spinham=spinham, spin_directions=[[0, 0, 1]])








.. GENERATED FROM PYTHON SOURCE LINES 29-33

Once created it can be used to compute parts of the magnon Hamiltonian

Correction to the classical energy
==================================

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python


    print(lswt.E_2())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    -3.5




.. GENERATED FROM PYTHON SOURCE LINES 37-39

Coefficients of the one-operator terms
======================================

.. GENERATED FROM PYTHON SOURCE LINES 39-42

.. code-block:: Python


    print(lswt.O())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [0.+0.j]




.. GENERATED FROM PYTHON SOURCE LINES 43-45

Magnon energies
===============

.. GENERATED FROM PYTHON SOURCE LINES 45-49

.. code-block:: Python


    print(lswt.omega(k=[0, 0, 0]))






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [1.+0.j]




.. GENERATED FROM PYTHON SOURCE LINES 50-59

Parallelization
===============

Typically one wants to compute magnon energies for a set of k-points. Often for a
rather large set of k-points. Magnopy offers simple interface to parallelize the
calculations over the k-points using multiprocessing. See
:py:func:`magnopy.multiprocess_over_k` for details. For example, to compute magnon
energies for the set of k-points (that are given as absolute coordinates in reciprocal
space) using two processes use

.. GENERATED FROM PYTHON SOURCE LINES 59-70

.. code-block:: Python



    kpoints = np.linspace([0, 0, 0], [1, 0, 0], 1000)

    results = magnopy.multiprocess_over_k(
        kpoints=kpoints,
        relative=False,
        function=lswt.omega,
        number_processors=2,
    )








.. GENERATED FROM PYTHON SOURCE LINES 71-72

Note that ``results[i]`` is equivalent to ``lswt.omega(k=kpoints[i], relative=False)``.

.. GENERATED FROM PYTHON SOURCE LINES 72-78

.. code-block:: Python


    print(results[42])

    print(lswt.omega(k=kpoints[42], relative=False))






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [1.00176727+0.j]
    [1.00176727+0.j]





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.131 seconds)


.. _sphx_glr_download_master-tutorial_1_python-library_plot_8_lswt.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_8_lswt.ipynb <plot_8_lswt.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_8_lswt.py <plot_8_lswt.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_8_lswt.zip <plot_8_lswt.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_