.. _Example: Vortex formation and propagation in disk:

Example: Vortex formation and propagation in disk
-------------------------------------------------

This example computes the evolution of a vortex in a flat cylinder
magnetised along a direction orthogonal to the main axis.  

We use the same geometry as in the :ref:`Hysteresis loop for thin
disk example <example hysteresis disk>`: a flat cylinder, 20 nm thick and 200 nm in diameter (the mesh
is contained in :download:`nanodot.nmesh.h5
</example_vortex/nanodot.nmesh.h5>`):

.. image:: /example_vortex/nanodot_mesh.png
  :align: center
  :width: 515
  :height: 346

To simulate the magnetised disc, we use the following
script (:download:`nanodot.py </example_vortex/nanodot.py>`):

.. include:: /example_vortex/nanodot.py
  :literal:

We would like to compute the magnetisation behaviour in the applied
fields ranging from ``[12e3, 0, 0] A/m`` to ``[-200e3, 0, 0] A/m`` in
steps of ``-5e3 A/m``. The command for this is::

  Hs = nmag.vector_set( direction=[1,0,0],
                        norm_list=[12.0, 7.0, [], -200.0],
                        units=1e3*SI('A/m')
                      )

  sim.hysteresis(Hs,
                 save=[('averages', at('convergence')),
                       ('fields',   at('convergence')),
                       ('restart',  at('convergence')) 
                      ]
                )

The :ref:`ncol` command allows us to extract the data and we redirect it to
a text file with name :download:`nmag.dat </example_vortex/nmag.dat>`::

  $ ncol nanodot H_ext_0 m_Py_0 > nmag.dat

Plotting the data with `Gnuplot`_::

  $ gnuplot make_comparison_plot.gnu

which uses the script in :download:`make_comparison_plot.gnu </example_vortex/make_comparison_plot.gnu>`:

.. include:: /example_vortex/make_comparison_plot.gnu
  :literal:

The resulting graph is shown here:

.. image:: /example_vortex/nanodot_evo.png
  :align: center
  :width: 750
  :height: 525

and we can see that the results from :ref:`nsim` match those from `magpar`_.
The magnetisation configurations during the switching process are
shown in the following snapshots:

.. figure:: /example_vortex/nanodot-1.png
  :align: center
  :alt: nanodot-1

  Magnetisation configuration for a decreasing applied field of 20 kA/m. The x-axis is increasing from left to right for this and the subsequent plots.

.. figure:: /example_vortex/nanodot-2.png
  :align: center
  :alt: nanodot-2

  Magnetisation configuration for a decreasing applied field of 15 kA/m.

.. figure:: /example_vortex/nanodot-3.png
  :align: center
  :alt: nanodot-3

  Magnetisation configuration for a decreasing applied field of 10 kA/m.

.. figure:: /example_vortex/nanodot-4.png
  :align: center
  :alt: nanodot-4

  Magnetisation configuration for a decreasing applied field of -30 kA/m.

.. figure:: /example_vortex/nanodot-5.png
  :align: center
  :alt: nanodot-5

  Magnetisation configuration for a decreasing applied field of -95 kA/m.

.. figure:: /example_vortex/nanodot-6.png
  :align: center
  :alt: nanodot-6

  Magnetisation configuration for a decreasing applied field of -100 kA/m.

We see that during magnetisation reversal a vortex nucleates on the
boundary of the disc when the field is sufficiently decreased from its
saturation value. As the field direction is aligned with the x-axis,
the vortex appears in the disc region with the largest y component,
and it moves downwards towards the centre along the y-axis. With a
further decrease of the applied field the vortex moves towards the
opposite side of the disc with respect to the nucleation position, and
it is eventually expelled when the magnetisation aligns with the field
direction over all the disc.