.. index:: pair_style spin/magelec

pair_style spin/magelec command
================================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style spin/magelec cutoff

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

Examples
""""""""

.. code-block:: LAMMPS

   pair_style spin/magelec 4.5
   pair_coeff * * magelec 4.5 0.00109 1.0 1.0 1.0

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

Style *spin/me* computes a magneto-electric interaction between
pairs of magnetic spins. According to the derivation reported in
:ref:`(Katsura) <Katsura1>`, this interaction is defined as:

.. math::

   \vec{\omega}_i & = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times\vec{D}(r_{ij}) \\
   \vec{F}_i & = -\sum_{j}^{Neighb} \frac{\partial D(r_{ij})}{\partial r_{ij}} \left(\vec{s}_{i}\times \vec{s}_{j} \right) \cdot \vec{r}_{ij}

where :math:`\vec{s}_i` and :math:`\vec{s}_j` are neighboring magnetic
spins of two particles.

From this magneto-electric interaction, each spin i will be submitted
to a magnetic torque omega, and its associated atom can be submitted to a
force F for spin-lattice calculations (see :doc:`fix nve/spin <fix_nve_spin>`),
such as:

.. math::

    \vec{F}^{i} & = -\sum_{j}^{Neighbor} \left( \vec{s}_{i}\times \vec{s}_{j} \right) \times \vec{E} \\
    \vec{\omega}^{i} = -\frac{1}{\hbar} \sum_{j}^{Neighbor} \vec{s}_j \times \left(\vec{E}\times r_{ij} \right)

with h the Planck constant (in metal units) and :math:`\vec{E}` an
electric polarization vector.  The norm and direction of E are giving
the intensity and the direction of a screened dielectric atomic
polarization (in eV).

More details about the derivation of these torques/forces are reported in
:ref:`(Tranchida) <Tranchida4>`.

----------

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_style spin/exchange <pair_spin_exchange>`, :doc:`pair_eam <pair_eam>`,

**Default:** none

----------

.. _Katsura1:

**(Katsura)** H. Katsura, N. Nagaosa, A.V. Balatsky. Phys. Rev. Lett., 95(5), 057205. (2005)

.. _Tranchida4:

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