Commit JT 111519

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  \begin{equation}

    \bm{H}_{ex} ~=~ -\sum_{i,j,i\neq j}^{N} {J} \left(r_{ij} \right)\, \vec{s}_{i}\cdot \vec{s}_{j} \nonumber

    H_{ex} = 

    -\sum_{i,j}^N J_{ij} (r_{ij}) \,\vec{s}_i \cdot \vec{s}_j 

    %&{\rm ~if~}& \vec{m}_i^I \times \vec{m}_i^F  

  , \nonumber

  \end{equation}

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Define a computation that calculates magnetic quantities for a system

of atoms having spins.

This compute calculates 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.

This compute calculates the following 6 magnetic quantities:

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

magnetization, :ulb,l

the fourth quantity is the norm of the total magnetization, :l

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

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

to the work of "(Nurdin)"_#Nurdin1.

to the work of "(Nurdin)"_#Nurdin1. :l

:ule

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

:c,image(Eqs/pair_spin_exchange_interaction.jpg)

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:

:c,image(Eqs/pair_spin_exchange_function.jpg)

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.

  magtot[2] *= scale;

  magtot[3] = sqrt((magtot[0]*magtot[0])+(magtot[1]*magtot[1])+(magtot[2]*magtot[2]));

  spintemperature = hbar*tempnumtot;

  spintemperature /= (kb*tempdenomtot);

  // spintemperature /= (kb*tempdenomtot);

  spintemperature /= (2.0*kb*tempdenomtot);

  vector[0] = magtot[0];

  vector[1] = magtot[1];