Orbital contribution to the magnetic properties of iron as a function of dimensionality

TL;DR

This paper investigates how the orbital contribution affects the magnetic properties of iron across different dimensional systems using a comprehensive Hartree-Fock approach, revealing significant differences from simplified models.

Contribution

It introduces a full Hartree-Fock method to accurately compute orbital magnetic moments and anisotropy energy in low-dimensional iron systems, highlighting the limitations of simplified Hamiltonians.

Findings

Full HF yields larger orbital moments and MAE than simplified models.

Orbital Polarization Ansatz agrees qualitatively for orbital moments but not for MAE.

Full HF is necessary for accurate orbital magnetism in low-dimensional systems.

Abstract

The orbital contribution to the magnetic properties of Fe in systems of decreasing dimensionality (bulk, surfaces, wire and free clusters) is investigated using a tight-binding hamiltonian in an $s, p,$ and $d$ atomic orbital basis set including spin-orbit coupling and intra-atomic electronic interactions in the full Hartree-Fock (HF) scheme, i.e., involving all the matrix elements of the Coulomb interaction with their exact orbital dependence. Spin and orbital magnetic moments and the magnetocrystalline anisotropy energy (MAE) are calculated for several orientations of the magnetization. The results are systematically compared with those of simplified hamiltonians which give results close to those obtained from the local spin density approximation. The full HF decoupling leads to much larger orbital moments and MAE which can reach values as large as 1$\mu_B$ and several tens of meV, respectively, in the monatomic wire at the equilibrium distance. The reliability of the results obtained by adding the so-called Orbital Polarization Ansatz (OPA) to the simplified hamiltonians is also discussed. It is found that when the spin magnetization is saturated the OPA results for the orbital moment are in qualitative agreement with those of the full HF model. However there are large discrepancies for the MAE, especially in clusters. Thus the full HF scheme must be used to investigate the orbital magnetism and MAE of low dimensional systems.