For large-scale computation of the exchange coupling constants Jij, we reconstruct the Liechtenstein formula for localized orbital representation and simplify the energy integrations by adopting the finite pole approximation of the Fermi function proposed by Ozaki [Phys. Rev. B 75, 035123 (2007)]. We calculate the exchange coupling constant J1NN of the first-nearest-neighbor sites in body-centered-cubic Fe systems of various sizes to estimate the optimal computational parameters that yield appropriate values at the lowest computational cost. It is shown that the number of poles needed for a computational accuracy of 0.05 meV is determined as ∼ 60, whereas the number of necessary Matsubara poles needed to obtain similar accuracy, which was determined in previous studies, is on the order of 1000. Finally, we show Jij as a function of atomic distance, and compared it with one derived from Korringa-Kohn-Rostoker Green's function formalism. The distance profile of Jij derived by KKR formalism agrees well with that derived by our study, and this agreement supports the reliability of our newly derived formalism. arXiv:1907.08341v1 [cond-mat.mtrl-sci]

We report the crystal structure of Nd–Fe alloys as candidates for grain-boundary phases in Nd–Fe–B sintered magnets. We find that the crystal structure of the fluorite Nd–Fe alloys is stable for a wide composition range. We also demonstrate that solid solution of Ga is effective in stabilizing the fluorite crystal structure of Nd–Fe alloys, which is consistent with experimental observations reporting crystalline Nd–Fe alloys at the grain boundaries of Ga-added Nd–Fe–B permanent magnets.

Using the scheme of Delaunay and Gabriel graphs, we analyzed the amorphous structures of computationally created Nd-Fe alloys for several composition ratios based on melt quench simulations with finite temperature first-principles molecular dynamics. By the comparison of the radial distribution functions of the whole system and those derived from the Delaunay and Gabriel graphs, it was shown that the Gabriel graphs represent the first nearest neighbor networks well in the examined amorphous systems. From the Gabriel graph analyses, we examined the coordination structures of amorphous Nd-Fe alloys statistically. We found that the ranges of distributions of coordination numbers vary depending on the composition ratio. The angular distributions among three adjacent atoms were also analyzed, and it was found that the angular distributions behave differently in the Nd-rich and Fe-rich samples. We found that the orders in the amorphous system becomes stronger as increasing the Nd ratio, which corresponds to the appearance of crystalline grain boundary phases at high Nd composition ratio [T. T. Sasaki et al., Acta Mater. 115, 269-277 (2016)].

We investigate the exchange coupling constant Jij in NdxFe1−x amorphous alloys with different compositions within the framework of first-principles calculation. We observed a strong atomicdependence of Jij and its fluctuations. We show that the composition strongly affects the distance dependence of Jij . Composition dependence of calculated Curie temperatures is modest for x < 0.5. To examine the effect of the local environment on the exchange couplings, we demonstrate combined analyses of the coordination structure and exchange coupling constants using the Gabriel graph. Our study reveals that the Curie temperatures are mostly dominated by the averaged Jij and coordination numbers determined by the pairs of neighboring atoms. We also observed that the exchange couplings between Fe-Fe and Fe-Nd become stronger with increasing the number of surrounding Nd atoms.