.. _spin-waves example:

Example: Spin-waves in periodic system
--------------------------------------

Starting from a magnetisation out of equilibrium, we study the time
development of the magnetisation, and track -visually- the spin waves.

The geometry is a thin film with dimensions 30 nm x 9 nm x 0.2 nm along 
the x,y and z axes, respectively. The mesh is centered at (0,0,0)
and periodic along the x direction, so that the nodes with coordinates 
(15.0,y,z) will be considered as equivalent to the nodes with coordinates (-15.0,y,z).

.. image:: /example_periodic_spinwaves/periodic_mesh.png
  :align: center
  :width: 629
  :height: 376

The mesh is contained in :download:`periodic.nmesh </example_periodic_spinwaves/periodic.nmesh>` and 
has been produced using `Netgen`_ (from  :download:`periodic.geo </example_periodic_spinwaves/periodic.geo>`) and the :ref:`nmeshmirror` command to create required periodic structure ::

  $ nmeshmirror netgen.nmesh 1e-6 1e-6 -1,0,0 periodic.nmesh

.. _Relaxation script:

Relaxation script
~~~~~~~~~~~~~~~~~
To see how the system relaxes, we use the following
script (:download:`spinwaves.py </example_periodic_spinwaves/spinwaves.py>`):

.. include:: spinwaves.py
  :literal:

To execute this script, we call the :ref:`nsim` executable, for example (on linux)::

  $ nsim spinwaves.py

As in the previous examples, we first need to import the modules
necessary for the simulation, define the material of the magnetic
object, load the mesh and set the initial configuration of the
magnetisation. Here, we start from a spatially non-homogeneous
configuration in order to excite spin waves. |Nmag| allows us to provide a
function to be sampled on the mesh that defines a particular
magnetisation configuration.

.. image:: /example_periodic_spinwaves/initial_magn.png
  :align: center
  :width: 552
  :height: 389

In our case, we use the function ::

  def perturbed_magnetisation(pos):
      x,y,z = pos
      newx = x*1e9
      newy = y*1e9
      if 8<newx<14 and -3<newy<3:
          # the magnetisation is twisted a bit
          return [1.0, 5.*(math.cos(math.pi*((newx-11)/6.)))**3 *\
                          (math.cos(math.pi*(newy/6.)))**3, 0.0]
      else:
          return [1.0, 0.0, 0.0]

which is then passed on to :ref:`set_m` ::
 
  # set initial magnetisation
  sim.set_m(perturbed_magnetisation)

.. _Visualising the magnetisation evolution:

Visualising the magnetisation evolution
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Once the calculation has finished, we can see how the system relaxed
by means of snapshots of the magnetisation evolution.

The :ref:`nmagpp` command allows us to create vtk files
from the data saved with the ``save`` option in the ``relax`` method::

  nmagpp --vtk=fields spinwaves

The first few frames that show the evolution of the magnetic
configuration are shown below.

.. figure:: /example_periodic_spinwaves/evolution-1.png
  :align: center
  :alt: evolution-1

  Initial magnetisation configuration.

.. figure:: /example_periodic_spinwaves/evolution-2.png
  :align: center
  :alt: evolution-2

  Magnetisation configuration after 0.15 ps. It is clearly visible
  that the spin waves travel from the center of the disturbance to the
  right and penetrate the system immediately from the left (due to the
  periodic boundary conditions in the x-direction).

.. figure:: /example_periodic_spinwaves/evolution-3.png
  :align: center
  :alt: evolution-3

  Magnetisation configuration after 0.25 ps.