# fix precession/spin command

## Syntax

``` LAMMPS
fix ID group precession/spin style args
```

-   ID, group are documented in [fix](fix) command

-   precession/spin = style name of this fix command

-   style = *zeeman* or *anisotropy* or *cubic* or *stt*

        *zeeman* args = H x y z
          H = intensity of the magnetic field (in Tesla)
          x y z = vector direction of the field
        *anisotropy* args = K x y z
          K = intensity of the magnetic anisotropy (in eV)
          x y z = vector direction of the anisotropy
        *cubic* args = K1 K2c n1x n1y n1x n2x n2y n2z n3x n3y n3z
          K1 and K2c = intensity of the magnetic anisotropy (in eV)
          n1x to n3z = three direction vectors of the cubic anisotropy
        *stt* args = J x y z
          J = intensity of the spin-transfer torque field
          x y z = vector direction of the field

## Examples

``` LAMMPS
fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0
fix 1 3 precession/spin anisotropy 0.001 0.0 0.0 1.0
fix 1 iron precession/spin cubic 0.001 0.0005 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0
fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0 anisotropy 0.001 0.0 0.0 1.0
```

## Description

This fix applies a precession torque to each magnetic spin in the group.

Style *zeeman* is used for the simulation of the interaction between the
magnetic spins in the defined group and an external magnetic field:

$$H_{Zeeman} = -g \sum_{i=0}^{N}\mu_{i}\, \vec{s}_{i} \cdot\vec{B}_{ext}$$

with:

-   $\vec{B}_{ext}$ the external magnetic field (in T)
-   $g$ the Lande factor (hard-coded as $g=2.0$)
-   $\vec{s}_i$ the unitary vector describing the orientation of spin
    $i$
-   $\mu_i$ the atomic moment of spin $i$ given as a multiple of the
    Bohr magneton $\mu_B$ (for example, $\mu_i \approx 2.2$ in bulk
    iron).

The field value in Tesla is multiplied by the gyromagnetic ratio,
$g \cdot \mu_B/\hbar$, converting it into a precession frequency in
rad.THz (in metal units and with $\mu_B = 5.788\cdot 10^{-5}$ eV/T).

As a comparison, the figure below displays the simulation of a single
spin (of norm $\mu_i = 1.0$) submitted to an external magnetic field of
$\vert B_{ext}\vert = 10.0\; \mathrm{Tesla}$ (and oriented along the z
axis). The upper plot shows the average magnetization along the external
magnetic field axis and the lower plot the Zeeman energy, both as a
function of temperature. The reference result is provided by the plot of
the Langevin function for the same parameters.

![image](JPG/zeeman_langevin.jpg){.align-center width="600px"}

The temperature effects are accounted for by connecting the spin $i$ to
a thermal bath using a Langevin thermostat (see [fix
langevin/spin](fix_langevin_spin) for the definition of this
thermostat).

Style *anisotropy* is used to simulate an easy axis or an easy plane for
the magnetic spins in the defined group:

$$H_{aniso} = -\sum_{{ i}=1}^{N} K_{an}(\mathbf{r}_{i})\, \left(
\vec{s}_{i} \cdot \vec{n}_{i} \right)^2$$

with $n$ defining the direction of the anisotropy, and $K$ (in eV) its
intensity. If $K > 0$, an easy axis is defined, and if $K < 0$, an easy
plane is defined.

Style *cubic* is used to simulate a cubic anisotropy, with three
possible easy axis for the magnetic spins in the defined group:

$$H_{cubic} = -\sum_{{ i}=1}^{N} K_{1}
\Big[
\left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2 +
\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2
\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 +
\left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 \Big]
+K_{2}^{(c)} \left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2
\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2$$

with $K_1$ and $K_{2c}$ (in eV) the intensity coefficients and
$\vec{n}_1$, $\vec{n}_2$ and $\vec{n}_3$ defining the three anisotropic
directions defined by the command (from *n1x* to *n3z*). For
$\vec{n}_1 = (1 0 0)$, $\vec{n}_2 =
(0 1 0)$, and $\vec{n}_3 = (0 0 1)$, $K_1 < 0$ defines an iron type
anisotropy (easy axis along the $(0 0 1)$-type cube edges), and
$K_1 > 0$ defines a nickel type anisotropy (easy axis along the
$(1 1 1)$-type cube diagonals). $K_2^c >
0$ also defines easy axis along the $(1 1 1)$-type cube diagonals. See
chapter 2 of [(Skomski)](Skomski1) for more details on cubic
anisotropies.

Style *stt* is used to simulate the interaction between the spins and a
spin-transfer torque. See equation (7) of [(Chirac)](Chirac1) for more
details about the implemented spin-transfer torque term.

In all cases, the choice of $(x y z)$ only imposes the vector directions
for the forces. Only the direction of the vector is important; its
length is ignored (the entered vectors are normalized).

Those styles can be combined within one single command line.

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

The norm of all vectors defined with the precession/spin command have to
be non-zero. For example, defining \"fix 1 all precession/spin zeeman
0.1 0.0 0.0 0.0\" would result in an error message. Since those vector
components are used to compute the inverse of the field (or anisotropy)
vector norm, setting a zero-vector would result in a division by zero.
::::

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

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

No information about this fix is written to [binary restart
files](restart).

The [fix_modify](fix_modify) *energy* option is supported by this fix to
add the energy associated with the spin precession torque to the global
potential energy of the system as part of [thermodynamic
output](thermo_style). The default setting for this fix is [fix_modify
energy no](fix_modify).

This fix computes a global scalar which can be accessed by various
[output commands](Howto_output). The scalar is the potential energy (in
energy units) discussed in the previous paragraph. The scalar value is
an \"extensive\" quantity.

No information about this fix is written to [binary restart
files](restart).

## Restrictions

The *precession/spin* style is part of the SPIN package. This style is
only enabled if LAMMPS was built with this package, and if the
atom_style \"spin\" was declared. See the [Build package](Build_package)
page for more info.

## Related commands

[atom_style spin](atom_style)

## Default

none

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

::: {#Skomski1}
**(Skomski)** Skomski, R. (2008). Simple models of magnetism. Oxford
University Press.
:::

::: {#Chirac1}
**(Chirac)** Chirac, Theophile, et al. Ultrafast antiferromagnetic
switching in NiO induced by spin transfer torques. Physical Review B
102.13 (2020): 134415.
:::