.. 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_4_magnetic_field.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_4_magnetic_field.py>`
        to download the full example code.

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

.. _sphx_glr_master-tutorial_1_python-library_plot_4_magnetic_field.py:


Magnetic field
**************

.. include:: ../../exercises/4.inc

Magnetic field is an external effect. However, magnopy, perhaps counterintuitively, stores
it as an interaction parameter of the type :py:attr:`magnopy.SpinHamiltonian.p1`, i. e.
one spin and one site parameter.

This is a design choice that we made. It allows us to take care of the magnetic field in
one place (in the Hamiltonian) and treat it on the same grounds as other terms of the
Hamiltonian.

Said that, we defined a convenience method, that convert a vector of the magnetic flux
density into the one spin & one site parameter of the Hamiltonian:
:py:meth:`magnopy.SpinHamiltonian.add_magnetic_field`.

.. GENERATED FROM PYTHON SOURCE LINES 20-24

.. code-block:: Python


    import numpy as np
    import magnopy








.. GENERATED FROM PYTHON SOURCE LINES 25-27

For example, to add an external magnetic field directed along the y axis with the value of
1.42 Tesla use

.. GENERATED FROM PYTHON SOURCE LINES 28-52

.. code-block:: Python


    # Cubic ferromagnet
    cell = np.eye(3)

    atoms = dict(
        names=["Fe"],
        positions=[[0.5, 0.5, 0.5]],
        spins=[2.5],
        g_factors=[2],
    )

    # Choose convention
    convention = magnopy.Convention(
        multiple_counting=True, spin_normalized=False, c21=1, c22=1
    )

    # Create a Hamiltonian
    spinham = magnopy.SpinHamiltonian(cell=cell, atoms=atoms, convention=convention)

    # Try to add magnetic field
    spinham.add_magnetic_field(B=(0.0, 1.42, 0.0))

    print(len(spinham.p1))





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

 .. code-block:: none

    0




.. GENERATED FROM PYTHON SOURCE LINES 53-61

Surprisingly no magnetic field has been added. This is a subtle detail in magnopy
that originates from the |magnopy-mag-vs-nomag|_ problem. In short: magnetic atoms are
those that already have a parameter (of any group) associated with it. In this example the
Hamiltonian is empty, thus magnopy considers all atoms to be non-magnetic.

We are left with two choices: either add some other parameters to the model, that will
make atoms magnetic or explicitly tell magnopy to which atoms we want to add coupling
with the magnetic field

.. GENERATED FROM PYTHON SOURCE LINES 62-74

.. code-block:: Python


    # Add magnetic field
    spinham.add_magnetic_field(B=(0.0, 1.42, 0.0), alphas=[0])

    # Now there is one parameter associated with magnetic field
    print(len(spinham.p1))

    for alpha, parameter in spinham.p1:
        print(
            f'Atom "{spinham.atoms.names[alpha]}" -> {parameter[0]:.5f} {parameter[1]:.5f} {parameter[2]:.5f}'
        )





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

 .. code-block:: none

    1
    Atom "Fe" -> 0.00000 0.16439 0.00000




.. GENERATED FROM PYTHON SOURCE LINES 75-83

Technically, parameters are defined as

..  math::

    \mathbf{J}_{\alpha} = \dfrac{\mu_B g_{\alpha} \mathbf{B}}{C_1}

where :math:`\mu_B` is Bohr magneton, :math:`g_{\alpha}` is
``spinham.atoms.g_factors[alpha]`` and :math:`C_1` is ``spinham.convention.c1``.

.. GENERATED FROM PYTHON SOURCE LINES 84-95

.. code-block:: Python


    # Bohr magneton in meV / Tesla
    mu_B = magnopy.si.BOHR_MAGNETON / (magnopy.si.MILLI * magnopy.si.ELECTRON_VOLT)

    print(
        mu_B
        * spinham.atoms.g_factors[0]
        * np.array([0.0, 1.42, 0.0])
        / spinham.convention.c1
    )





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

 .. code-block:: none

    [0.         0.16439004 0.        ]





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

   **Total running time of the script:** (0 minutes 0.002 seconds)


.. _sphx_glr_download_master-tutorial_1_python-library_plot_4_magnetic_field.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_4_magnetic_field.ipynb <plot_4_magnetic_field.ipynb>`

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

      :download:`Download Python source code: plot_4_magnetic_field.py <plot_4_magnetic_field.py>`

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

      :download:`Download zipped: plot_4_magnetic_field.zip <plot_4_magnetic_field.zip>`


.. only:: html

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

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