=========
 Modules 
=========

Overview: 

- ExchangeField
- StrayField
- AnisotropyField
- ExternalField
- LandauLifshitzGilbert

LandauLifshitzGilbert
---------------------

This is the module that is needed to compute the Landau-Lifshitz-Gilbert
equation.  It is included by default by the create_solver function and
thus must not be specified in its module inclusion list.

+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| Variable           |   Mode    | Type    | Unit      | Description                                         |
+====================+===========+=========+===========+=====================================================+
| M                  |  in/out   |  VF     | A/m       | The current magnetization vector field              |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| dMdt               |    out    |  VF     | A/m per s | Change of magnetization M (e.g. LHS of LLG-Equation)|
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| H_eff              |    out    |  VF     | A/m       | Effective magnetic field                            |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| E_eff              |    out    |  S      | J         | Effectice field energy                              |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| alpha              | parameter |  F      |           | Damping constant                                    |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| Ms                 | parameter |  F      | A/m       | Saturation magnetization                            |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+

Input variables: Any effective field contribution H_xyz from activated modules (A/m, VF)

ExchangeField
-------------

+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| Variable           |   Mode    | Type    | Unit      | Description                                         |
+====================+===========+=========+===========+=====================================================+
| H_exch             |    out    |  VF     | A/m       | Exchange field                                      |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| E_exch             |    out    |  S      | J         | Exchange field energy                               |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| A                  | parameter |  F      | J/m       | Exchange stiffness constant                         |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+

Input variables: M (A/m, VF), Ms (A/m, F)

StrayField
----------

+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| Variable           |   Mode    | Type    | Unit      | Description                                         |
+====================+===========+=========+===========+=====================================================+
| H_stray            |    out    |  VF     | A/m       | Strayfield                                          |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+
| E_stray            |    out    |  S      | J         | Strayfield energy                                   |
+--------------------+-----------+---------+-----------+-----------------------------------------------------+

Input variables: M (A/m, VF)

Example:
   
.. code-block:: python

   from magnum import *

   # 100x100 cells, cellsize 1 nm x 1 nm x 4 nm
   mesh = RectangularMesh((100,100,1), (1e-9, 1e-9, 4e-9))
   world = World(mesh, Body("all", Material.Py(), Everywhere()))
   solver = create_solver(world, [StrayField, ExchangeField])

   # Initialize magnetization M
   solver.state.M = (8e5,0,0) 
   # or:
   # solver.state.M = readOMF("M.omf")

   # Calculate and store stray field generated by M
   writeOMF("strayfield.ohf", solver.state.H_stray) 

   # Print stray field energy
   print(solver.state.E_stray)

AnisotropyField
---------------

- Inputs: M
- Outputs: H_aniso, E_aniso
- Defines parameters: k_uniaxial, k_cubic, axis1, axis2