Merge branch 'pppm_spin' of github.com:julient31/lammps into pppm_spin

\documentclass[preview]{standalone}

\usepackage{varwidth}

\usepackage[utf8x]{inputenc}

\usepackage{amsmath,amssymb,graphics,bm,setspace}

\begin{document}

\begin{varwidth}{50in}

  \begin{equation}

    \mathcal{H}_{\rm long}= 

    -\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi} 

    \sum_{i,j,i\neq j}^{N}

    \frac{g_i g_j}{r_{ij}^3}

    \Big(3 

    \left(\bm{e}_{ij}\cdot \bm{s}_{i}\right) 

    \left(\bm{e}_{ij}\cdot \bm{s}_{j}\right) 

    -\bm{s}_i\cdot\bm{s}_j \Big)

    \nonumber

  \end{equation}

  \begin{equation}

    \bm{\omega}_i = 

    \frac{\mu_0 (\mu_B)^2}{4\pi\hbar}\sum_{j}

    \frac{g_i g_j}{r_{ij}^3}

    \, \Big(

    3\,(\bm{e}_{ij}\cdot\bm{s}_{j})\bm{e}_{ij}

    -\bm{s}_{j} \Big) \nonumber

  \end{equation}

  \begin{equation}

    \bm{F}_i =

    \frac{3\, \mu_0 (\mu_B)^2}{4\pi} \sum_j

    \frac{g_i g_j}{r_{ij}^4}

    \Big[\big( (\bm{s}_i\cdot\bm{s}_j) 

    -5(\bm{e}_{ij}\cdot\bm{s}_i)

    (\bm{e}_{ij}\cdot\bm{s}_j)\big) \bm{e}_{ij}+

    \big(

    (\bm{e}_{ij}\cdot\bm{s}_i)\bm{s}_j+

    (\bm{e}_{ij}\cdot\bm{s}_j)\bm{s}_i

    \big)

    \Big]

    \nonumber

  \end{equation}

\end{varwidth}

\end{document}

    accuracy = desired relative error in forces

  {ewald/omp} value = accuracy

    accuracy = desired relative error in forces

  {ewald/dipole} value = accuracy

    accuracy = desired relative error in forces

  {ewald/dipole/spin} value = accuracy

    accuracy = desired relative error in forces

  {pppm} value = accuracy

    accuracy = desired relative error in forces

  {pppm/cg} values = accuracy (smallq)

    accuracy = desired relative error in forces

  {pppm/stagger} value = accuracy

    accuracy = desired relative error in forces

  {pppm/dipole} value = accuracy

    accuracy = desired relative error in forces

  {pppm/dipole/spin} value = accuracy

    accuracy = desired relative error in forces

  {msm} value = accuracy

    accuracy = desired relative error in forces

  {msm/cg} value = accuracy (smallq)

but in a more efficient manner than the {ewald} style.  The 1/r^6

capability means that Lennard-Jones or Buckingham potentials can be

used without a cutoff, i.e. they become full long-range potentials.

The {ewald/disp} style can also be used with point-dipoles

"(Toukmaji)"_#Toukmaji and is currently the only kspace solver in

LAMMPS with this capability.

The {ewald/dipole} style adds long-range standard Ewald summations 

for dipole-dipole interactions.

The {ewald/dipole/spin} style adds long-range standard Ewald 

summations for magnetic dipole-dipole interactions between

magnetic spins.

:line

charge value which determines whether a particle is considered charged

or not.  Its default value is 1.0e-5.

The {pppm/dipole} style invokes a particle-particle particle-mesh solver 

for dipole-dipole interactions. 

The {pppm/dipole/spin} style invokes a particle-particle particle-mesh solver 

for magnetic dipole-dipole interactions between magnetic spins. 

The {pppm/tip4p} style is identical to the {pppm} style except that it

adds a charge at the massless 4th site in each TIP4P water molecule.

It should be used with "pair styles"_pair_style.html with a

pair_style spin/dipole/cut command :h3

pair_style spin/dipole/long command :h3

pair_style spin/dipole/long/qsymp command :h3

[Syntax:]

pair_style spin/dipole/cut cutoff 

pair_style spin/dipole/long cutoff

pair_style spin/dipole/long/qsymp cutoff :pre

pair_style spin/dipole/long cutoff :pre

cutoff = global cutoff for Magnetic dipole energy and forces

cutoff = global cutoff for magnetic dipole energy and forces

(optional) (distance units) :ulb,l

:ule

pair_coeff 2 3 1.0 1.0 2.5 4.0 scale 0.5

pair_coeff 2 3 1.0 1.0 2.5 4.0 :pre

pair_style spin/dipole/long/qsymp 10.0

pair_coeff * * 1.0 1.0

pair_coeff 2 3 1.0 1.0 2.5 4.0 :pre

[Description:]

Style {spin/dipole/cut} computes a short-range dipole-dipole

interactions between pairs of magnetic particles that each 

interaction between pairs of magnetic particles that each 

have a magnetic spin. 

The magnetic dipole-dipole interactions are computed by the

following formulas for the energy (E), force

(F), and torque (T) between particles I and J.

:c,image(Eqs/pair_dipole.jpg)

where qi and qj are the charges on the two particles, pi and pj are

the dipole moment vectors of the two particles, r is their separation

distance, and the vector r = Ri - Rj is the separation vector between

the two particles.  Note that Eqq and Fqq are simply Coulombic energy

and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the

torques do not act symmetrically.  These formulas are discussed in

"(Allen)"_#Allen2 and in "(Toukmaji)"_#Toukmaji2.

Also note, that in the code, all of these terms (except Elj) have a

C/epsilon prefactor, the same as the Coulombic term in the LJ +

Coulombic pair styles discussed "here"_pair_lj.html.  C is an

energy-conversion constant and epsilon is the dielectric constant

which can be set by the "dielectric"_dielectric.html command.  The

same is true of the equations that follow for other dipole pair

styles.

Style {lj/sf/dipole/sf} computes "shifted-force" interactions between

pairs of particles that each have a charge and/or a point dipole

moment. In general, a shifted-force potential is a (slightly) modified

potential containing extra terms that make both the energy and its

derivative go to zero at the cutoff distance; this removes

(cutoff-related) problems in energy conservation and any numerical

instability in the equations of motion "(Allen)"_#Allen2. Shifted-force

interactions for the Lennard-Jones (E_LJ), charge-charge (Eqq),

charge-dipole (Eqp), dipole-charge (Epq) and dipole-dipole (Epp)

potentials are computed by these formulas for the energy (E), force

(F), and torque (T) between particles I and J:

:c,image(Eqs/pair_dipole_sf.jpg)

:c,image(Eqs/pair_dipole_sf2.jpg)

following formulas for the magnetic energy, magnetic precession 

vector omega and mechanical force between particles I and J.

where epsilon and sigma are the standard LJ parameters, r_c is the

cutoff, qi and qj are the charges on the two particles, pi and pj are

the dipole moment vectors of the two particles, r is their separation

distance, and the vector r = Ri - Rj is the separation vector between

the two particles.  Note that Eqq and Fqq are simply Coulombic energy

and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the

torques do not act symmetrically.  The shifted-force formula for the

Lennard-Jones potential is reported in "(Stoddard)"_#Stoddard.  The

original (non-shifted) formulas for the electrostatic potentials,

forces and torques can be found in "(Price)"_#Price2. The shifted-force

electrostatic potentials have been obtained by applying equation 5.13

of "(Allen)"_#Allen2. The formulas for the corresponding forces and

torques have been obtained by applying the 'chain rule' as in appendix

C.3 of "(Allen)"_#Allen2.

:c,image(Eqs/pair_spin_dipole.jpg)

If one cutoff is specified in the pair_style command, it is used for

both the LJ and Coulombic (q,p) terms.  If two cutoffs are specified,

they are used as cutoffs for the LJ and Coulombic (q,p) terms

respectively. This pair style also supports an optional {scale} keyword

as part of a pair_coeff statement, where the interactions can be

scaled according to this factor. This scale factor is also made available

for use with fix adapt.

where si and sj are the spin on two magnetic particles, 

r is their separation distance, and the vector e = (Ri - Rj)/|Ri - Rj| 

is the direction vector between the two particles.  

Style {lj/cut/dipole/long} computes long-range point-dipole

interactions as discussed in "(Toukmaji)"_#Toukmaji2. Dipole-dipole,

dipole-charge, and charge-charge interactions are all supported, along

with the standard 12/6 Lennard-Jones interactions, which are computed

with a cutoff.  A "kspace_style"_kspace_style.html must be defined to

use this pair style.  Currently, only "kspace_style

ewald/disp"_kspace_style.html support long-range point-dipole

interactions.

Style {lj/long/dipole/long} also computes point-dipole interactions as

discussed in "(Toukmaji)"_#Toukmaji2. Long-range dipole-dipole,

dipole-charge, and charge-charge interactions are all supported, along

with the standard 12/6 Lennard-Jones interactions.  LJ interactions

can be cutoff or long-ranged.

For style {lj/long/dipole/long}, if {flag_lj} is set to {long}, no

cutoff is used on the LJ 1/r^6 dispersion term.  The long-range

portion is calculated by using the "kspace_style

ewald_disp"_kspace_style.html command.  The specified LJ cutoff then

determines which portion of the LJ interactions are computed directly

by the pair potential versus which part is computed in reciprocal

space via the Kspace style.  If {flag_lj} is set to {cut}, the LJ

interactions are simply cutoff, as with "pair_style

lj/cut"_pair_lj.html.  If {flag_lj} is set to {off}, LJ interactions

are not computed at all.

If {flag_coul} is set to {long}, no cutoff is used on the Coulombic or

dipole interactions.  The long-range portion is calculated by using

{ewald_disp} of the "kspace_style"_kspace_style.html command. If

{flag_coul} is set to {off}, Coulombic and dipole interactions are not

computed at all.

Atoms with dipole moments should be integrated using the "fix

nve/sphere update dipole"_fix_nve_sphere.html or the "fix

nvt/sphere update dipole"_fix_nvt_sphere.html command to rotate the

dipole moments.  The {omega} option on the "fix

langevin"_fix_langevin.html command can be used to thermostat the

rotational motion.  The "compute temp/sphere"_compute_temp_sphere.html

command can be used to monitor the temperature, since it includes

rotational degrees of freedom.  The "atom_style

hybrid dipole sphere"_atom_style.html command should be used since

it defines the point dipoles and their rotational state.

The magnitude and orientation of the dipole moment for each particle

can be defined by the "set"_set.html command or in the "Atoms" section

of the data file read in by the "read_data"_read_data.html command.

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, or by mixing as described below:

epsilon (energy units)

sigma (distance units)

cutoff1 (distance units)

cutoff2 (distance units) :ul

The latter 2 coefficients are optional.  If not specified, the global

LJ and Coulombic cutoffs specified in the pair_style command are used.

If only one cutoff is specified, it is used as the cutoff for both LJ

and Coulombic interactions for this type pair.  If both coefficients

are specified, they are used as the LJ and Coulombic cutoffs for this

type pair.

Style {spin/dipole/long} computes long-range magnetic dipole-dipole

interaction.

A "kspace_style"_kspace_style.html must be defined to

use this pair style.  Currently, "kspace_style 

ewald/dipole/spin"_kspace_style.html and "kspace_style

pppm/dipole/spin"_kspace_style.html support long-range magnetic 

dipole-dipole interactions.

:line

Styles with a {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are

functionally the same as the corresponding style without the suffix.

They have been optimized to run faster, depending on your available

hardware, as discussed on the "Speed packages"_Speed_packages.html doc

page.  The accelerated styles take the same arguments and should

produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,

USER-OMP and OPT packages, respectively.  They are only enabled if

LAMMPS was built with those packages.  See the "Build

package"_Build_package.html doc page for more info.

You can specify the accelerated styles explicitly in your input script

by including their suffix, or you can use the "-suffix command-line

switch"_Run_options.html when you invoke LAMMPS, or you can use the

"suffix"_suffix.html command in your input script.

See the "Speed packages"_Speed_packages.html doc page for more

instructions on how to use the accelerated styles effectively.

:line

[Mixing, shift, table, tail correction, restart, rRESPA info]:

For atom type pairs I,J and I != J, the epsilon and sigma coefficients

and cutoff distances for this pair style can be mixed.  The default

mix value is {geometric}.  See the "pair_modify" command for details.

For atom type pairs I,J and I != J, the A, sigma, d1, and d2

coefficients and cutoff distance for this pair style can be mixed.  A

is an energy value mixed like a LJ epsilon.  D1 and d2 are distance

values and are mixed like sigma.  The default mix value is

{geometric}.  See the "pair_modify" command for details.

This pair style does not support the "pair_modify"_pair_modify.html

shift option for the energy of the Lennard-Jones portion of the pair

interaction; such energy goes to zero at the cutoff by construction.

The "pair_modify"_pair_modify.html table option is not relevant

for this pair style.

files"_restart.html, so pair_style and pair_coeff commands do not need

to be specified in an input script that reads a restart file.

This pair style can only be used via the {pair} keyword of the

"run_style respa"_run_style.html command.  It does not support the

{inner}, {middle}, {outer} keywords.

[Restrictions:]

The {lj/cut/dipole/cut}, {lj/cut/dipole/long}, and

{lj/long/dipole/long} styles are part of the DIPOLE package.  They are

only enabled if LAMMPS was built with that package.  See the "Build

package"_Build_package.html doc page for more info.

The {lj/sf/dipole/sf} style is part of the USER-MISC package.  It is

only enabled if LAMMPS was built with that package.  See the "Build

package"_Build_package.html doc page for more info.

The {spin/dipole/cut} and {spin/dipole/long} styles are part of

the SPIN package.  They are only enabled if LAMMPS was built with that 

package.  See the "Build package"_Build_package.html doc page for more 

info.

Using dipole pair styles with {electron} "units"_units.html is not

Using dipole/spin pair styles with {electron} "units"_units.html is not

currently supported.

[Related commands:]

"pair_coeff"_pair_coeff.html, "set"_set.html, "read_data"_read_data.html,

"fix nve/sphere"_fix_nve_sphere.html, "fix nvt/sphere"_fix_nvt_sphere.html

"pair_coeff"_pair_coeff.html, "kspace_style"_kspace_style.html

"fix nve/spin"_fix_nve_spin.html

[Default:] none

:link(Allen2)

[(Allen)] Allen and Tildesley, Computer Simulation of Liquids,

Clarendon Press, Oxford, 1987.

:link(Toukmaji2)

[(Toukmaji)] Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,

10913 (2000).

:link(Stoddard)

[(Stoddard)] Stoddard and Ford, Phys Rev A, 8, 1504 (1973).

:link(Price2)

[(Price)] Price, Stone and Alderton, Mol Phys, 52, 987 (1984).

set 		group all spin 2.2 -1.0 0.0 0.0

velocity 	all create 100 4928459 rot yes dist gaussian

pair_style 	hybrid/overlay eam/alloy spin/exchange 3.5

pair_style 	hybrid/overlay eam/alloy spin/exchange 3.5 spin/dipole/long 8.0

pair_coeff 	* * eam/alloy Fe_Mishin2006.eam.alloy Fe

pair_coeff 	* * spin/exchange exchange 3.4 0.02726 0.2171 1.841

pair_coeff	* * spin/dipole/long 8.0

neighbor 	0.1 bin

neigh_modify 	every 10 check yes delay 20

kspace_style 	ewald/dipole/spin 1.0e-4

fix 		1 all 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_modify 	1 energy yes

fix 		2 all langevin/spin 0.0 0.0 21

dump 		100 all custom 1 dump_iron.lammpstrj type x y z c_outsp[1] c_outsp[2] c_outsp[3]

run 		2000

# min_style 	spin

# min_modify	alpha_damp 1.0 discrete_factor 10

# minimize 	1.0e-16 1.0e-16 10000 10000