Electron correlation effects and ferromagnetism in iron

Electron correlation effects in Fe are analysed using a first-principles linear combination of atomic orbitals scheme. In our approach, we first use a local orbital density functional solution to introduce a Hubbard Hamiltonian without fitting parameters. In a second step, we introduce a many-body solution to this Hamiltonian using a dynamical mean-field approximation. Our analysis shows that magnetism in Fe is an effect associated with the first atomic Hund’s rule. Moreover, we also find important correlation effects in the Fe spin-polarized density of states. The photoemission spectra can be explained using a value of U eff as large as 4 eV, provided that the satellite peaks appearing around 3–5 eV below the Fermi energy are interpreted appropriately. The electronic properties of ferromagnetic metals are still a subject of controversy [1–3]. Although density functional theory-local density approximation (DFT-LDA) calculations yield the correct magnetization for the itinerant-electron ferromagnets Fe, Co and Ni, the origin of ferromagnetism in these metals and the role of electron correlations are not completely understood (e.g. see [4, 5]); in particular, the relative importance of the local Coulomb interaction for d orbitals, U eff , versus intra-atomic exchange (first Hund’s rule) is not completely established. Even from an experimental point of view, there is a lack of agreement on whether or not a satellite peak exists in the photoemission spectrum of iron around 5 eV below the Fermi energy [2]. In the conventional view of itinerant ferromagnetism [6], spin polarization is determined by the Stoner parameter, I , that defines the energy of the atomic d orbitals as (Ed − Ind), nd being the occupation number of the orbital under consideration. In the case of Fe, DFT-LDA calculations yield a value I = 3.9 eV [7], and a surprisingly large value of U eff ∼ 4–6 eV [8, 9] for the effective Coulomb interaction between the d electrons. Since the atomic-like properties of the d states are of crucial importance for the magnetic properties of these materials, linear 0953-8984/02/230421+07$30.00 © 2002 IOP Publishing Ltd Printed in the UK L421 L422 Letter to the Editor combination of atomic orbitals (LCAO) methods provide the appropriate conceptual framework for understanding those properties and for analysing the role of electron correlations. In LCAO theories of ferromagnetism, including Hubbard Hamiltonians, I is written as (Ũ eff +4J x) [10], where J x defines the screened intrasite exchange interaction between the atomic d electrons having the same spin; it is commonly accepted that J x practically coincides with its atomic value [8]. In the case of Fe, J x = 0.83 eV and, therefore, we should take Ũ eff ∼ 0.6 eV to recover the value I = 3.9 eV that corresponds to the correct magnetization. This result suggests the presence of dramatic electron correlation effects in Fe,which would be responsible for the renormalization of U eff from ∼5 eV to Ũ eff ∼ 0.6 eV. On the other hand, the value of U eff inferred from the photoemission spectra [11–13] by identifying photoemission peaks with quasi-particle peaks yields U eff ≈ 2 eV [1, 9]. This result seems to indicate that electron correlation effects for Fe are not strong, in contradiction to the previous analysis. The purpose of this letter is to show that these apparent contradictions disappear once electron correlation effects [14] are properly analysed using a first-principles LCAO scheme. In our approach, reminiscent of the LDA+U scheme [15], we first formulate a local density (LD) solution for a generalized Hubbard Hamiltonian. This LD solution provides the link between the generalized Hubbard Hamiltonian and local orbital DFT-LDA methods, allowing us to obtain that Hamiltonian from first principles, without having to introduce fitting parameters. In a second step, we introduce a many-body solution for the Hubbard Hamiltonian using a dynamical mean-field (DMF) approximation [16]: in this way we analyse the spin-polarized electron density of states (DOS) for Fe and compare it with the experimental evidence [11–13]. From our analysis, we obtain two different results. First, using our LD solution for the Hubbard Hamiltonian, we show that electron correlation effects screen strongly the effective Coulomb interaction contributing to the Stoner parameter: in this scenario, Ũ eff is not larger than 0.6– 0.7 eV. We find, however, that the effective interaction appearing in the Hubbard Hamiltonian is around 4 eV, in reasonable agreement with other first-principles calculations [8, 9]; using this value and the many-body techniques mentioned above, we also find that the spin-polarized DOS for Fe is in good agreement with the photoemission data, provided that we interpret appropriately the satellite peaks appearing in the spectrum around 3–5 eV below the Fermi energy [9]. Our starting point is the generalized Hubbard Hamiltonian: