Magnetocrystalline anisotropy and orbital polarization in ferromagnetic transition metals

Abstract

The magnetocrystalline anisotropy energies ͑MAE's͒ of the ferromagnetic metals bcc Fe, fcc and hcp Co, and fcc Ni have been calculated by using the ab initio tight-binding method. Disentangling the strong correlation among the d orbitals with the Hamiltonian in the local spin-density approximation, we have investigated the orbital polarizations induced by the Hubbard U and Racah B. The experimental MAE of fcc Ni is found with the value of U close to that determined from experiments and used in other theories. With the values of U and J corresponding to the experimental MAE's, the orbital moments for Fe and Co are also in close agreement with experiment.Obtaining the magnetocrystalline anisotropy energies ͑MAE's͒ of Fe, Co, and Ni from ab initio calculations within the local-spin-density approximation ͑LSDA͒ to densityfunctional theory is of considerable current interest. 1-6 From various high-quality LSDA calculations, the best case is Fe, where the computed values differ from experiment by a factor of about 2. The result for hcp Co is far worse, and for Ni, the sign is not even correct. The effect of the so-called spinother-orbit coupling is far too small to bring theory and experiment into accord. 6 The discrepancy between theory and experiment, especially in the case of Ni, is usually attributed to the LSDA.The LSDA predicted MAE's and orbital moments can be improved for Fe and Co ͑Refs. 2 and 7͒ by introducing the Brooks' orbital polarization ͑OPB͒ term 8 which mimics Hund's second rule. However for Ni, the predicted easy axis is still wrong. 2 In OPB, OP is driven by the Racah parameter B, with an energy functional related to the orbital moment ͗L ͘ given by ⌬E OPB ϭϪ 1 2 B͗L ͘ 2 . 9 It was argued that the key

Effective anisotropies and energy barriers of magnetic nanoparticles with Néel surface anisotropy

“…We would like to emphasize here that the model itself has a phenomenological character since it is not based on the spin-orbit coupling considerations. A more adequate approach should involve first principle calculations of the magnetic moments and MAE with atomic resolution, like in Co/Cu ( 5,33 ). However at the present state of the art this task remains difficult.…”

“…Quantum abinitio studies have revealed different anisotropy and magnetic moment at the surface of magnetic clusters embedded in matrices 5 . Synchrotron radiation studies have confirmed that both spin and orbital moments at the surface differ significantly from their bulk counterparts 6 .…”

Gutzwiller-Correlated Wave Functions: Application to Ferromagnetic Nickel

“…The one-particle dynamics of models for correlated lattice electrons can be determined, in principle, within the dynamical mean-field theory (DMFT) [9,10,11] which becomes exact in the limit of an infinite number of nearest neighbors (coordination number Z → ∞). The 'static approximation' to DMFT is the 'LDA+U' scheme which has been applied to a variety of correlated-electron systems [12,13,14]. Moreover, DMFT has been extended in various ways, e.g., a combination of the LDA-GW approximation and the DMFT has been put forward [15].…”

“…Recent correlated-electron theories remove the SDFT shortcomings only partially. For example, with LDA+U-type calculations it seems to be possible to adjust to experiment the orbital moment, the magnetic anisotropy, and the Fermi surface topology [13,14]; however, other quantities, especially the entire quasi-particle band structure, remain elusive within these correlated-electron theories.…”

Gutzwiller wave functions for correlated electrons: theory and applications

“…The one-particle dynamics of models for itinerant ferromagnets can be determined, in principle, within the dynamical mean-field theory [31,32]. The 'static approximation' to DMFT is the 'LDA þ U' scheme which has been applied to itinerant ferromagnetism recently [33,34]. Moreover, DMFT has been extended in various ways, e.g.…”