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Define a computation that calculates magnetic quantities for a system

of atoms having spins.

This compute calculates 6 magnetic quantities.

This compute calculates the following 6 magnetic quantities:

The three first quantities are the x,y and z coordinates of the total

magnetization.

The fourth quantity is the norm of the total magnetization.

The fifth quantity is the magnetic energy.

The sixth one is referred to as the spin temperature, according

* the three first quantities are the x,y and z coordinates of the total

  magnetization,

* the fourth quantity is the norm of the total magnetization,

* The fifth quantity is the magnetic energy (in eV),

* The sixth one is referred to as the spin temperature, according

  to the work of :ref:`(Nurdin) <Nurdin1>`.

The simplest way to output the results of the compute spin calculation

is to define some of the quantities as variables, and to use the thermo and

thermo\_style commands, for example:

between the magnetic spins in the defined group and an external

magnetic field:

.. image:: Eqs/force_spin_zeeman.jpg

.. image:: Eqs/fix_spin_zeeman.jpg

   :align: center

with mu0 the vacuum permeability, muB the Bohr magneton (muB = 5.788 eV/T

in metal units).

with:

* Bext the external magnetic field (in T)

* g the Lande factor (hard-coded as g=2.0)

* si the unitary vector describing the orientation of spin i

* mui the atomic moment of spin i given as a multiple of the

  Bohr magneton muB (for example, mui ~ 2.2 in bulk iron).

The field value in Tesla is multiplied by the gyromagnetic

ratio, g\*muB/hbar, converting it into a precession frequency in

rad.THz (in metal units and with muB = 5.788 eV/T).

As a comparison, the figure below displays the simulation of a

single spin (of norm mui = 1.0) submitted to an external

magnetic field of \|Bext\| = 10.0 Tesla (and oriented along the z

axis). 

The upper plot shows the average magnetization along the

external magnetic field axis and the lower plot the Zeeman

energy, both as a function of temperature.

The reference result is provided by the plot of the Langevin 

function for the same parameters.

.. image:: JPG/zeeman_langevin.jpg

   :align: center

The temperature effects are accounted for by connecting the spin

i to a thermal bath using a Langevin thermostat (see 

:doc:`fix\_langevin\_spin <fix_langevin_spin>` for the definition of 

this thermostat).

Style *anisotropy* is used to simulate an easy axis or an easy plane

for the magnetic spins in the defined group:

   :align: center

where si and sj are two neighboring magnetic spins of two particles,

rij = ri - rj is the inter-atomic distance between the two particles,

rij = \|ri - rj\| is the inter-atomic distance between the two particles,

and J(rij) is a function defining the intensity and the sign of the exchange

interaction for different neighboring shells. This function is defined as:

   :align: center

where a, b and d are the three constant coefficients defined in the associated

"pair\_coeff" command (see below for more explanations).

"pair\_coeff" command, and Rc is the radius cutoff associated to

the pair interaction (see below for more explanations).

The coefficients a, b, and d need to be fitted so that the function above matches with

the value of the exchange interaction for the N neighbor shells taken into account.