.. index:: pair_style spin/neel

pair_style spin/neel command
============================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style spin/neel cutoff

* cutoff = global cutoff pair (distance in metal units)

Examples
""""""""

.. code-block:: LAMMPS

   pair_style spin/neel 4.0
   pair_coeff * * neel 4.0 0.0048 0.234 1.168 2.6905 0.705 0.652
   pair_coeff 1 2 neel 4.0 0.0048 0.234 1.168 0.0 0.0 1.0

Description
"""""""""""

Style *spin/neel* computes the Neel pair anisotropy model
between pairs of magnetic spins:

.. math::

   \mathcal{H}_{N\acute{e}el}=-\sum_{{ i,j=1,i\neq j}}^N g_1(r_{ij})\left(({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})({\mathbf{e}}_{ij}
   \cdot {\mathbf{s}}_{j})-\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3} \right)
   +q_1(r_{ij})\left( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^2 -\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3}\right)
   \left( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^2 -\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3} \right)
   + q_2(r_{ij}) \Big( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i}) ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{j})^3 + ({\mathbf{e}}_{ij}\cdot
   {\mathbf{s}}_{j}) ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^3\Big)

where :math:`\mathbf{s}_i` and :math:`\mathbf{s}_j` are two neighboring magnetic spins of two particles,
:math:`r_{ij} = \vert \mathbf{r}_i - \mathbf{r}_j \vert` is the inter-atomic distance between the two particles,
:math:`\mathbf{e}_{ij} = \frac{\mathbf{r}_i - \mathbf{r}_j}{\vert \mathbf{r}_i - \mathbf{r}_j\vert}` is their normalized separation vector and :math:`g_1`,
:math:`q_1` and :math:`q_2` are three functions defining the intensity of the dipolar
and quadrupolar contributions, with:

.. math::

   g_1(r_{ij}) &= g(r_{ij}) + \frac{12}{35} q(r_{ij}) \\
   q_1(r_{ij}) &= \frac{9}{5} q(r_{ij}) \\
   q_2(r_{ij}) &= - \frac{2}{5} q(r_{ij})

With the functions :math:`g(r_{ij})` and :math:`q(r_{ij})` defined and fitted according to
the same Bethe-Slater function used to fit the exchange interaction:

.. math::

   {J}\left( r_{ij} \right) = 4 a \left( \frac{r_{ij}}{d}  \right)^2 \left( 1 - b \left( \frac{r_{ij}}{d}  \right)^2 \right) e^{-\left( \frac{r_{ij}}{d} \right)^2 }\Theta (R_c - r_{ij})

where :math:`a`, :math:`b` and :math:`d` are the three constant coefficients defined in the
associated "pair_coeff" command.

The coefficients :math:`a`, :math:`b`, and :math:`d` need to be fitted so that the function
above matches with the values of the magneto-elastic constant of the
materials at stake.

Examples and more explanations about this function and its
parameterization are reported in :ref:`(Tranchida) <Tranchida6>`. More
examples of parameterization will be provided in future work.

From this DM interaction, each spin :math:`i` will be submitted to a magnetic
torque :math:`\mathbf{\omega}` and its associated atom to a force :math:`\mathbf{F}` (for spin-lattice
calculations only).

More details about the derivation of these torques/forces are reported
in :ref:`(Tranchida) <Tranchida6>`.

----------

Restrictions
""""""""""""

All the *pair/spin* styles are part of the SPIN package.  These styles
are only enabled if LAMMPS was built with this package, and if the
atom_style "spin" was declared.  See the :doc:`Build package <Build_package>` doc page for more info.

Related commands
""""""""""""""""

:doc:`atom_style spin <atom_style>`, :doc:`pair_coeff <pair_coeff>`,
:doc:`pair_eam <pair_eam>`,

**Default:**

none

----------

.. _Tranchida6:

**(Tranchida)** Tranchida, Plimpton, Thibaudeau and Thompson,
Journal of Computational Physics, 372, 406-425, (2018).
