In this work, we present the program MAELAS to calculate magnetocrystalline anisotropy energy, anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way by Density ...Functional Theory calculations. The program is based on the length optimization of the unit cell proposed by Wu and Freeman to calculate the magnetostrictive coefficients for cubic crystals. In addition to cubic crystals, this method is also implemented and generalized for other types of crystals that may be of interest in the study of magnetostrictive materials. As a benchmark, some tests are shown for well-known magnetic materials.
Program Title: MAELAS
CPC Library link to program files: https://doi.org/10.17632/gxcdg3z7t6.1
Developer’s repository link:https://github.com/pnieves2019/MAELAS
Code Ocean capsule: https://codeocean.com/capsule/0361425
Licensing provisions: BSD 3-clause
Programming language: Python3
Nature of problem: To calculate anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way based on Density Functional Theory methods.
Solution method: In the first stage, the unit cell is relaxed through a spin-polarized calculation without spin-orbit coupling. Next, after a crystal symmetry analysis, a set of deformed lattice and spin configurations are generated using the pymatgen library 1. The energy of these states is calculated by the first-principles code VASP 3, including the spin-orbit coupling. The anisotropic magnetostrictive coefficients are derived from the fitting of these energies to a quadratic polynomial 2. Finally, if the elastic tensor is provided 4, then the magnetoelastic constants are also calculated.
Additional comments including restrictions and unusual features: This version supports the following crystal systems: Cubic (point groups 432, 4̄3m, m3̄m), Hexagonal (6mm, 622, 6̄2m, 6∕mmm), Trigonal (32, 3m, 3̄m), Tetragonal (4mm, 422, 4̄2m, 4∕mmm) and Orthorhombic (222, 2mm, mmm).
References:
1 S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Comput. Mater. Sci. 68, 314 (2013).
2 R. Wu, A. J. Freeman, Journal of Applied Physics 79, 6209–6212 (1996).
3 G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.
4 S. Zhang and R. Zhang, Comput. Phys. Commun. 220, 403 (2017).
•Software to calculate anisotropic magnetostrictive coefficients.•It also calculates anisotropic magnetoelastic constants.•Evaluation of magnetocrystalline anisotropy energy.•Calculations in an automated way by Density Functional Theory calculations.•It supports the main crystal symmetries in the research field of magnetostriction.
MAELAS is a computer program for the calculation of magnetocrystalline anisotropy energy, anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way. The method ...originally implemented in version 1.0 of MAELAS was based on the length optimization of the unit cell, proposed by Wu and Freeman, to calculate the anisotropic magnetostrictive coefficients. We present here a revised and updated version (v2.0) of MAELAS, where we added a new methodology to compute anisotropic magnetoelastic constants from a linear fitting of the energy versus applied strain. We analyze and compare the accuracy of both methods showing that the new approach is more reliable and robust than the one implemented in version 1.0, especially for non-cubic crystal symmetries. This analysis also helps us find that the accuracy of the method implemented in version 1.0 could be improved by using deformation gradients derived from the equilibrium magnetoelastic strain tensor, as well as potential future alternative methods like the strain optimization method. Additionally, we clarify the role of the demagnetized state in the fractional change in length, and derive the expression for saturation magnetostriction for polycrystals with trigonal, tetragonal and orthorhombic crystal symmetry. In this new version, we also fix some issues related to trigonal crystal symmetry found in version 1.0.
Program title: MAELAS
CPC Library link to program files:https://doi.org/10.17632/gxcdg3z7t6.2
Developer's repository link:https://github.com/pnieves2019/MAELAS
Code Ocean capsule:https://codeocean.com/capsule/2689126
Licensing provisions: BSD 3-clause
Programming language: Python3
Journal reference of previous version: P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, Comput. Phys. Commun. 264, 107964 (2021)
Does the new version supersede the previous version?: Yes
Reasons for the new version: To implement a more accurate methodology to compute magnetoelastic constants and magnetostrictive coefficients, and fix some issues related to trigonal crystal symmetry.
Summary of revisions:•New method to calculate magnetoelastic constants and magnetostrictive coefficients derived from the magnetoelastic energy.•Correction of the trigonal crystal symmetry.•Implementation of the saturation magnetostriction for polycrystals with trigonal, tetragonal and orthorhombic crystal symmetry.•In the visualization tool MAELASviewer, we included the possibility to choose the type of reference demagnetized state in the calculation of the fractional change in length.
Nature of problem: To calculate anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way based on Density Functional Theory methods.
Solution method: In the first stage, the unit cell is relaxed through a spin-polarized calculation without spin-orbit coupling (SOC). Next, after a crystal symmetry analysis, a set of deformed lattice and spin configurations are generated using the pymatgen library 1. The energy of these states is calculated by the Vienna Ab-initio Simulation Package (VASP) 2, including SOC. The anisotropic magnetoelastic constants are derived from the fitting of these energies to a linear polynomial. Finally, if the elastic tensor is provided 3, then the magnetostrictive coefficients are also calculated from the theoretical relations between elastic and magnetoelastic constants.
Additional comments including restrictions and unusual features: This version supports the following crystal systems: Cubic (point groups 432, 4¯3m, m3¯m), Hexagonal (6mm, 622, 6¯2m, 6/mmm), Trigonal (32, 3m, 3¯m), Tetragonal (4mm, 422, 4¯2m, 4/mmm) and Orthorhombic (222, 2mm, mmm).
1S.P. Ong, W.D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V.L. Chevrier, K.A. Persson, G. Ceder, Comput. Mater. Sci. 68, 314 (2013).2G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.3S. Zhang, R. Zhang, Comput. Phys. Commun. 220, 403 (2017).
•New version (v2.0) of MAELAS with a more accurate methodology.•Revision of the trigonal symmetry.•Software to calculate anisotropic magnetostrictive coefficients.•It also calculates anisotropic magnetoelastic constants.•Magnetostriction of single crystals and polycrystals.
We present a methodology based on deformations of the unit cell that allows to compute the isotropic magnetoelastic constants, isotropic magnetostrictive coefficients and spontaneous volume ...magnetostriction associated to the exchange magnetostriction. This method is implemented in the python package MAELAS (v3.0), so that it can be used to obtain these quantities by first–principles calculations and classical spin–lattice models in an automated way. We show that the required reference state to obtain the spontaneous volume magnetostriction combines the equilibrium volume of the paramagnetic state and magnetic order of the ground state. In the framework of a classical spin–lattice model, we find that the analysis of volume dependence of this method jointly to the knowledge of the spatial derivative of the exchange interactions can reveal the equilibrium volume of the paramagnetic state and spontaneous volume magnetostriction unambiguously without involving any calculation of the paramagnetic state. We identify an error in the theoretical expression of the isotropic magnetostrictive coefficient λα1,0 for uniaxial crystals given in previous publications, which is corrected in this work. The presented computational tool may be helpful to provide a better understanding and characterization of the relationship between the exchange interaction and magnetoelasticity.
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•New version (v3.0) of MAELAS capable to compute exchange magnetostriction.•Software to calculate isotropic magnetoelastic constants.•It also calculates isotropic magnetostrictive coefficients.•Isotropic and anisotropic components of spontaneous volume magnetostriction.•The results are printed using the universal notation proposed by E. du T. Lacheisserie.
Hybridization between f electrons and conduction bands (c-f hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn5 heavy fermion ...superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of T = 6 K. The used photon energy of 122 eV corresponds to Ce 4d−4f resonance. Calculations carried out with the relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra, indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining f-electron character when approaching Fermi energy. We have also observed a considerable variation of f-electron spectral weight at EF, which is normally determined by both matrix element effects and wave vector dependent c-f hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of 4 f-electron enhanced spectral intensity at EF around Γ and M points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of 4f-electron density for a range of values of the parameters used in the model.
Hybridization between f electrons and conduction bands (c-f hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn5 heavy fermion ...superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of T = 6 K. The used photon energy of 122 eV corresponds to Ce 4d-4f resonance. Calculations carried out with relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining f-electron character when approaching Fermi energy. We have also observed a considerable variation of felectron spectral weight at EF , which is normally determined by both matrix element effects and wave vector dependent c-f hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of 4f-electron enhanced spectral intensity at EF aroundΓ andM points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of 4f-electron density for a range of values of the parameters used in the model.
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•Thermal decomposition of SPS samples results in UFG microstructure (<200 nm).•Decomposed samples have up to 65% higher flexural strength, while 10% lower hardness.•Elastic properties ...of present phases can be accurately calculated by computer modelling.
The application of non-equilibrium methods such as Mechanical Alloying and Field Assisted Sintering enables the formation of a single solid solution in immiscible systems, or the ones characterized by a miscibility gap. This work shows that W-Cr solid solution can be used as an intermediate step to produce ultrafine-grained composite alloys with rod-like microstructural features. It is shown that a significant increase in strength can be achieved without an increase in hardness using this top-down material design.
GGA+U has been used as a framework for computational study of UH2, and α- and β-UH3, exploring specific features of the polar U-H bonding and its influence on magnetic and cohesion properties, ...including elastic parameters and vibrational properties. The description of the U-5f states with direct Coulomb U = 0.5 eV and equal exchange J = 0.5 eV not only reproduce equilibrium volumes but provides a realistic description of total magnetic moments, consisting of smaller spin and larger antiparallel orbital components. For UH2 and α-UH3, the spin-axis is aligned along the 111 direction. For β-UH3, there is a significant difference between both size and orientation U moments of atoms at the 2a and 6c Wyckoff positions. The former has U moments aligned along 111, while in the latter, not fixed to any specific direction by symmetry, they deviate by 10∘. The method corroborates previous bonding analyses, indicating a prominent hybridization and charge transfer, affecting the 6d and 7s states of U, being partly transferred to the H-1s states, revealed by the Bader analysis. Analyzing individual effective inter-site magnetic coupling parameters it was possible to identify sources of relatively high Curie temperatures of 170 K for both UH3 variants and 120 K for UH2. Our results give predictions of elastic coefficients (consistent with the known bulk modulus in the case of β-UH3) and phonon densities of states, yielding expected infrared, Raman, and Hyper Raman active modes.
We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the interelectronic interactions can be evaluated exactly. The system has been selected due to its ...tunability, i.e., its electron wave functions can be modified much easier than in, e.g., quantum dots. We determine many-particle states for Ne = 2 and 3 electrons and calculate the 3- and 4-state interaction parameters, and discuss their importance. For that purpose, we combine the first- and second-quantization schemes and hence are able to single out the component single-particle contributions to the resultant many-particle state. The method provides both the ground- and the first-excited-state energies, as the exact diagonalization of the many-particle Hamiltonian is carried out. DRN provides one of the few examples for which one can determine theoretically all interaction microscopic parameters to a high accuracy. Thus the evolution of the single-particle vs. many-particle contributions to each state and its energy can be determined and tested with the increasing system size. In this manner, we contribute to the wave-function engineering with the interactions included for those few-electron systems.
The recently proposed local-correlation-driven pairing mechanism, describing ferromagnetic phases (FM1 and FM2) coexisting with spin-triplet superconductivity (SC) within a single orbitally ...degenerate Anderson lattice model, is extended to the situation with an applied Zeeman field. The model provides and rationalizes in a semiquantitative manner the principal features of the phase diagram observed for UGe2 in the field absence cf., Phys. Rev. B 97, 224519 (2018). As spin-dependent effects play a crucial role for both the ferromagnetic and SC states, the role of the Zeeman field is to single out different stable spin-triplet SC phases. This analysis should thus be helpful in testing the proposed real-space pairing mechanism, which may be regarded as complementary to spin-fluctuation theory suitable for He3. Specifically, we demonstrate that the presence of the two distinct phases, FM1 and FM2, and the associated field-driven metamagnetic transition between them, induces a respective metasuperconducting phase transformation. At the end, we discuss briefly how the spin fluctuations might be incorporated as a next step in the renormalized quasiparticle picture considered herein.
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