Ab-initio Wannier Functions, Coulomb Matrix Elements, Hartree (-Fock) and LSDA Calculations for the 3d Transition Metals Fe, Co, Ni and Cu

We show that ab-initio band structure methods, namely the linearized muffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA), can be used for a first-principles calculation of well localized Wannier functions. This is achieved by using a method proposed by Marzari and Vanderbilt. The resulting maximally localized Wannier functions for the 3d transition metals Fe, Co, Ni and Cu have at least 87% of their charge density within the home muffin-tin sphere. These Wannier functions serve as a minimal basis, i.e. a one-particle basis containing only 4s, 4p and 3d-orbitals, in which the many-particle Hamiltonian is expanded. We propose two independent methods to evaluate Coulomb matrix elements from Wannier functions. The tight-binding (hopping) matrix elements are obtained from completely non-interacting valence electrons moving in the effective frozen-core potential. Hence, in contrast to other approaches which use the local density approximation (LDA) as the starting point, we start from a well defined situation where the problem of double counting interactions (already included in the effective LDA band structure) is avoided. The result is an electronic multi-band Hamiltonian in second quantization with first-principles one- and two-particle matrix elements which is studied within the Hartree-Fock approximation. For the 3d ferromagnets, the resulting magnetic moments of this treatment are found to be about 20 to 30% larger than within the local spin-density approximation (LSDA) and experimental results. The band structure shows the 3d-bands below the 4s and 4p-bands. Responsible for this behavior is the Fock self-energy term which subtracts the self-interactions included in the Hartree self-energy term. We find on-site direct Coulomb matrix elements (Hubbard-U's) on the magnitude of 21 to 25 eV for 3d Wannier states. These U-values are much larger than commonly expected or used in model studies of 3d ferromagnets. We discuss reasons why it may be justified to use smaller U's in model Hamiltonian studies.

Download PDF file of thesis here: thesis.pdf

Here are the slides I used during my doctoral colloquium: talk.pdf

Computational flow diagram of how I arrived at my results.

After the doctoral colloquium