\(\renewcommand{\AA}{\text{Å}}\)

pair_style spin/dmi command

Syntax

pair_style spin/dmi cutoff

  • cutoff = global cutoff pair (distance in metal units)

Examples

pair_style spin/dmi 4.0
pair_coeff * * dmi 2.6 0.001 1.0 0.0 0.0
pair_coeff 1 2 dmi 4.0 0.00109 0.0 0.0 1.0

Description

Style spin/dmi computes the Dzyaloshinskii-Moriya (DM) interaction between pairs of magnetic spins. According to the expression reported in (Rohart), one has the following DM energy:

\[\mathbf{H}_{dm} = \sum_{{ i,j}=1,i\neq j}^{N} \left( \vec{e}_{ij} \times \vec{D} \right) \cdot\left(\vec{s}_{i}\times \vec{s}_{j}\right),\]

where \(\vec{s}_i\) and \(\vec{s}_j\) are two neighboring magnetic spins of two particles, \(\vec{e}_ij = \frac{r_i - r_j}{\left| r_i - r_j \right|}\) is the unit vector between sites i and j, and \(\vec{D}\) is the DM vector defining the intensity (in eV) and the direction of the interaction.

In (Rohart), \(\vec{D}\) is defined as the direction normal to the film oriented from the high spin-orbit layer to the magnetic ultra-thin film.

The application of a spin-lattice Poisson bracket to this energy (as described in (Tranchida)) allows to derive a magnetic torque omega, and a mechanical force F (for spin-lattice calculations only) for each magnetic particle i:

\[\vec{\omega}_i = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times \left(\vec{e}_{ij}\times \vec{D} \right) ~~{\rm and}~~ \vec{F}_i = -\sum_{j}^{Neighb} \frac{1}{r_{ij}} \vec{D} \times \left( \vec{s}_{i}\times \vec{s}_{j} \right)\]

More details about the derivation of these torques/forces are reported in (Tranchida).

For the spin/dmi pair style, the following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, and set in the following order:

  • rc (distance units)

  • |D| (energy units)

  • Dx, Dy, Dz (direction of D)

Note that rc is the radius cutoff of the considered DM interaction, |D| is the norm of the DM vector (in eV), and Dx, Dy and Dz define its direction.

None of those coefficients is optional. If not specified, the spin/dmi pair style cannot be used.

Restrictions

All the pair/spin styles are part of the SPIN package. These styles are only enabled if LAMMPS was built with this package, and if the atom_style “spin” was declared. See the Build package page for more info.

Default

none

(Rohart) Rohart and Thiaville, Physical Review B, 88(18), 184422. (2013).

(Tranchida) Tranchida, Plimpton, Thibaudeau and Thompson, Journal of Computational Physics, 372, 406-425, (2018).