\(\renewcommand{\AA}{\text{Å}}\)

# pair_style spin/magelec command

## Syntax

    pair_style spin/magelec cutoff

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

## Examples

    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 (Katsura), this interaction is defined as:

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

where \(\vec{s}_i\) and \(\vec{s}_j\) 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 fix nve/spin), such as:

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

with h the Planck constant (in metal units) and \(\vec{E}\) 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 (Tranchida).

## 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 Build package page for more info.

## Related commands

atom_style spin, pair_coeff, pair_style spin/exchange, pair_eam,

## Default

none

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

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