optimises magnetic structure by minimizing the energy using non-linear optimization algorithms
optm = OPTMAGSTR(obj, Option1, Value1, ...)
Input:
obj sw class object.
Options:
func Function that produce the magnetic moments, ordering wave
vector and normal vector from the optimization
parameters in the following form:
[M, k, n] = @(x)func(M0, x)
where M is (3,nMagExt) size matrix. k is the ordering
wave vector, its size is (1,3). n is the normal vector
of the spin rotation plane, its size is (1,3). The
default is @gm_spherical3d. For planar magnetic structure
use @gm_planar.
xmin Minimum limit of the optimisation parameters, optional.
xmax Maximum limit of the optimisation parameters, optional.
x0 Starting value of the optimisation parameters. If empty
or undefined, then random values are used.
boundary Boundary conditions of the extended unit cell.
'free' Free, interactions between extedned unit cells are
omitted.
'per' Periodic, interactions between extended unit cells
are retained.
Default is {'per' 'per' 'per'}.
epsilon The smalles value of incommensurability that is tolerated
without warning. Default is 1e-5.
nRun Number of runs. If random starting parameters are given, the
optimisation process will be rerun nRun times and the best
result (lowest ground state energy per spin) will be saved in
the result.
title Gives a title string to the simulation that is saved in the
output.
Limits only on selected prameters:
Limits can be given on any input parameter of the constraint function by
giving the name of the parameter, see the help of the used constraint
function in the following format: optmagstr('ParName',[min max],...).
For example to fix the nTheta value of @gm_planar during the optimisation
to zero use:
optmagstr(obj,'func',@gm_planar,'nTheta',[0 0]);
Optimisation parameters:
tolx Minimum change of x when convergence reached, default
value is 1e-4.
tolfun Minimum change of the R value when convergence reached,
default value is 1e-5.
maxfunevals Maximum number of function evaluations, default value
is 1e7.
maxiter Maximum number of iterations, default value is 1e4.
Output:
'optm' is a struct type variable with the following fields:
obj sw object that contains the optimised magnetic structure.
x Optimised paramters, dimensions are [1 nPar].
fname Name of the contraint function.
xname Cell containing the name of the x parameters, dimensions are
[1 nPar].
e Energy per spin in the optimised structure.
exitflag Exit flag of the optimisation code, see fminsearch.
output Detailed output of the optimisation code, see fminsearch.
param Input parameters, stored in a struct.
Example:
tri = sw_model('triAF',1);
X1 = [0 0 0 0 pi/2 0];
X2 = [0 1/2 1/2 0 pi/2 0];
optRes = tri.optmagstr('func',@gm_planar,'xmin',X1,'xmax',X2);
plot(tri)
The example determined the magnetic structure of the triangular lattice
antiferromagnet assuming planar magnetic structure and constraining the
moments into the [0 y z] plane (nTheta = 90 deg, nPhi = 0 deg or
n = [1 0 0]). Then plots the magnetic structure.
See also SW, SW.ANNEAL, GM_SPHERICAL3D, GM_PLANAR, FMINSEARCH.