# pair_style spin/dipole/cut command

# pair_style spin/dipole/long command

## Syntax

``` LAMMPS
pair_style spin/dipole/cut cutoff
pair_style spin/dipole/long cutoff
```

-   cutoff = global cutoff for magnetic dipole energy and forces
    (optional) (distance units)

## Examples

``` LAMMPS
pair_style spin/dipole/cut 10.0
pair_coeff * * 10.0
pair_coeff 2 3 8.0

pair_style spin/dipole/long 9.0
pair_coeff * * 10.0
pair_coeff 2 3 6.0
```

## Description

Style *spin/dipole/cut* computes a short-range dipole-dipole interaction
between pairs of magnetic particles that each have a magnetic spin. The
magnetic dipole-dipole interactions are computed by the following
formulas for the magnetic energy, magnetic precession vector omega and
mechanical force between particles I and J.

$$\begin{aligned}
\mathcal{H}_{\rm long} & =
-\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi}
\sum_{i,j,i\neq j}^{N}
 \frac{g_i g_j}{r_{ij}^3}
 \biggl(3
 \left(\vec{e}_{ij}\cdot \vec{s}_{i}\right)
 \left(\vec{e}_{ij}\cdot \vec{s}_{j}\right)
 -\vec{s}_i\cdot\vec{s}_j \biggr) \\
 \mathbf{\omega}_i & =
 \frac{\mu_0 (\mu_B)^2}{4\pi\hbar}\sum_{j}
 \frac{g_i g_j}{r_{ij}^3}
 \, \biggl(
 3\,(\vec{e}_{ij}\cdot\vec{s}_{j})\vec{e}_{ij}
 -\vec{s}_{j} \biggr) \\
 \mathbf{F}_i & =
 \frac{3\, \mu_0 (\mu_B)^2}{4\pi} \sum_j
 \frac{g_i g_j}{r_{ij}^4}
 \biggl[\bigl( (\vec{s}_i\cdot\vec{s}_j)
 -5(\vec{e}_{ij}\cdot\vec{s}_i)
 (\vec{e}_{ij}\cdot\vec{s}_j)\bigr) \vec{e}_{ij}+
 \bigl(
 (\vec{e}_{ij}\cdot\vec{s}_i)\vec{s}_j+
 (\vec{e}_{ij}\cdot\vec{s}_j)\vec{s}_i
 \bigr)
 \biggr]
\end{aligned}$$

where $\vec{s}_i$ and $\vec{s}_j$ are the spin on two magnetic
particles, r is their separation distance, and the vector $\vec{e}_{ij}
= \frac{r_i - r_j}{\left| r_i - r_j \right|}$ is the direction vector
between the two particles.

Style *spin/dipole/long* computes long-range magnetic dipole-dipole
interaction. A [kspace_style](kspace_style) must be defined to use this
pair style. Currently, [kspace_style ewald/dipole/spin](kspace_style)
and [kspace_style pppm/dipole/spin](kspace_style) support long-range
magnetic dipole-dipole interactions.

------------------------------------------------------------------------

The [pair_modify](pair_modify) table option is not relevant for this
pair style.

This pair style does not support the [pair_modify](pair_modify) tail
option for adding long-range tail corrections to energy and pressure.

This pair style writes its information to [binary restart
files](restart), so pair_style and pair_coeff commands do not need to be
specified in an input script that reads a restart file.

## Restrictions

The *spin/dipole/cut* and *spin/dipole/long* styles are part of the SPIN
package. They are only enabled if LAMMPS was built with that package.
See the [Build package](Build_package) page for more info.

Using dipole/spin pair styles with *electron* [units](units) is not
currently supported.

## Related commands

[pair_coeff](pair_coeff), [kspace_style](kspace_style) [fix
nve/spin](fix_nve_spin)

## Default

none