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MAELAS code v2.0

Authors: P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut

Date: June 7, 2021

The main new features of version 2.0 are:

• New methodology derived from the magnetoelastic energy for direct calculation of magnetoelastic constants through a linear fitting of the energy versus strain. This new method can be executed by adding tag -mode 2 in the command line. The method implemented in version 1.0 (based on the quadratic fitting of the energy versus length) is also available in version 2.0, and it can be executed using tag -mode 1. The new method -mode 2 is more accurate than -mode 1, especially for non-cubic crystals.

• We fixed some issues related to the trigonal (I) symmetry in version 1.0:

  • The deformation gradient and measuring length direction for λ₁₂ in trigonal (I) symmetry has been changed.

  • We also corrected the theoretical relations between λ^γ,1, λ^γ,2 and λ₂₁ with the magnetoelastic and elastic constants in trigonal (I) symmetry.

More details about these updates can be found in the Manual, as well as in the preprint version of the manuscript for version 2.0

P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, “MAELAS 2.0: A new version of a computer program for the calculation of magneto-elastic properties”, 2021, arXiv:2106.03624

https://arxiv.org/abs/2106.03624

MAELAS code is a software to calculate anisotropic magnetostrictive coefficients and magnetoelastic constants up to second order. It generates required input files for VASP code to perform Density Functional Theory calculations, and it deduces:

-mode 1 = the value of magnetostrictive coefficients from the calculated energies given by VASP. If the elastic tensor is provided, then it can also calculate the magnetoelastic constants.

-mode 2 = the value of magnetolastic constants from the calculated energies given by VASP. If the elastic tensor is provided, then it can also calculate the magnetostrictive coefficients.

MAELAS can also be used with other DFT codes instead of VASP, after file conversion to VASP format files.

The MAELAS code requires to have Python3(>=3.6). For example, in Ubuntu Linux machine you can check the installed version of python3 by opening a terminal and typing

python3 --version

In case you need to install python3 in your machine, you can type

sudo apt-get update
sudo apt-get install python3

Note that in some HPC clusters you might need to load the Python module (ml Python).

To install MAELAS code, download and extract the .zip file, go to the folder that contains the file setup.py and type

python3 setup.py install --user

This procedure will also install all required dependecies automatically

pymatgen(>=2020.4.29)
scikit-learn(>=0.23.1)
pyfiglet(>=0.8.post0)
argparse(>=1.4.0)
numpy(>=1.18.4)
matplotlib(>=3.2.1)
scipy(>=1.4.1)
setuptools(>=40.8.0)

More available options for the installation can be found in the file INSTALL. By default, the executable file "maelas" is installed in the folder /home/$USER/.local/bin/ where $USER is the name of your user name folder. This folder should be included to the PATH variable by adding the following line in the file /home/$USER/.bashrc

export PATH=/home/$USER/.local/bin/:$PATH

Then you should close the terminal and open the terminal again.

If you need to install pip3 on Ubuntu Linux, then type

sudo apt-get update
sudo apt-get install python3-pip

Running MAELAS code consists in the following five steps.

If your initial POSCAR is not relaxed and you want to perform a cell relaxation before calculating the magnetostriction coefficients, then you can use MAELAS code to generate INCAR and KPOINTS files to relax the structure with VASP. To do so, in the terminal you should copy your initial POSCAR in the same folder where you want to generate the input files for VASP, and after going to this folder then type

maelas -r -i POSCAR0 -k 40

where tag -r indicates that you want to generate VASP files for cell relaxation, -i POSCAR0 is the input non-relaxed POSCAR file (you can name it whatever you want) and -k 40 is the length parameter that determines a regular mesh of k-points. It will generate 4 files: POSCAR, INCAR, KPOINTS, and vasp_jsub_rlx. Here, one still needs to copy manually the POTCAR file in this folder in order to have all required files for VASP run. The generated file vasp_jsub_rlx is a script to submit jobs in HPC facilities, one can specify some settings in this script by adding more tags in the command line. Note that the user might need to modify vasp_jsub_rlx (it is in PBS Pro format) depending on the cluster or local computer batch scheduling. For instance,

maelas -r -i POSCAR0 -k 40 -t 48 -c 24 -q qprod -a OPEN-00-00 -f /scratch/example_rlx

where -t 48 indicates that the number of maximum CPU hours for the VASP calculation is 48 hours, -c 24 means that the number of cores for the VASP calculation is 24, -q qprod set to production queue the type of queue in HPC facilities, -a OPEN-00-00 is the project identification number for running jobs in HPC facilities and -f /scratch/example_rlx is the folder where you want to run VASP calculations. All these data are included in the generated vasp_jsub_rlx file, so one can submit this VASP job immediately in HPC facilities by typing

qsub vasp_jsub_rlx

This procedure might be helpful for high-throughput routines. More options can be added in vasp_jsub_rlx file through the terminal command line, to see them just type

maelas -h

Note that generated INCAR and KPOINTS files contain standard setting for cell relaxation. The user might need to change these files in order to include more advanced settings.

In case your structure is already relaxed or you do not want to perform a cell relaxation, then you can skip this step and move to step 2.

It is recommended to verify the Magnetocrystalline Anisotropy Energy (MAE) before the calculation of magnetostriction coefficients. In order to test MAE, copy the relaxed POSCAR, POTCAR in the same folder where you want to generate the input files for VASP jobs. In the terminal, after going to this folder then type

maelas -m -i POSCAR_rlx -k 70 -s1 1 0 0 -s2 0 0 1

where -m indicates that you want to generate input VASP files for the calculation of MAE, -i POSCAR_rlx is the initial relaxed POSCAR file (you can name it whatever you want), -k 70 is the length parameter that determines a regular mesh of k-points, -s1 1 0 0 is the first spin direction to calculate MAE: s1x s1y s1z, while -s2 0 0 1 is the second spin direction to calculate MAE: s2x s2y s2z. It will generate the following files:

• POSCAR_0_0 (it is the same POSCAR as )
• INCAR_0_C (non-collinear calculation where C=1,2 is the spin orientation case)
• INCAR_std (collinear calculation to generate the WAVECAR and CHGCAR files to run non-collinear calculations)
• KPOINTS (file for the kpoint generation of VASP)
• vasp_mae, vasp_mae_jsub, and vasp_mae_0 (interconnected bash scripts to run VASP calculations automatically)
• vasp_mae_cp_oszicar (bash script to get the calculated OSZICAR_0_0_C files after VASP calculation is finished)

The generated files vasp_mae, vasp_mae_jsub and vasp_mae_0 are interconnected scripts to submit jobs in HPC facilities. One needs only to execute the file vasp_mae in order to run all VASP jobs automatically. Note that the user might need to modify vasp_mae_jsub (it is in PBS Pro format) depending on the cluster or local computer batch scheduling. You can specify some job settings in these scripts by adding more tags in the command line. For instance,

maelas -m -i POSCAR_rlx -k 70 -s1 1 0 0 -s2 0 0 1 -t 48 -c 24 -q qprod -a OPEN-00-00 -f /scratch/example_mag

where -t 48 indicates that the number of maximum CPU hours for the VASP calculation is 48 hours,-c 24 means that the number of cores for the VASP calculation is 24, -q qprod set to production queuethe type of queue in HPC facilities, -a OPEN-00-00 is the project identification number for running jobs in HPC facilities and -f /scratch/example_mag is the folder where you want to run VASP calculations. This procedure might be helpful for high-throughput routines. More options can be added in these script files through the terminal command line, to see them just type

maelas -h

Copy the relaxed POSCAR and POTCAR in the same folder where you want to generate the input files for VASP run. In the terminal, after going to this folder then type

maelas -g -mode 1 -i POSCAR_rlx -k 70 -n 7 -s 0.01

or

maelas -g -mode 2 -i POSCAR_rlx -k 70 -n 7 -s 0.01 

where -g jointly with -mode 1 indicates that you want to generate input VASP files for the calculation of anisotropic magnetostrictive coefficients, while -g jointly with -mode 2 indicates that you want to generate input VASP files for the calculation of anisotropic magnetoelastic constants. -i POSCAR_rlx is the initial relaxed POSCAR file (you can name it whatever you want), -k 70 is the length parameter that determines a regular mesh of k-points, -n 7 means that it will generate 7 distorted states for each magnetostrictive coefficient and -s 0.01 is the maximum value of the parameter s for the deformation gradient Fij(s) to generate the distorted POSCAR files. It will generate the following files:

• POSCAR_A_B (volume-conserving distorted cell where A=magnetostrictive coefficient (-mode 1) or magnetoelastic constant (-mode 2), B=1,...,n distorted cell for each magnetostrictive coefficient or magnetoelastic constant)
• INCAR_A_C (non-collinear calculation where A=magnetostrictive coefficient (-mode 1) or magnetoelastic constant (-mode 2), C=1,2 is the spin orientation case)
• INCAR_std (collinear calculation to generate the WAVECAR and CHGCAR files to run non-collinear calculations)
• KPOINTS
• vasp_maelas, vasp_jsub, and vasp_0 (interconnected bash scripts to run VASP calculations automatically)
• vasp_cp_oszicar (bash script to get calculated OSZICAR_A_B_C files after VASP calculation finish)

The generated files vasp_maelas, vasp_jsub and vasp_0 are interconnected scripts to submit jobs in HPC facilities, one can specify some job settings in these scripts by adding more tags in the command line. Note that the user might need to modify vasp_jsub (it is in PBS Pro format) depending on the cluster or local computer batch scheduling. For instance,

maelas -g -mode 1 -i POSCAR_rlx -k 70 -n 7 -s 0.01 -t 48 -c 24 -q qprod -a OPEN-00-00 -f /scratch/example_mag

where -t 48 indicates that the number of maximum CPU hours for the VASP calculation is 48 hours, -c 24 means that the number of cores for the VASP calculation is 24, -q qprod set to production queue the type of queue in HPC facilities, -a OPEN-00-00 is the project identification number for running jobs in HPC facilities and -f /scratch/example_mag is the folder where you want to run VASP calculations. This procedure might be helpful for high-throughput routines. More options can be added in these script files through the terminal command line, to see them just type

maelas -h

Note that generated INCAR_std, INCAR_A_C, and KPOINTS files contain standard setting for collinear and non-collinear calculations. The user can modify these files in order to add more advanced settings.

For each generated POSCAR_A_B one should run first a collinear calculation using INCAR_std and use the generated WAVECAR and CHGCAR files to run non-collinear calculations for each INCAR_A_C (C=1,2) using the same POSCAR_A_B. This procedure can be automatically done in HPC facilities just by running the generated bash script

./vasp_maelas

Note that the user might need to modify vasp_jsub depending on the cluster or local computer queuing system. This will launch independent jobs for each POSCAR_A_B. Each job will run 3 VASP calculations: a collinear one to generate WAVECAR and CHGCAR files, and two non-collinear for INCAR_A_1 and INCAR_A_2. The jobs will be executed in subfolders P_A_B inside the folder indicated by tag -f in the step 3.

Once all jobs are finished, then one can easily get calculated non-collinear OSZICAR files (needed in step 5), by running the bash script

./vasp_cp_oszicar

it will copy these OSZICAR files and name them as OSZICAR_A_B_C (C=1,2) in the same folder where this script is executed.

Finally, to derive the anisotropic magnetostrictive coefficients (-mode 1) or magnetoelastic constants (-mode 2), one needs to have in the same folder the following files:

• POSCAR_rlx (the relaxed POSCAR file used as input in step 3)
• POSCAR_A_B (distorted POSCAR generated in step 3)
• OSZICAR_A_B_C (non-collinear OSZICAR files calculated in step 4 for each POSCAR_A_B and INCAR_A_C)

Next, in the terminal go to this folder a type

maelas -d -mode 1 -i POSCAR_rlx -n 7

or

maelas -d -mode 2 -i POSCAR_rlx -n 7 -s 0.01

where -d jointly with -mode 1 means that you want to derive the anisotropic magnetostrictive coefficients from the calculated OSZICAR files, while -d jointly with -mode 2 will derive the anisotropic magnetoelastic constants from the calculated OSZICAR files. -i POSCAR_rlx is the relaxed POSCAR file used as input in step 3 (you can name it whatever you want) and -n 7 is the number of distorted states for each magnetostrictive coefficient (-mode 1) or magnetoelastic constant (-mode 2) used in step 3. For -mode 2 it is also necessary to write the maximum applied strain in step 3 -s 0.01.

It will derive and print the calculated spin-dependent magnetostrictive coefficients (-mode 1) or magnetoelastic constants (-mode 2) in the terminal. If you want to print it in a file (for example, results.out), then you can type

maelas -d -mode 1 -i POSCAR_rlx -n 7 > results.out

or

maelas -d -mode 2 -i POSCAR_rlx -n 7 -s 0.01 > results.out

In -mode 1, the energy values extracted from OSZICAR_A_B_C files are shown in generated files ene_A_C.dat and fit_ene_A_C.png. The energy difference between the two spin configurations for each magnetostrictive coefficient are shown in Fig. dE_A.png.

In -mode 2, the energy values extracted from OSZICAR_A_B_C files are shown in generated files ene_A_C.dat. The energy difference between the two spin configurations and linear fitting for each magnetoelastic constant are shown in Fig. dE_A.png.

If the elastic tensor is provided as input, then MAELAS can also calculate the magnetoelastic constants -mode 1 or magnetostrictive coefficients -mode 2. To do so, one needs to add tags -b and -e with the name of the file containing the elastic tensor with the same format and units (GPa), as written by AELAS code (file ELADAT). You can check this format in the Examples folder. Hence, you could type

maelas -d -mode 1 -i POSCAR_rlx -n 7 -b -e ELADAT

or

maelas -d -mode 2 -i POSCAR_rlx -n 7 -s 0.01 -b -e ELADAT

where ELADAT is the name of the file (it could be whatever name you want) with the elastic tensor data.

Step 1: Cell relaxation

maelas -r -i POSCAR0 -k 40
qsub vasp_jsub_rlx

Step 2: Test MAE

maelas -m -i POSCAR_rlx -k 70 -s1 1 0 0 -s2 0 0 1
./vasp_mae
./vasp_mae_cp_oszicar

Step 3: Generate VASP inputs for calculation of magnetostrictive coefficients

maelas -g -mode 1 -i POSCAR_rlx -k 70 -n 7 -s 0.01

Step 4: Run VASP calculations

./vasp_maelas
./vasp_cp_oszicar

Step 5a: Derivation of anisotropic magnetostrictive coefficients

maelas -d -mode 1 -i POSCAR_rlx -n 7

Step 5b: Derivation of anisotropic magnetostrictive coefficients and magnetoelastic constants

maelas -d -mode 1 -i POSCAR_rlx -n 7 -b -e ELADAT  

Step 1: Cell relaxation

maelas -r -i POSCAR0 -k 40
qsub vasp_jsub_rlx

Step 2: Test MAE

maelas -m -i POSCAR_rlx -k 70 -s1 1 0 0 -s2 0 0 1
./vasp_mae
./vasp_mae_cp_oszicar

Step 3: Generate VASP inputs for calculation of magnetoelastic constants

maelas -g -mode 2 -i POSCAR_rlx -k 70 -n 7 -s 0.01

Step 4: Run VASP calculations

./vasp_maelas
./vasp_cp_oszicar

Step 5a: Derivation of anisotropic magnetoelastic constants

maelas -d -mode 2 -i POSCAR_rlx -n 7 -s 0.01

Step 5b: Derivation of anisotropic magnetoelastic constants and magnetostrictive coefficients

maelas -d -mode 2 -i POSCAR_rlx -n 7 -s 0.01 -b -e ELADAT  

User can see all possible optional arguments typing

maelas -h

Doing so, it will print the following text in the terminal:

usage: maelas.py [-h] [-i POS] [-n NDIST] [-s STRAIN] [-k KP] [-g] [-d] [-r]
                 [-b] [-e ELAS] [-c CORE] [-t TIME] [-f VASP_FOLD] [-m MPI]
                 [-a P_ID] [-l LOAD_MODULE] [-q QUEUE]

MAELAS code v1.0

optional arguments:

  -h, --help      Show this help message and exit
  
  -mode MODE            -mode 1: Scheme for the direct calculation of the
                        magnetostrictive coefficients. -mode 2: Scheme for the
                        direct calculation of the magnetoelastic constants.
                        Mode 2 is more accurate for non-cubic symmetries
                        (default: 2)
                        
  -i POS                Name of the initial non-distorted POSCAR file
                        (default: POSCAR)
                        
  -n NDIST              Number of distorted states for the direct calculation
                        for each magnetostriction coefficient (-mode 1) or
                        magnetoelastic contant (-mode 2)(default: 7)
                        
  -s STRAIN             Maximum value of the parameter s for the deformation
                        gradient Fij(s) to generate the distorted POSCAR files
                        (default: 0.01)
                        
  -k KP                 VASP automatic k-point mesh generation to create the
                        KPOINTS file (default: 60)
                        
  -g                    Generation of required VASP files for the direct
                        calculation of magnetostriction coefficients (-mode 1)
                        or magnetoelastic constants (-mode 2). Notation of the
                        generated output files: POSCAR_A_B (distorted cell
                        where A=magnetostriction coefficient (-mode 1) or
                        magnetoelastic constant (-mode 2), B=distorted cell),
                        INCAR_A_C (non-collinear calculation where C=spin
                        orientation case), INCAR_std (collinear calculation).
                        How to run the VASP calculations: For each generated
                        POSCAR_A_B one should run first a collinear
                        calculation using INCAR_std and use the generated
                        WAVECAR and CHGCAR files to run non-collinear
                        calculations for each INCAR_A_C using the same
                        POSCAR_A_B. It also generates bash scripts to run VASP
                        calculations easily (vasp_maelas, vasp_jsub, vasp_0)
                        and to get calculated OSZICAR_A_B_C files
                        (vasp_cp_oszicar)
                        
  -d                    Derivation of magnetostriction coefficients (-mode 1)
                        or magnetoelastic contants (-mode 2) from the energy
                        written in the OSZICAR files. WARNING!: OSZICAR files
                        must be in the same folder where you run MAELAS using
                        the notation OSZICAR_A_B_C obtained for POSCAR_A_B and
                        INCAR_A_C. Distorted POSCAR files (POSCAR_A_B) must be
                        in this folder too (jointly with the initial non-
                        distorted POSCAR which should be specified using tag
                        -i). Specify the number of distorted states to be
                        considered in the calculation of magnetostriction
                        coefficients using tag -n, and the same maximum
                        applied strain (tag -s) used in the generation of VASP
                        input files. Energy values extracted from
                        OSZICAR_A_B_C files are shown in files ene_A_C.dat and
                        fit_ene_A_C.png. The energy difference between the two
                        spin configurations for each magnetostriction mode are
                        shown in Figs. dE_A.png
                        
  -r                    Generation of required VASP files for the cell
                        relaxation
                        
  -m                    Generation of required VASP files to test MAE
  
  -s1 SPIN1 SPIN1 SPIN1
                        First spin direction to calculate MAE: s1x s1y s1z
                        
  -s2 SPIN2 SPIN2 SPIN2
                        Second spin direction to calculate MAE: s2x s2y s2z
                        
  -b                    Indirect calculation of the magnetoelastic constants
                        from the calculated magnetostriction coefficients and
                        provided elastic tensor (-mode 1) or indirect
                        calculation of the magnetostrictive coefficients from
                        the calculated magnetoelastic constants and provided
                        elastic tensor (-mode 2). For this option the tag -d
                        must be included as well as tag -e with the name of
                        the elastic tensor file
                        
  -e ELAS               File with the elastic tensor data in the same format
                        and units (GPa) as it is written by ELAS code (file
                        ELADAT). You can check this format in the Examples
                        folder
                        
  -sp SYMPRE            Tolerance for symmetry finding (default: 0.01)
  
  -sa SYMANG            Angle tolerance for symmetry finding (default: 5.0)
  
  -sg SG0               Space group number 1-230. If it is equal to 0, then it
                        will be determined by a symmetry analysis (default: 0)
                        
  -c CORE               Number of cores for the VASP calculation (default: 24)
  
  -t TIME               Number of maximum CPU hours for the VASP calculation
                        (default: 48)
                        
  -f VASP_FOLD          Folder where you will run VASP calculations (default:
                        /scratch)
  
  -mp MPI               Command for mpi run of VASP (default: mpiexec.hydra)
  
  -a P_ID               Project id for running jobs in HPC facilities
                        (default: OPEN-X-X)
                        
  -l LOAD_MODULE        Module of VASP that should be loaded (default:
                        VASP/5.4.4-intel-2017c-mkl=cluster)
  
  -q QUEUE              Type of queue to be used for VASP calculations in HPC
                        facilities (default: qprod)

MAELAS has been designed to read and write files for VASP code automatically. However, it is possible to use MAELAS with other DFT codes instead of VASP, after file conversion to VASP format files. Although, this process might require some extra work for the user. Namely, converting initial and distorted POSCAR files into the other DFT code format, reading the spin direction of each state from INCAR_A_C files (variable SAXIS) and write the calculated energies in a OSZICAR-like file (called OSZICAR_A_B_C) on the penultimate line and third column with same format as in VASP (this is the place where MAELAS reads the energy value of each OSZICAR_A_B_C file). See the Manual for more details.

In the folder Examples/LAMMPS we provide an example of an interface between MAELAS and program LAMMPS (classical spin-molecular dynamics).

Current version supports the following crystal systems:

Cubic (I) (space groups 207-230)

Hexagonal (I) (space groups 177-194)

Trigonal (I) (space groups 149-167)

Tetragonal (I) (space groups 89-142)

Orthorhombic (space groups 16-74)

The crystal systems not supported by MAELAS might be included in the new versions of the code.

We have also developed an online visualization tool called MAELASviewer that is available at

https://maelasviewer.herokuapp.com

This interactive applet shows the magnetostriction for the supported crystal systems of MAELAS. Users can simulate the Joule and Wiedemann effects.

Published version 1.0:

P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, “MAELAS: MAgneto-ELAStic properties calculation via computational high-throughput approach”, Comput. Phys. Commun. 264, 107964 (2021).

https://doi.org/10.1016/j.cpc.2021.107964

Preprint version 1.0:

P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, “MAELAS: MAgneto-ELAStic properties calculation via computational high-throughput approach”, 2020, arXiv:2009.01638

https://arxiv.org/abs/2009.01638

Preprint version 2.0:

P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, “MAELAS 2.0: A new version of a computer program for the calculation of magneto-elastic properties”, 2021, arXiv:2106.03624

https://arxiv.org/abs/2106.03624