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+
+
+
+ 20240815151159-a9e5c8ebdb8d3cb7f7704bcd1d686fd13113ef8d
+ 20240815151159
+
+ JOSS Admin
+ admin@theoj.org
+
+ The Open Journal
+
+
+
+
+ Journal of Open Source Software
+ JOSS
+ 2475-9066
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+ 10.21105/joss
+ https://joss.theoj.org
+
+
+
+
+ 08
+ 2024
+
+
+ 9
+
+ 100
+
+
+
+ mamonca: magnetic Monte Carlo code
+
+
+
+ Osamu
+ Waseda
+ https://orcid.org/0000-0002-1677-4057
+
+
+ Tilmann
+ Hickel
+ https://orcid.org/0000-0003-0698-4891
+
+
+ Jörg
+ Neugebauer
+ https://orcid.org/0000-0002-7903-2472
+
+
+
+ 08
+ 15
+ 2024
+
+
+ 6194
+
+
+ 10.21105/joss.06194
+
+
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+
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+ Software archive
+ 10.5281/zenodo.13309692
+
+
+ GitHub review issue
+ https://github.com/openjournals/joss-reviews/issues/6194
+
+
+
+ 10.21105/joss.06194
+ https://joss.theoj.org/papers/10.21105/joss.06194
+
+
+ https://joss.theoj.org/papers/10.21105/joss.06194.pdf
+
+
+
+
+
+ Uppsala atomistic spin dynamics user
+guide
+ Hellsvik
+ 2011
+ Hellsvik, J., Skubic, B., &
+Taroni, A. (2011). Uppsala atomistic spin dynamics user
+guide.
+
+
+ Atomistic spin model simulations of magnetic
+nanomaterials
+ Evans
+ Journal of Physics: Condensed
+Matter
+ 10
+ 26
+ 10.1088/0953-8984/26/10/103202
+ 2014
+ Evans, R. F., Fan, W. J., Chureemart,
+P., Ostler, T. A., Ellis, M. O., & Chantrell, R. W. (2014).
+Atomistic spin model simulations of magnetic nanomaterials. Journal of
+Physics: Condensed Matter, 26(10), 103202.
+https://doi.org/10.1088/0953-8984/26/10/103202
+
+
+ TB2J: A python package for computing magnetic
+interaction parameters
+ He
+ Computer Physics
+Communications
+ 264
+ 10.1016/j.cpc.2021.107938
+ 2021
+ He, X., Helbig, N., Verstraete, M.
+J., & Bousquet, E. (2021). TB2J: A python package for computing
+magnetic interaction parameters. Computer Physics Communications, 264,
+107938.
+https://doi.org/10.1016/j.cpc.2021.107938
+
+
+ Quantum lattice model solver
+h\Phi
+ Kawamura
+ Computer Physics
+Communications
+ 217
+ 10.1016/j.cpc.2017.04.006
+ 2017
+ Kawamura, M., Yoshimi, K., Misawa,
+T., Yamaji, Y., Todo, S., & Kawashima, N. (2017). Quantum lattice
+model solver h\Phi. Computer Physics Communications, 217, 180–192.
+https://doi.org/10.1016/j.cpc.2017.04.006
+
+
+ Le phénomène magnétocalorique
+ Weiss
+ J. Phys. Theor. Appl.
+ 1
+ 7
+ 10.1051/jphystap:019170070010300
+ 1917
+ Weiss, P., & Piccard, A. (1917).
+Le phénomène magnétocalorique. J. Phys. Theor. Appl., 7(1), 103–109.
+https://doi.org/10.1051/jphystap:019170070010300
+
+
+ Ab initio calculation of phase boundaries in
+iron along the bcc-fcc transformation path and magnetism of iron
+overlayers
+ Friák
+ Physical Review B
+ 5
+ 63
+ 10.1103/PhysRevB.63.052405
+ 2001
+ Friák, M., Šob, M., & Vitek, V.
+(2001). Ab initio calculation of phase boundaries in iron along the
+bcc-fcc transformation path and magnetism of iron overlayers. Physical
+Review B, 63(5), 052405.
+https://doi.org/10.1103/PhysRevB.63.052405
+
+
+ The ALPS project release 2.0: Open source
+software for strongly correlated systems
+ Bauer
+ Journal of Statistical Mechanics: Theory and
+Experiment
+ 05
+ 2011
+ 10.1088/1742-5468/2011/05/P05001
+ 2011
+ Bauer, B., Carr, L., Evertz, H. G.,
+Feiguin, A., Freire, J., Fuchs, S., Gamper, L., Gukelberger, J., Gull,
+E., Guertler, S., & others. (2011). The ALPS project release 2.0:
+Open source software for strongly correlated systems. Journal of
+Statistical Mechanics: Theory and Experiment, 2011(05), P05001.
+https://doi.org/10.1088/1742-5468/2011/05/P05001
+
+
+ Understanding molecular simulation: From
+algorithms to applications
+ Frenkel
+ 2023
+ Frenkel, D., & Smit, B. (2023).
+Understanding molecular simulation: From algorithms to applications.
+Elsevier.
+
+
+ “Coarse” stability and bifurcation analysis
+using time-steppers: A reaction-diffusion example
+ Theodoropoulos
+ Proceedings of the National Academy of
+Sciences
+ 18
+ 97
+ 10.1073/pnas.97.18.9840
+ 2000
+ Theodoropoulos, C., Qian, Y.-H.,
+& Kevrekidis, I. G. (2000). “Coarse” stability and bifurcation
+analysis using time-steppers: A reaction-diffusion example. Proceedings
+of the National Academy of Sciences, 97(18), 9840–9843.
+https://doi.org/10.1073/pnas.97.18.9840
+
+
+ The atomic simulation environment—a python
+library for working with atoms
+ Larsen
+ Journal of Physics: Condensed
+Matter
+ 27
+ 29
+ 10.1088/1361-648X/aa680e
+ 2017
+ Larsen, A. H., Mortensen, J. J.,
+Blomqvist, J., Castelli, I. E., Christensen, R., Dułak, M., Friis, J.,
+Groves, M. N., Hammer, B., Hargus, C., & others. (2017). The atomic
+simulation environment—a python library for working with atoms. Journal
+of Physics: Condensed Matter, 29(27), 273002.
+https://doi.org/10.1088/1361-648X/aa680e
+
+
+ Pyiron: An integrated development environment
+for computational materials science
+ Janssen
+ Computational Materials
+Science
+ 163
+ 10.1016/j.commatsci.2018.07.043
+ 2019
+ Janssen, J., Surendralal, S.,
+Lysogorskiy, Y., Todorova, M., Hickel, T., Drautz, R., & Neugebauer,
+J. (2019). Pyiron: An integrated development environment for
+computational materials science. Computational Materials Science, 163,
+24–36.
+https://doi.org/10.1016/j.commatsci.2018.07.043
+
+
+ Ab initio based models for
+temperature-dependent magnetochemical interplay in bcc fe-mn
+alloys
+ Schneider
+ Physical Review B
+ 2
+ 103
+ 10.1103/PhysRevB.103.024421
+ 2021
+ Schneider, A., Fu, C.-C., Waseda, O.,
+Barreteau, C., & Hickel, T. (2021). Ab initio based models for
+temperature-dependent magnetochemical interplay in bcc fe-mn alloys.
+Physical Review B, 103(2), 024421.
+https://doi.org/10.1103/PhysRevB.103.024421
+
+
+
+
+
+
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+
+
+
+
+
+
+
+Journal of Open Source Software
+JOSS
+
+2475-9066
+
+Open Journals
+
+
+
+6194
+10.21105/joss.06194
+
+mamonca: magnetic Monte Carlo code
+
+
+
+https://orcid.org/0000-0002-1677-4057
+
+Waseda
+Osamu
+
+
+*
+
+
+https://orcid.org/0000-0003-0698-4891
+
+Hickel
+Tilmann
+
+
+
+
+https://orcid.org/0000-0002-7903-2472
+
+Neugebauer
+Jörg
+
+
+
+
+
+Max-Planck-Institut für Eisenforschung, Max-Planck-Straße
+1, D-40237 Düsseldorf, Germany
+
+
+
+
+* E-mail:
+
+
+1
+11
+2023
+
+9
+100
+6194
+
+Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)
+2022
+The article authors
+
+Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)
+
+
+
+Python
+Heisenberg-Landau model
+Spin dynamics
+Metadynamics
+Thermodynamic integration
+
+
+
+
+
+ Summary
+
Magnetic interactions account for a significant portion of free
+ energy in certain materials, ranging from relatively simple systems
+ such as iron to complex magneto-caloric effects of Heusler alloys
+ (Weiss
+ & Piccard, 1917). More specifically, in the case of iron,
+ the ground state would be wrongly predicted without considering
+ magnetic interactions
+ (Friák
+ et al., 2001). In Heusler systems, the understanding of
+ magnetic properties could allow for the development of highly
+ efficient refrigeration systems. In materials science, the Heisenberg
+ model is frequently employed to heuristically compute the magnetic
+ part of the potential energy. There are two main methods to make use
+ of the Heisenberg model at finite temperature: one is the Monte Carlo
+ method for an efficient free energy minimization, the other is spin
+ dynamics for the calculation of spin configuration evolution. The
+ Monte Carlo method has the advantage of obtaining the free energy
+ rapidly, while spin dynamics also delivers the kinetics of the system.
+ mamonca allows for the evaluation of the
+ Heisenberg Hamiltonian with extended terms using both Monte Carlo
+ method and spin dynamics.
+
+
+ Model
+
mamonca is based on the Heisenberg Landau
+ model of the format:
+
+
+ ℋ=−12∑ij,κJij,κmi2κ+1mj2κ+1+∑i,κAi,κmi2κ
+
where
+
+ i
+ and
+
+ j
+ go over all atoms and
+
+ κ
+ is the exponent (
+
+ κ=1
+ and
+
+ Ai,κ=0
+ for all
+
+ i
+ and
+
+ κ
+ for the classical Heisenberg model) and
+
+ mi
+ is the magnetic moment of the atom
+
+ i.
+ These parameters can be set independently via
+ mamonca.set_landau_parameters for the
+ longitudinal parameters
+
+ Ai,κ
+ and mamonca.set_heisenberg_parameters for the
+ Heisenberg parameters
+
+ Jij,κ.
+ The evaluation takes place either via Metropolis Monte Carlo method or
+ spin dynamics. More technical details and simple examples are given in
+ notebooks/first_steps.ipynb.
+
+
+ Statement of need
+
mamonca is a C++-based python software
+ package for the computation of magnetic interactions in solid
+ materials. Its interactive and modular nature makes it for a user who
+ wants to obtain the magnetic behavior of simple to complex systems as
+ well as combining it with other tools on the fly. All inputs and
+ outputs are given by setters (starting with
+ set_) and getters (starting with
+ get_), in order for
+ mamonca to spare file-reading and writing, in
+ strong contrast to other existing software packages
+ (Bauer
+ et al., 2011;
+ Evans
+ et al., 2014;
+ Hellsvik
+ et al., 2011;
+ Kawamura
+ et al., 2017). As a result, it has excellent interactivity, as
+ the parameters can be changed on the fly, as well as the outputs can
+ be retrieved at any interval chosen by the user. With
+ mamonca, the user can analyse any structure
+ that can be defined by other software packages such as Atomic
+ Structure Environment (ASE)
+ (Larsen
+ et al., 2017) or pyiron
+ (Janssen
+ et al., 2019), as mamonca takes only the
+ exchange parameters and does not require the knowledge of the
+ structure, which is a strong contrast to existing software packages
+ (Bauer
+ et al., 2011;
+ Kawamura
+ et al., 2017). mamonca has also high
+ flexibility in defining the Hamiltonian, as it allows the user to
+ define not only the classical Heisenberg model, but higher order
+ components including the longitudinal variation, as it has been
+ employed for Fe-Mn systems
+ (Schneider
+ et al., 2021). In order to validate the code, a comparison of
+ results produced with mamonca with those
+ obtained in
+ (Schneider
+ et al., 2021) is given in the notebook
+ notebooks/first_steps.ipynb. The input
+ parameters for the Hamiltonian can be straightforwardly obtained using
+ a workflow tool such as pyiron, or other calculation software packages
+ such as TB2J
+ (He
+ et al., 2021). A typical workflow with pyiron would consist of
+ a general set of physical parameters (chemical element, lattice
+ parameter etc.), is given in the notebook
+ notebooks/first_steps.ipynb, which is then
+ evaluated by the software of user’s choice. The results can be
+ straightforwardly evaluated to obtain the exchange parameters with the
+ existing tools inside pyiron. Finally, mamonca
+ can run to deliver the finite temperature effects of the magnetic
+ part. A full workflow example including the acquisition of magnetic
+ interaction parameters is given in the notebook
+ notebooks/fitting.ipynb. This means, the user
+ in principle needs only to insert physical parameters to obtain the
+ magnetic finite temperature behaviour they are interested in. In
+ addition to the classical Monte Carlo and spin-dynamics,
+ mamonca allows also for an addition of
+ Metadynamics
+ (Theodoropoulos
+ et al., 2000) and magnetic thermodynamic integration (Chap. 9
+ (Frenkel
+ & Smit, 2023)), which can deliver the free energy
+ variation. It is crucial to include these features within the code, as
+ they have to be applied at each step of the simulation and cannot be
+ evaluated in the post-processing. To authors’ knowledge, it is the
+ only one code that is able to run Monte Carlo calculations with
+ Metadynamics and magnetic thermodynamic integration. Both
+ thermodynamic integration and Metadynamics are shown in the notebook
+ notebooks/first_steps.ipynb for simple
+ systems.
+
+
+ Acknowledgements
+
We gratefully acknowledge the financial support from the German
+ Research Foundation (DFG) under grant HI 1300/15-1 within the DFG-ANR
+ project C-TRAM.