# min_style spin command

# min_style spin/cg command

# min_style spin/lbfgs command

## Syntax

``` LAMMPS
min_style spin
min_style spin/cg
min_style spin/lbfgs
```

## Examples

``` LAMMPS
min_style  spin/lbfgs
min_modify line spin_cubic discrete_factor 10.0
```

## Description

Apply a minimization algorithm to use when a [minimize](minimize)
command is performed.

Style *spin* defines a damped spin dynamics with an adaptive timestep,
according to:

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

with $\lambda$ a damping coefficient (similar to a magnetic damping).
$\lambda$ can be defined by setting the *alpha_damp* keyword with the
[min_modify](min_modify) command.

The minimization procedure solves this equation using an adaptive
timestep. The value of this timestep is defined by the largest
precession frequency that has to be solved in the system:

$${\Delta t}_{\rm max} = \frac{2\pi}{\kappa \left|\vec{\omega}_{\rm max} \right|}$$

with $\left|\vec{\omega}_{\rm max}\right|$ the norm of the largest
precession frequency in the system (across all processes, and across all
replicas if a spin/neb calculation is performed).

$\kappa$ defines a discretization factor *discrete_factor* for the
definition of this timestep. *discrete_factor* can be defined with the
[min_modify](min_modify) command.

Style *spin/cg* defines an orthogonal spin optimization (OSO) combined
to a conjugate gradient (CG) algorithm. The [min_modify](min_modify)
command can be used to couple the *spin/cg* to a line search procedure,
and to modify the discretization factor *discrete_factor*. By default,
style *spin/cg* does not employ the line search procedure and uses the
adaptive time-step technique in the same way as style *spin*.

Style *spin/lbfgs* defines an orthogonal spin optimization (OSO)
combined to a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)
algorithm. By default, style *spin/lbfgs* does not employ line search
procedure. If the line search procedure is not used then the discrete
factor defines the maximum root mean squared rotation angle of spins by
equation *pi/(5\*Kappa)*. The default value for Kappa is 10. The
*spin_cubic* line search option can improve the convergence of the
*spin/lbfgs* algorithm.

The [min_modify](min_modify) command can be used to activate the line
search procedure, and to modify the discretization factor
*discrete_factor*.

For more information about styles *spin/cg* and *spin/lbfgs*, see their
implementation reported in [(Ivanov)](Ivanov1).

:::: note
::: title
Note
:::

All the *spin* styles replace the force tolerance by a torque tolerance.
See [minimize](minimize) for more explanation.
::::

:::: note
::: title
Note
:::

The *spin/cg* and *spin/lbfgs* styles can be used for magnetic NEB
calculations only if the line search procedure is deactivated. See
[neb/spin](neb_spin) for more explanation.
::::

## Restrictions

The *spin*, *spin/cg*, and *spin/lbfgps* 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.

This minimization procedure is only applied to spin degrees of freedom
for a frozen lattice configuration.

## Related commands

[min_style](min_style), [minimize](minimize), [min_modify](min_modify)

## Default

The option defaults are *alpha_damp* = 1.0, *discrete_factor* = 10.0,
*line* = spin_none and *norm* = euclidean.

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

::: {#Ivanov1}
**(Ivanov)** Ivanov, Uzdin, Jonsson. arXiv preprint arXiv:1904.02669,
(2019).
:::