# fix langevin/spin command

## Syntax

    fix ID group-ID langevin/spin T Tdamp seed

-   ID, group-ID are documented in [fix](fix) command
-   langevin/spin = style name of this fix command
-   T = desired temperature of the bath (temperature units, K in metal
    units)
-   Tdamp = transverse magnetic damping parameter (adim)
-   seed = random number seed to use for white noise (positive integer)

## Examples

``` LAMMPS
fix 2 all langevin/spin 300.0 0.01 21
```

## Description

Apply a Langevin thermostat as described in [(Mayergoyz)](Mayergoyz1) to
the magnetic spins associated to the atoms. Used with [fix
nve/spin](fix_nve_spin), this command performs Brownian dynamics (BD). A
random torque and a transverse dissipation are applied to each spin i
according to the following stochastic differential equation:

$$\frac{d \vec{s}_{i}}{dt} = \frac{1}{\left(1+\lambda^2 \right)} \left( \left(
\vec{\omega}_{i} +\vec{\eta} \right) \times \vec{s}_{i} + \lambda\, \vec{s}_{i}
\times\left( \vec{\omega}_{i} \times\vec{s}_{i} \right) \right)$$

with $\lambda$ the transverse damping, and $\eta$ a random vector. This
equation is referred to as the stochastic Landau-Lifshitz (sLL)
equation.

The components of $\eta$ are drawn from a Gaussian probability law.
Their amplitude is defined as a proportion of the temperature of the
external thermostat T (in K in metal units).

More details about this implementation are reported in
[(Tranchida)](Tranchida2).

Note: due to the form of the sLL equation, this fix has to be defined
just before the nve/spin fix (and after all other magnetic fixes). As an
example:

``` LAMMPS
fix 1 all precession/spin zeeman 0.01 0.0 0.0 1.0
fix 2 all langevin/spin 300.0 0.01 21
fix 3 all nve/spin lattice moving
```

is correct, but defining a force/spin command after the langevin/spin
command would give an error message.

Note: The random \# *seed* must be a positive integer. A Marsaglia
random number generator is used. Each processor uses the input seed to
generate its own unique seed and its own stream of random numbers. Thus
the dynamics of the system will not be identical on two runs on
different numbers of processors.

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

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to [binary restart
files](restart). Because the state of the random number generator is not
saved in restart files, this means you cannot do \"exact\" restarts with
this fix, where the simulation continues on the same as if no restart
had taken place. However, in a statistical sense, a restarted simulation
should produce the same behavior.

This fix is not invoked during [energy minimization](minimize).

## Restrictions

The *langevin/spin* fix is part of the SPIN package. This style is only
enabled if LAMMPS was built with this package. See the [Build
package](Build_package) page for more info.

The numerical integration has to be performed with *fix nve/spin* when
*fix langevin/spin* is enabled.

This fix has to be the last defined magnetic fix before the time
integration fix (e.g. *fix nve/spin*).

## Related commands

[fix nve/spin](fix_nve_spin), [fix precession/spin](fix_precession_spin)

## Default

none

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

::: {#Mayergoyz1}
**(Mayergoyz)** I.D. Mayergoyz, G. Bertotti, C. Serpico (2009). Elsevier
(2009)
:::

::: {#Tranchida2}
**(Tranchida)** Tranchida, Plimpton, Thibaudeau and Thompson, Journal of
Computational Physics, 372, 406-425, (2018).
:::