lammps/doc/src/tutorial_spin.txt

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

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

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Tutorial for the SPIN package in LAMMPS :h3

This tutorial explains how to use the spin dynamics in LAMMPS,
and to perform spin and spin--lattice simulations using the 
SPIN package. As an illustration, input files are documented. 
First of all, LAMMPS has to be compiled with the SPIN package 
activated. Then, the data file and input scripts have to be 
modified to include the  magnetic spins and to handle them.

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[Overview of the spin and spin--lattice dynamics]

At the atomic scale, magnetic materials can be seen as ensemble of
atoms, each one of them carying a magnetic moment, refered to as its 
atomic spin. In ref "Antropov"_#Antropov, a formalism allowing to 
simulate approximate classical spins, and to couple them to lattice 
vibrations was introduced. Each of these spins is simulated via a 
classical vector, associated to each magnetic atom, and whose 
trajectory is defined by an equation of motion.
Lattice vibrations are simulated by the usual equations of MD. 
A mechanical potential (EAM, Finnis-Siclair, or Dudarev-Derlet) ensure 
the cohesion of the particles. The coupling between the magnetic and 
lattice degrees of freedom is performed via the inter-atomic dependence
of the magnetic interactions.
:ole


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[Preparation of the data file]

For the mechanical potentials, the data file is similar to a standard LAMMPS 
data file for {atom_style full}.  The DPs and the {harmonic bonds} connecting 
them to their DC should appear in the data file as normal atoms and bonds.

For the magnetic interactions, no data file is necessary, every interaction
input will be define in the input file. :pre


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[Basic input file]

Up to know, spin simulations only accept the metal units. 

The atom style should be set to {spin}, so that you
can define atomic spin vectors.


The set group command defines the Lande factor (the norm) of
the magnetic vectors in a given group, and their initial 
oriantation. The command is:

set group A B C D E F :pre

with A, B, C, D, E, and F the following input parameters:
A is set to all, or to the number of a specific and pre-defined 
group of atoms, 
B is set to {spin} or {spin/random}, depending on if the spins of 
the group have to be initialized in a particulat direction, or randomly. 

If B is defined as {spin}, the C is the Lande factor for the spins of
the group, and [D,E,F] is the vector giving the direction for the
initialization.

If B is defined as {spin/random}, C is a number giving the seed for the random 
difinition of the directions, and D is the Lande factor of the spins
in this group. E and F are not defined. 

Examples: 
set group all spin 1.72 1.0 0.0 0.0
set group all spin/random 11 1.72

setting the initial direction of all spins, with a Lande factor of 1.72, 
and either in the x direction, or randomly. :l


The pair style has to be set to {pair/spin}. The command is

pair_style pair/spin A

with A a global radius cutoff.

The different pair interactions and their associated coefficients can then be 
defined via the pair coeff command. 

pair_coeff A B C D E F G H

where A and B are setting the pair concerned by this pair coeff command. 
For example, A=1 and B=2 to set the pair coefficients between spins of 
type 1 and spins of type 2. Use {*} for setting a pair coeffcient between 
all pairs of spins. 

C defines the type of the interaction. It can be set to {exchange} for an 
exchange interaction, {dmi} for a Dzyaloshinskii-Moriya (DM) interaction, or to 
{me} for a magneto-electric (ME) interaction. 

If C is set to {exchange}, D is the radius cutoff (in Angtrom) associated 
to the exchange interaction, and E, F and G are the three parameters of the 
Bethe--Slater function (E in eV, F without dimension, and G in Angtrom). 
H is not defined.

If C is set to {dmi}, D is the radius cutoff (in Angtrom) associated to the DM 
interaction, E is the intensity of the interaction in eV (which is also the 
norm of the DM vector), and [F, G, H] are giving the direction of the DM
vector.

If C is set to {me}, D is the radius cutoff (in Angtrom) associated to the ME 
interaction, E is the intensity of the interaction in eV (which corresponds to 
the intensity of the electric polarization), and [F, G, H] are giving the 
direction of the polarization vector.

Examples:
pair_coeff * * exchange 4.0 0.0446928 0.003496 1.4885
pair_coeff * * dmi 2.6 0.001 0.0 0.0 1.0

are setting an exchange interaction between every type of spins, with a radius 
cutoff of 4.0 Angtrom, and E=0.0446928 eV, F=0.003496, and G=1.4885 Angtrom as 
coefficient for the associated Bethe--Slater function, and a DM interaction
with a radius cutoff of 2.6 Angtrom, an intensity of 0.001 eV and a DM vector 
in the direction [0.0 0.0 1.0]. :l


A fix has to be set to {force/spin} to define local magnetic forces, like the Zeeman
interaction or an anisotropic interaction. The command is:

fix A B C D E F G H

with A the label of the associated fix, B defining to which group of spins the 
force is applied to, C defined as {force/spin} for magnetic local fixes, and
D defining the type of this fix. D can be equal to {zeeman} for a Zeeman interaction,
or to {anisotropy} for an anisotropic interaction.

If D is set to {zeeman}, then E gives the intensity of the applied magnetic field (in 
Tesla), and [F, G, H] the direction of this field.

If is set to {anisotropy}, hen E gives the intensity of the anisotropic field (in eV),
and [F, G, H] the direction of this anisotropy.

Examples:
fix 1 all force/spin zeeman 1.0 0.0 0.0 1.0
fix 2 all force/spin anisotropy 0.001 0.0 1.0 0.0

are setting two fixes, the first one, labelled 1, is applied to all spins and defines
a Zeeman interaction corresponding to a field of 1 Tesla in the z direction, whereas
the second fix, labelled 2, is also applied to all spins, and defines a uniaxial 
anisotropy of intensity 0.001 eV, in the direction y. :l


To simulate the temperature effects, a fix has to be set to {langevin/spin}. The command
is

fix A B C D E F G

where A is the label of the associated fix, B defines to which spins the fix is applied,
and C is set equal to {langevin/spin}. Then, D defines the temperature of the random bath
(in K), E is the transverse magnetic damping (no dimension), F is a longitudinal magnetic
damping, and G the seed for the random variables.

Note: the transverse damping is not implemented into LAMMPS yet. It is necessary for 
micromagnetic simulations only. 

Examples:
fix 2 all langevin/spin 300.0 0.01 0.0 21

is setting a fix labelled as 2, which is connecting all spins to a random bath. The temperature
of this bath is set to 300 K, and the value of the transverse Gilbert damping is set to 0.01.
The seed is set to 21.


For LAMMPS to understand that the motion of spins has to be taken into account, one has to set 
a fix to {nve/spin}. The command is: 

fix A B C D

with A the label of this fix, B defining to which group of atoms this fix is applied to, C has
to be set to {nve/spin}, and D can be set to {serial} for a serial calculation, with one 
processor only, or to {mpi} for a parallel calculation, with N processors.

Example:
fix 3 all nve/spin mpi

is setting a fix labelled 3, and applies it to all the particles. The calculation is running in
parallel as the option {mpi} is defined.


Two main outputs of the computed magnetic quntities can be performed. 

The first one is via a compute and a fix options. The compute command is defined as: 

compute A B C 

with A the label of this compute, B to which group of particles it is applied to, and finally, 
the option {compute/spin} has to be set. 
This compute is associated to a fix to define the output frequency and format. A typical command is:

fix A B C D E F G H

where A is the label of the fix, B the group of particles it is applied to, C defines the type of the
output fix, for example we chose to use {ave/time}, which can output every N timesteps, and perform 
a time average over those steps. D, E, and F are the usual command of {ave/time}. G stands for the 
magnetic quantities that are computed by {compute/spin}. Those quantities are:  

c_mag[1]   Physical time (in ps)
c_mag[2]   Magnetization along x (adim)
c_mag[3]   Magnetization along y (adim)
c_mag[4]   Magnetization along z (adim)
c_mag[5]   Magnetization Norm (adim)
c_mag[6]   Magnetic energy (in eV)
c_mag[7]   Spin temperature (in K)

And H stands for the output format, and is defined as in other . 

Example:
compute 1 all compute/spin
fix 3 all ave/time 1 1 10 c_mag[1] c_mag[2] c_mag[3] c_mag[4] c_mag[5] c_mag[6] c_mag[7] 
file mag_output.dat format %20.16g

is defining a compute of the magnetic quantities applied to all spins. The fix then outputs 
every magnetic quantities every 10 time steps without performing any time average. These 
quantities are stored in a file called mag_output.dat, with a special format (defined by %20.16g)


It is also possible to output the evolution of the spin configuration. This can be done with 
the dump command. The only difference with a regular dump command is that the velocities 
vi are replaced by the spin components spi. 

Example:
dump 1 all custom 100 dump_spin.lammpstrj type x y z spx spy spz

is dumping every 100 timesteps the spin configuration in a file called dump_spin.lammpstrj.


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:link(Antropov)
[(Antropov)] Antropov, Katsnelson, Harmon, Van Schilfgaarde, and Kusnezov, Phys Rev B, 54(2), 1019 (1996)