$$\renewcommand{\AA}{\text{Å}}$$

# pair_style spin/dipole/long command¶

## Syntax¶

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¶

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.

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

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 must be defined to use this pair style. Currently, kspace_style ewald/dipole/spin and kspace_style pppm/dipole/spin support long-range magnetic dipole-dipole interactions.

The pair_modify table option is not relevant for this pair style.

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

This pair style writes its information to binary restart files, 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 page for more info.

Using dipole/spin pair styles with electron units is not currently supported.

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