.. _Example: Cubic Anisotropy:

Example: Cubic Anisotropy
-------------------------

In this example we will study the behaviour of a 10 x 10 x 10 nm iron
cube with :ref:`cubic_anisotropy` in an external field.

.. _Cubic anisotropy simulation script:

Cubic anisotropy simulation script
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. include:: cube.py
  :literal:

We will now discuss the :download:`cube.py </example_cubic_anis/cube.py>` script step-by-step:

After creating the simulation object we define a magnetic material ``Fe``
with cubic anisotropy representing iron::

  Fe = nmag.MagMaterial(name="Fe",
                        Ms=SI(1700e3, "A/m"),
                        exchange_coupling=SI(21e-12, "J/m"),
                        anisotropy=nmag.cubic_anisotropy(axis1=[1,0,0],
                                                         axis2=[0,1,0],
                                                         K1=SI(48e3, "J/m^3")))

We load the mesh and set initial magnetisation pointing in +z direction
(that is, in a local minimum of anisotropy energy density).

Finally, we use :ref:`hysteresis` to apply gradually stronger fields in +x direction (up to 50 mT)::

  Hs = nmag.vector_set(direction=[1.0, 0, 0.0001],
                       norm_list=[0, 1, [], 19, 19.1, [], 21, 22, [], 50],
                       units=0.001*si.Tesla/si.mu0)

Note that we sample more often the region between 19 and 21 mT where
magnetisation direction changes rapidly due to having crossed the anisotropy
energy "barrier" between +z and +x (as can be seen in the graph below).

.. _Analyzing the result:

Analyzing the result
~~~~~~~~~~~~~~~~~~~~

First, we extract the magnitude of the applied field and the x component of
magnetisation::

  ncol cube H_ext_0 M_Fe_0 > cube_hext_vs_m.txt

Then we compare the result with OOMMF's result (generated from the
equivalent scene description :download:`oommf/cube.mif </example_cubic_anis/oommf/cube.mif>`)
using the following `Gnuplot`_ script:

.. include:: cube_hext_vs_m.gnu
  :literal:

which gives the following result:

.. image:: /example_cubic_anis/cube_hext_vs_m.png
  :align: center
  :width: 800
  :height: 600

|Nmag| provides advanced capabilities to conveniently handle
arbitrary-order anisotropy energy functions. Details can be found in
the documentation of the :ref:`MagMaterial` class.