Efficient Algorithm Based on Liechtenstein Method for Computing Exchange Coupling Constants Using Localized Basis Set

Abstract

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]

Remarkably enhanced Curie temperature in monolayer CrI3 by hydrogen and oxygen adsorption: A first-principles calculations

“…We have computed exchange coupling constants using jx, a post-processing code for OpenMX , 49,50 . We have first computed J for pristine CrI 3 , obtaining the nearest-neighbor value and corresponding Curie temperature that are presented in Table II.…”

First-principles determination of intergranular atomic arrangements and magnetic properties in rare-earth permanent magnets

“…Other expressions of the Liechtenstein method [ 18 ] to calculate have been given without using -matrix in order to apply the method to first-principles schemes that do not directly use the concept of multiple scattering [ 66 ]. For amorphous Nd-Fe alloys, has been evaluated by a formalism that accelerates the computation of with non-orthogonal basis sets [ 67 ]. Figure 6 shows between Nd-Fe pairs as a function of the interatomic distance for amorphous Nd Fe alloys, where is derived from the magnetic ground state.…”

“…The average of the interatomic distances for, e.g., the nearest-neighbor Nd-Fe pairs in amorphous Nd Other expressions of the Liechtenstein method [18] to calculate ij J have been given without using t -matrix in order to apply the method to first-principles schemes that do not directly use the concept of multiple scattering [66]. For amorphous Nd-Fe alloys, ij J has been evaluated by a formalism that accelerates computation of ij J with non-orthogonal basis sets [67].…”

Local force method for the ab initio tight-binding model with spin-dependent hopping

“…Recently, the local force method has been applied to the SDFT Hamiltonian with various spatially localized bases such as the LMTO [30][31][32], linear-combination of pseudo atomic orbital (LCPAO) [33,34], and Wannier orbital [35]. Especially, the Wannier-based approach has the broadest applicability, since one can construct Wannier functions irrespective of the choice of the basis of the SDFT calculation [36][37][38].…”

“…While such non-local terms are crucial for the self-consistent mapping to the effective spin model, the numerical cost to take account of them is extraordinarily expensive. Thus the effect of these terms has yet to be investigated in the previous studies [34,35]. In this paper, we present a formalism using the kernel polynomial method (KPM), which is known as a realspace solver for the bilinear Hamiltonian [40,41].…”