spinw.optmagstr method

general magnetic structure optimizer

Syntax

optm = optmagstr(obj,Name,Value)

Description

optm = optmagstr(obj,Name,Value) is a general magnetic structure optimizer that as the name suggests is general however usually less efficient than spinw.optmagk or spinw.optmagsteep. However this function enables the usage of constraint functions to improve the optimization. This function is most usefull if there is 1-2 parameters that has to be optimized, such as a canting angle of the spins in magnetic field. To optimize large number of spin angles spinw.optmagsteep might be faster.

Examples

The example determines the propagation vector of the ground state of the triangular lattice antiferromagnet. The magnetic structure is constrained to be planar in the $xy$ -plane. The gm_planard constraint function is used where the first 3 parameter determined the propagation vector, followed by the polar angles of the magnetic moments (here there is only 1 magnetic moment in the unit cell) which is fixed to 0. Finally the last 2 parameters corresponds to the polar angles of the normal to the spin-plane which is the $z$ -axis ( $\theta=0$ , $\varphi=0$ ). The optimized magnetic structure is plotted.

tri = sw_model('triAF',1)
X1 = [0 0 0 0 0 0]
X2 = [0 1/2 1/2 0 0 0]
optRes = tri.optmagstr('func',@gm_planard,'xmin',X1,'xmax',X2)
km = optRes.x(1:3)

Output

km =
         0    0.3333    0.3333

plot(tri)

Input Arguments

obj: spinw object.

Name-Value Pair Arguments

'func'

Function that produces the spin orientations, propagation vector and normal vector from the optimization parameters and has the following argument list:

[M, k, n] = @(x)func(M0, x)

here M is matrix with dimensions of $[3\times n_{magExt}]$ , k is the propagation vector (row vector with 3 elements), n is the normal vector of the spin rotation plane (row vector with 3 elements). The default value is @gm_spherical3d. For planar magnetic structures use @gm_planar.

'xmin'

Lower limit of the optimisation parameters.

'xmax'

Upper limit of the optimisation parameters.

'x0'

Starting value of the optimisation parameters. If empty or undefined, then random values are used within the given limits.

'boundary'

Boundary conditions of the magnetic cell:

'free' Free, interactions between extedned unit cells are omitted.
'per' Periodic, interactions between extended unit cells are retained.

Default value is {'per' 'per' 'per'}.

'epsilon'

The smallest value of incommensurability that is tolerated without warning. Default value is $10^{-5}$ .

'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 kept.

'title'

Gives a title string to the simulation that is saved in the output.

'tid'

Determines if the elapsed and required time for the calculation is displayed. The default value is determined by the tid preference stored in swpref. The following values are allowed (for more details see sw_timeit):

0 No timing is executed.
1 Display the timing in the Command Window.
2 Show the timing in a separat pup-up window.

Limits on selected prameters

Limits can be given on any input parameter of the constraint function by giving the name of the parameter. For parameter names see the help of the used constraint function. Limits per optimization parameter can be given 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

The optimization parameters are identical to the input options of the Matlab built-in optimizer fminsearch.

'tolx': Minimum change of x when convergence reached, default value is $10^{-4}$ .
'tolfun': Minimum change of the $R$ value when convergence reached, default value is $10^{-5}$ .
'maxfunevals': Maximum number of function evaluations, default value is $10^7$ .
'maxiter': Maximum number of iterations, default value is $10^4$ .

Output Arguments

optm

Struct type variable with the following fields:

obj spinw object that contains the optimised magnetic structure.
x Optimised paramters in a row vector with $n_{par}$ number of elements.
fname Name of the contraint function.
xname Cell containing the name of the $x$ parameters with $n_{par}$ elements.
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.