\(\renewcommand{\AA}{\text{Å}}\)

# pair_style spin/neel command

## Syntax

    pair_style spin/neel cutoff

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

## Examples

    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:

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

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

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

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

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

where \(a\), \(b\) and \(d\) are the three constant coefficients defined in the associated “pair_coeff” command.

The coefficients \(a\), \(b\), and \(d\) 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 (Tranchida). More examples of parameterization will be provided in future work.

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

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_eam,

## Default

none

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