Magnetostatic dipolar energy of large periodic Ni fcc nanowires, slabs and spheres
| Autor: | Cabria Álvaro, Iván |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Computation
General Physics and Astronomy 02 engineering and technology Método de Ewald 010402 general chemistry 01 natural sciences Matrix (mathematics) Ewald method Time complexity Physics Nanomagnetismo Magnetic moment Energía dipolar magnetostática Surfaces and Interfaces General Chemistry 021001 nanoscience & nanotechnology Condensed Matter Physics Symmetry (physics) 0104 chemical sciences Surfaces Coatings and Films Computational physics Dipole Nanomagnetism Magnetostatic dipolar energy SPHERES Zeeman energy 0210 nano-technology |
| Zdroj: | UVaDOC. Repositorio Documental de la Universidad de Valladolid instname |
| ISSN: | 0169-4332 |
| DOI: | 10.1016/j.apsusc.2019.05.307 |
| Popis: | Producción Científica The computational effort to calculate the magnetostatic dipolar energy, MDE, of a periodic cell of N magnetic moments is an O(N2) task. Compared with the calculation of the Exchange and Zeeman energy terms, this is the most computationally expensive part of the atomistic simulations of the magnetic properties of large periodic magnetic systems. Two strategies to reduce the computational effort have been studied: An analysis of the traditional Ewald method to calculate the MDE of periodic systems and parallel calculations. The detailed analysis reveals that, for certain types of periodic systems, there are many matrix elements of the Ewald method identical to another elements, due to some symmetry properties of the periodic systems. Computation timing experiments of the MDE of large periodic Ni fcc nanowires, slabs and spheres, up to 32000 magnetic moments in the periodic cell, have been carried out and they show that the number of matrix elements that should be calculated is approximately equal to N, instead of N2/2, if these symmetries are used, and that the computation time decreases in an important amount. The time complexity of the analysis of the symmetries is O(N3), increasing the time complexity of the traditional Ewald method. MDE is a very small energy and therefore, the usual required precision of the calculation of the MDE is so high, about 10−6 eV/cell, that the calculations of large periodic magnetic systems are very expensive and the use of the symmetries reduces, in practical terms, the computation time of the MDE in a significant amount, in spite of the increase of the time complexity. The second strategy consists on parallel calculations of the MDE without using the symmetries of the periodic systems. The parallel calculations have been compared with serial calculations that use the symmetries. Ministerio de Economía, Industria y Competitividad ( grant MAT2014-54378-R) Junta de Castilla y León (grants VA050U14 and VA124G18) |
| Databáze: | OpenAIRE |
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