magnopy-optimize-sd

This page explains how to use optimize spin direction via numerical minimization. See docs for magnopy-optimize-sd for full list of supported arguments. On this page we give examples of how to use the script and text and files that it can produce.

Spin Hamiltonian and its source

This script works with the spin Hamiltonian that is coming from some third-party software. At the moment magnopy supports TB2J and GROGU.

Hint

There is a number of ways to use this script with the hand-made Hamiltonian:

• Prepare the file that mimics the format of TB2J.

• Prepare the file that mimics the GROGU file format.

• Prepare the spin Hamiltonian programmatically and use the scenario of this command-line script from within your python script: magnopy.scenarios.optimize_sd().

Two parameters are required

• Source of the spin Hamiltonian (--spinham-source);

• Path to the file with the spin Hamiltonian (--spinham-filename)

For example, if "ferro-easy-axis.txt" is a file with the spin Hamiltonian and the source of the file is GROGU, then you can run the script as

Input files

• ferro-easy-axis.txt

magnopy-optimize-sd --spinham-source GROGU --spinham-filename ferro-easy-axis.txt

Output to the console

     ███╗   ███╗  █████╗   ██████╗  ███╗   ██╗  ██████╗  ██████╗  ██╗   ██╗     
     ████╗ ████║ ██╔══██╗ ██╔════╝  ████╗  ██║ ██╔═══██╗ ██╔══██╗ ╚██╗ ██╔╝     
     ██╔████╔██║ ███████║ ██║  ███╗ ██╔██╗ ██║ ██║   ██║ ██████╔╝  ╚████╔╝      
     ██║╚██╔╝██║ ██╔══██║ ██║  ╚██║ ██║╚██╗██║ ██║   ██║ ██╔═══╝    ╚██╔╝       
     ██║ ╚═╝ ██║ ██║  ██║ ╚██████╔╝ ██║ ╚████║ ╚██████╔╝ ██║         ██║        
     ╚═╝     ╚═╝ ╚═╝  ╚═╝  ╚═════╝  ╚═╝  ╚═══╝  ╚═════╝  ╚═╝         ╚═╝        
                           Version: 0.4.3                       ▄   ▄           
                     Documentation: magnopy.org                 █▀█▀█           
                    Release date: 9 January 2026                █▄█▄█           
                         License: GNU GPLv3                      ███   ▄▄       
               Copyright (C) 2023-2026  Magnopy Team             ████ █  █      
                                                                 ████    █      
              Generated on 9 January 2026 at 17:39:45            ▀▀▀▀▀▀▀▀       

=================================== Comment ====================================

Executed the command

  /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/envs/latest/bin/magnopy-optimize-sd --spinham-source GROGU --spinham-filename /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt -of /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results

which resulted in argument values

<< spinham_source       : GROGU
<< spinham_filename     : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt
<< energy_tolerance     : 1e-05
<< torque_tolerance     : 1e-05
<< supercell            : (1, 1, 1)
<< magnetic_field       : None
<< output_folder        : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results
<< spin_values          : None
<< no_html              : False
<< hide_personal_data   : False
<< make_sd_image        : None

Parameters are loaded from "GROGU", source file
<<< /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt

=========================== Optimization parameters ============================

Energy tolerance      : 1.00000e-05 meV
Torque tolerance      : 1.00000e-05
Magnetic flux density : None
Supercell             : 1 x 1 x 1 (original unit cell of the Hamiltonian)

Spin directions of the initial guess are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results/INITIAL_GUESS.txt

============================== Start optimization ==============================

─────┬─────────────┬─────────────┬─────────────
step │     E_0     │  delta E_0  │ max torque 
─────┴─────────────┴─────────────┴─────────────
1       -3.0994105     0.0603970     0.0153107
2       -3.0999999     0.0005894     0.0001748
3       -3.1000000     0.0000001     0.0000007
───────────────────────────────────────────────
Optimization is done.

==================================== Output ====================================

Classic energy of optimized state (E_0 = -3.100 meV) is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results/E_0.txt

Optimized spin directions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results/SPIN_DIRECTIONS.txt

Spin positions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results/SPIN_POSITIONS.txt

Image of spin directions is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/1/magnopy-results/SPIN_DIRECTIONS.html

=================================== Finished ===================================

Created files

• E_0.txt

• INITIAL_GUESS.txt

• SPIN_DIRECTIONS.txt

• SPIN_DIRECTIONS.html

• SPIN_POSITIONS.txt

Minimization domain

By default magnopy vary spins of the original unit cell. However, potential local or global minima that span several unit cells can be missed. To address this issue, magnopy offers an option of minimization on the supercell.

Supercell is defined by a number of the original unit cell's repetitions along each of its three lattice vectors (--superell). For example, if you want to minimize on the \(3\times7\times2\) supercell use the command

Input files

• ferro-easy-axis.txt

magnopy-optimize-sd --supercell 3 7 2 --spinham-source GROGU --spinham-filename ferro-easy-axis.txt

Output to the console

     ███╗   ███╗  █████╗   ██████╗  ███╗   ██╗  ██████╗  ██████╗  ██╗   ██╗     
     ████╗ ████║ ██╔══██╗ ██╔════╝  ████╗  ██║ ██╔═══██╗ ██╔══██╗ ╚██╗ ██╔╝     
     ██╔████╔██║ ███████║ ██║  ███╗ ██╔██╗ ██║ ██║   ██║ ██████╔╝  ╚████╔╝      
     ██║╚██╔╝██║ ██╔══██║ ██║  ╚██║ ██║╚██╗██║ ██║   ██║ ██╔═══╝    ╚██╔╝       
     ██║ ╚═╝ ██║ ██║  ██║ ╚██████╔╝ ██║ ╚████║ ╚██████╔╝ ██║         ██║        
     ╚═╝     ╚═╝ ╚═╝  ╚═╝  ╚═════╝  ╚═╝  ╚═══╝  ╚═════╝  ╚═╝         ╚═╝        
                           Version: 0.4.3                       ▄   ▄           
                     Documentation: magnopy.org                 █▀█▀█           
                    Release date: 9 January 2026                █▄█▄█           
                         License: GNU GPLv3                      ███   ▄▄       
               Copyright (C) 2023-2026  Magnopy Team             ████ █  █      
                                                                 ████    █      
              Generated on 9 January 2026 at 17:39:46            ▀▀▀▀▀▀▀▀       

=================================== Comment ====================================

Executed the command

  /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/envs/latest/bin/magnopy-optimize-sd --supercell 3 7 2 --spinham-source GROGU --spinham-filename /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt -of /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results

which resulted in argument values

<< spinham_source       : GROGU
<< spinham_filename     : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt
<< energy_tolerance     : 1e-05
<< torque_tolerance     : 1e-05
<< supercell            : [3, 7, 2]
<< magnetic_field       : None
<< output_folder        : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results
<< spin_values          : None
<< no_html              : False
<< hide_personal_data   : False
<< make_sd_image        : None

Parameters are loaded from "GROGU", source file
<<< /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt

=========================== Optimization parameters ============================

Energy tolerance      : 1.00000e-05 meV
Torque tolerance      : 1.00000e-05
Magnetic flux density : None
Supercell             : 3 x 7 x 2 (constructed supercell of the Hamiltonian)

Spin directions of the initial guess are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results/INITIAL_GUESS.txt

============================== Start optimization ==============================

─────┬─────────────┬─────────────┬─────────────
step │     E_0     │  delta E_0  │ max torque 
─────┴─────────────┴─────────────┴─────────────
1       -7.0948552    13.5571534     4.5401645
2      -54.2547892    47.1599340     3.9596976
3      -80.7719704    26.5171812     4.3508158
4      -98.6324990    17.8605286     5.1036858
5      -119.5294603    20.8969613     2.2223784
6      -123.6278088     4.0983485     1.1034898
7      -125.2687697     1.6409608     1.2803311
8      -127.1926346     1.9238649     1.2261236
9      -127.5383391     0.3457045     1.4649430
10     -128.5645058     1.0261667     0.7985383
11     -128.7302363     0.1657305     0.6065598
12     -129.0640431     0.3338068     0.3530385
13     -129.2056319     0.1415888     0.4356865
14     -129.4629634     0.2573315     0.3142072
15     -130.0123698     0.5494064     0.6639041
16     -130.0946101     0.0822403     0.3494989
17     -130.1543362     0.0597261     0.2544755
18     -130.1772714     0.0229352     0.1843818
19     -130.1918851     0.0146137     0.1327144
20     -130.1939105     0.0020254     0.0841144
21     -130.1986200     0.0047094     0.0390206
22     -130.1996041     0.0009841     0.0177790
23     -130.1997777     0.0001737     0.0152045
24     -130.1999204     0.0001427     0.0114347
25     -130.1999636     0.0000432     0.0067197
26     -130.1999916     0.0000280     0.0027828
27     -130.1999981     0.0000065     0.0011320
28     -130.1999990     0.0000009     0.0011093
29     -130.1999997     0.0000007     0.0006140
30     -130.1999998     0.0000001     0.0004501
31     -130.1999999     0.0000001     0.0003090
32     -130.1999999     0.0000000     0.0001728
33     -130.2000000     0.0000000     0.0001123
34     -130.2000000     0.0000000     0.0000818
35     -130.2000000     0.0000000     0.0000469
36     -130.2000000     0.0000000     0.0000685
37     -130.2000000     0.0000000     0.0000553
38     -130.2000000     0.0000000     0.0000467
39     -130.2000000     0.0000000     0.0000417
40     -130.2000000     0.0000000     0.0000224
41     -130.2000000     0.0000000     0.0000217
42     -130.2000000     0.0000000     0.0000076
───────────────────────────────────────────────
Optimization is done.

==================================== Output ====================================

Classic energy of optimized state (E_0 = -130.200 meV) is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results/E_0.txt

Optimized spin directions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results/SPIN_DIRECTIONS.txt

Spin positions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results/SPIN_POSITIONS.txt

Image of spin directions is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/2/magnopy-results/SPIN_DIRECTIONS.html

=================================== Finished ===================================

Created files

• E_0.txt

• INITIAL_GUESS.txt

• SPIN_DIRECTIONS.txt

• SPIN_DIRECTIONS.html

• SPIN_POSITIONS.txt

Then every spin in the \(3\times7\times2\) supercell is treated as an individual variable. Note, that the computational cost of minimization will grow with the size of the supercell.

Accuracy or tolerance conditions

Numerical optimization can continues indefinitely, improving accuracy of some target value with each step. In reality an algorithm should reach some tolerance values in the finite amount of steps.

The minimization algorithm implemented in magnopy [1] traces two values:

• --energy-tolerance

  Absolute value of the difference in total energy between two consecutive steps of the minimization.

• --torque-tolerance

  Maximum (among all spins of the unit cell or supercell) value of the torque vector.

An algorithm stops when both tolerance parameters are reached. The default values should lead to the reasonable results in most of the cases.

However, if you want to increase accuracy of one or both parameters, then use the command

Input files

• ferro-easy-axis.txt

magnopy-optimize-sd --energy-tolerance 0.000001 --torque-tolerance 0.001 --spinham-source GROGU --spinham-filename ferro-easy-axis.txt

Output to the console

     ███╗   ███╗  █████╗   ██████╗  ███╗   ██╗  ██████╗  ██████╗  ██╗   ██╗     
     ████╗ ████║ ██╔══██╗ ██╔════╝  ████╗  ██║ ██╔═══██╗ ██╔══██╗ ╚██╗ ██╔╝     
     ██╔████╔██║ ███████║ ██║  ███╗ ██╔██╗ ██║ ██║   ██║ ██████╔╝  ╚████╔╝      
     ██║╚██╔╝██║ ██╔══██║ ██║  ╚██║ ██║╚██╗██║ ██║   ██║ ██╔═══╝    ╚██╔╝       
     ██║ ╚═╝ ██║ ██║  ██║ ╚██████╔╝ ██║ ╚████║ ╚██████╔╝ ██║         ██║        
     ╚═╝     ╚═╝ ╚═╝  ╚═╝  ╚═════╝  ╚═╝  ╚═══╝  ╚═════╝  ╚═╝         ╚═╝        
                           Version: 0.4.3                       ▄   ▄           
                     Documentation: magnopy.org                 █▀█▀█           
                    Release date: 9 January 2026                █▄█▄█           
                         License: GNU GPLv3                      ███   ▄▄       
               Copyright (C) 2023-2026  Magnopy Team             ████ █  █      
                                                                 ████    █      
              Generated on 9 January 2026 at 17:39:47            ▀▀▀▀▀▀▀▀       

=================================== Comment ====================================

Executed the command

  /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/envs/latest/bin/magnopy-optimize-sd --energy-tolerance 0.000001 --torque-tolerance 0.001 --spinham-source GROGU --spinham-filename /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt -of /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results

which resulted in argument values

<< spinham_source       : GROGU
<< spinham_filename     : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt
<< energy_tolerance     : 1e-06
<< torque_tolerance     : 0.001
<< supercell            : (1, 1, 1)
<< magnetic_field       : None
<< output_folder        : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results
<< spin_values          : None
<< no_html              : False
<< hide_personal_data   : False
<< make_sd_image        : None

Parameters are loaded from "GROGU", source file
<<< /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt

=========================== Optimization parameters ============================

Energy tolerance      : 1.00000e-06 meV
Torque tolerance      : 1.00000e-03
Magnetic flux density : None
Supercell             : 1 x 1 x 1 (original unit cell of the Hamiltonian)

Spin directions of the initial guess are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results/INITIAL_GUESS.txt

============================== Start optimization ==============================

─────┬─────────────┬──────────────┬────────────
step │     E_0     │  delta E_0   │ max torque
─────┴─────────────┴──────────────┴────────────
1       -3.0999691     0.09856255     0.003513
2       -3.1000000     0.00003082     0.000136
3       -3.1000000     0.00000005     0.000000
───────────────────────────────────────────────
Optimization is done.

==================================== Output ====================================

Classic energy of optimized state (E_0 = -3.100 meV) is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results/E_0.txt

Optimized spin directions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results/SPIN_DIRECTIONS.txt

Spin positions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results/SPIN_POSITIONS.txt

Image of spin directions is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/3/magnopy-results/SPIN_DIRECTIONS.html

=================================== Finished ===================================

Created files

• E_0.txt

• INITIAL_GUESS.txt

• SPIN_DIRECTIONS.txt

• SPIN_DIRECTIONS.html

• SPIN_POSITIONS.txt

External magnetic field

File with the spin Hamiltonian specifies interaction parameters that are intrinsic to the material.

In order to add external effects, for instance an external magnetic field one can use --magnetic-field parameter.

This parameter expects three numbers, that specify three Cartesian components of the external magnetic field (magnetic flux density, B). Values are interpreted in Tesla.

For example, use the command

Input files

• ferro-easy-axis.txt

magnopy-optimize-sd --magnetic-field 1.7112 1.7112 0 --spinham-source GROGU --spinham-filename ferro-easy-axis.txt

Output to the console

     ███╗   ███╗  █████╗   ██████╗  ███╗   ██╗  ██████╗  ██████╗  ██╗   ██╗     
     ████╗ ████║ ██╔══██╗ ██╔════╝  ████╗  ██║ ██╔═══██╗ ██╔══██╗ ╚██╗ ██╔╝     
     ██╔████╔██║ ███████║ ██║  ███╗ ██╔██╗ ██║ ██║   ██║ ██████╔╝  ╚████╔╝      
     ██║╚██╔╝██║ ██╔══██║ ██║  ╚██║ ██║╚██╗██║ ██║   ██║ ██╔═══╝    ╚██╔╝       
     ██║ ╚═╝ ██║ ██║  ██║ ╚██████╔╝ ██║ ╚████║ ╚██████╔╝ ██║         ██║        
     ╚═╝     ╚═╝ ╚═╝  ╚═╝  ╚═════╝  ╚═╝  ╚═══╝  ╚═════╝  ╚═╝         ╚═╝        
                           Version: 0.4.3                       ▄   ▄           
                     Documentation: magnopy.org                 █▀█▀█           
                    Release date: 9 January 2026                █▄█▄█           
                         License: GNU GPLv3                      ███   ▄▄       
               Copyright (C) 2023-2026  Magnopy Team             ████ █  █      
                                                                 ████    █      
              Generated on 9 January 2026 at 17:39:48            ▀▀▀▀▀▀▀▀       

=================================== Comment ====================================

Executed the command

  /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/envs/latest/bin/magnopy-optimize-sd --magnetic-field 1.7112 1.7112 0 --spinham-source GROGU --spinham-filename /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt -of /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results

which resulted in argument values

<< spinham_source       : GROGU
<< spinham_filename     : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt
<< energy_tolerance     : 1e-05
<< torque_tolerance     : 1e-05
<< supercell            : (1, 1, 1)
<< magnetic_field       : [1.7112, 1.7112, 0.0]
<< output_folder        : /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results
<< spin_values          : None
<< no_html              : False
<< hide_personal_data   : False
<< make_sd_image        : None

Parameters are loaded from "GROGU", source file
<<< /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/resources/ferro-easy-axis.txt

=========================== Optimization parameters ============================

Energy tolerance      : 1.00000e-05 meV
Torque tolerance      : 1.00000e-05
Magnetic flux density : |1.71120, 1.71120, 0.00000| = 2.42000 Tesla
Supercell             : 1 x 1 x 1 (original unit cell of the Hamiltonian)

Spin directions of the initial guess are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results/INITIAL_GUESS.txt

============================== Start optimization ==============================

─────┬─────────────┬─────────────┬─────────────
step │     E_0     │  delta E_0  │ max torque 
─────┴─────────────┴─────────────┴─────────────
1       -3.2454556     0.3209259     0.1034110
2       -3.2784198     0.0329641     0.0173726
3       -3.2798659     0.0014461     0.0072023
4       -3.2801417     0.0002758     0.0030160
5       -3.2801564     0.0000147     0.0008648
6       -3.2801579     0.0000015     0.0000042
───────────────────────────────────────────────
Optimization is done.

==================================== Output ====================================

Classic energy of optimized state (E_0 = -3.280 meV) is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results/E_0.txt

Optimized spin directions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results/SPIN_DIRECTIONS.txt

Spin positions are saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results/SPIN_POSITIONS.txt

Image of spin directions is saved in file
>>> /home/docs/checkouts/readthedocs.org/user_builds/magnopy-tutorials/checkouts/latest/docs/source/master-tutorial/2_black-box/prompt-run_plot-1-optimize-sd/4/magnopy-results/SPIN_DIRECTIONS.html

=================================== Finished ===================================

Created files

• E_0.txt

• INITIAL_GUESS.txt

• SPIN_DIRECTIONS.txt

• SPIN_DIRECTIONS.html

• SPIN_POSITIONS.txt

to add magnetic field of \(2.42\) Tesla along the direction \((1, 1, 0)\) (i.e. in the \(xy\) plane, right in between the \(x\) and \(y\) axis).

References

[1]

Ivanov, A.V., Uzdin, V.M. and Jónsson, H., 2021. Fast and robust algorithm for energy minimization of spin systems applied in an analysis of high temperature spin configurations in terms of skyrmion density. Computer Physics Communications, 260, p.107749.