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

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 1µB 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.

Interfacial geometry dependence of the iron magnetic moment: The case of MgO/Fe/MgO

“…Notably, we found good agreement of our mm values with earlier calculations for supported Fe layers or clusters onto MgO. 16,17,37,38 For thicker Fe films, compensation of interface charge by the shallow Fe layers gradually decreases the enhancement of the surface magnetization towards the bulk Fe value. The interatomic distances along the out-of-plane (001) direction are also summarized in Table I.…”

Magnetocrystalline anisotropy of Fe and Co slabs and clusters onSrTiO3by first-principles

“…Nevertheless, the arguments put forward are rather general and could be very useful in the design of atomic-scale devices with optimized magnetic anisotropy. Note however, that if the nonsphericity of the Coulomb and exchange interaction [32] starts to play a dominant role in the electronic structure of the system, then orbital polarization effects arise [33,34] and our analysis of the MCA based on a perturbation treatment of the SOC only non longer applies, and more complex scenarii can occur as in the case of the giant magnetic anisotropy of single adatom on MgO [35].…”

Electronic transport in iron atomic contacts: From the infinite wire to realistic geometries

“…I is the Stoner parameter, which we take equal to 1 eV, as in our previous studies on iron. 22,25 H LCN is added to ensure quasilocal charge neutrality in systems with inequivalent atoms. 22 Its matrix elements ͗i͉Ĥ LCN ͉jЈ͘ are written as pen ͑⌬q i + ⌬q j ͒S ij ␦ Ј , where pen is the penalization factor ͑in practice, pen = 2.5 eV͒, ⌬q i is the deviation of the Mulliken charge of site i from the valence charge, and S ij ␦ Ј are the matrix elements of the overlap matrix S.…”