"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

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:link(ld,Manual.html)
:link(lc,Commands_all.html)

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pair_style spin/exchange command :h3

[Syntax:]

pair_style spin/exchange cutoff :pre

cutoff = global cutoff pair (distance in metal units) :ulb,l

:ule

[Examples:]

pair_style spin/exchange 4.0
pair_coeff * * exchange 4.0 0.0446928 0.003496 1.4885
pair_coeff 1 2 exchange 6.0 -0.01575 0.0 1.965 :pre

[Description:]

Style {spin/exchange} computes the exchange interaction between
pairs of magnetic spins:

:c,image(Eqs/pair_spin_exchange_interaction.jpg)

where si and sj are two neighboring magnetic spins of two particles,
rij = ri - rj is the inter-atomic distance between the two particles,
and J(rij) is a function defining the intensity and the sign of the exchange
interaction for different neighboring shells. This function is defined as:

:c,image(Eqs/pair_spin_exchange_function.jpg)

where a, b and d are the three constant coefficients defined in the associated
"pair_coeff" command (see below for more explanations).

The coefficients a, b, and d need to be fitted so that the function above matches with
the value of the exchange interaction for the N neighbor shells taken into account.
Examples and more explanations about this function and its parameterization are reported
in "(Tranchida)"_#Tranchida3.

From this exchange interaction, each spin i will be submitted
to a magnetic torque omega, and its associated atom can be submitted to a
force F for spin-lattice calculations (see "fix_nve_spin"_fix_nve_spin.html),
such as:

:c,image(Eqs/pair_spin_exchange_forces.jpg)

with h the Planck constant (in metal units), and eij = (ri - rj)/|ri-rj| the unit
vector between sites i and j.

More details about the derivation of these torques/forces are reported in
"(Tranchida)"_#Tranchida3.

For the {spin/exchange} pair style, the following coefficients must be defined
for each pair of atoms types via the "pair_coeff"_pair_coeff.html command as in
the examples above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html commands, and
set in the following order:

rc (distance units)
a  (energy units)
b  (adim parameter)
d  (distance units) :ul

Note that rc is the radius cutoff of the considered exchange interaction,
and a, b and d are the three coefficients performing the parameterization
of the function J(rij) defined above.

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

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[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"_Build_package.html doc page for more info.

[Related commands:]

"atom_style spin"_atom_style.html, "pair_coeff"_pair_coeff.html,
"pair_eam"_pair_eam.html,

[Default:] none

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:link(Tranchida3)
[(Tranchida)] Tranchida, Plimpton, Thibaudeau and Thompson,
Journal of Computational Physics, 372, 406-425, (2018).
