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Register a new userTotal Energy Studies for Ferromagnetic Nickel: What is the Optimum Combination of the Multi-band Gutzwiller Method and Density Functional Theory?
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The multi-band Gutzwiller method, combined with calculations based on density functional theory, is employed to study total energy curves of the ferromagnetic ground state of Ni. A new method is presented which allows flow of charge between d and s, p type orbitals in an approximate way. Further it is emphasized that the missing repulsive contribution to the total energy at large magnetic moments can be estimated from an analysis of specific DFT calculations.
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We present a detailed derivation of the Gutzwiller Density Functional Theory that covers all conceivable cases of symmetries and Gutzwiller wave functions. The method is used in a study of ferromagnetic nickel where we calculate ground state properties (lattice constant, bulk modulus, spin magnetic moment) and the quasi-particle band structure. Our method resolves most shortcomings of an ordinary Density Functional calculation on nickel. However, the quality of the results strongly depends on the particular choice of the double-counting correction. This constitutes a serious problem for all methods that attempt to merge Density Functional Theory with correlated-electron approaches based on Hubbard-type local interactions.
The minimum of the Gutzwiller energy functional depends on the number of parameters considered in the variational state. For a three-orbital Hubbard model we find that the frequently used diagonal Ansatz is very accurate in high-symmetry situations. For lower symmetry, induced by a crystal-field splitting or the spin-orbit coupling, the discrepancies in energy between the most general and a diagonal Gutzwiller Ansatz can be quite significant. We discuss approximate schemes that may be employed in multi-band cases where a minimization of the general Gutzwiller energy functional is too demanding numerically.
We use the Gutzwiller Density Functional Theory to calculate ground-state properties and bandstructures of iron in its body-centered-cubic (bcc) and hexagonal-close-packed (hcp) phases. For a Hubbard interaction $U=9, {rm eV}$ and Hunds-rule coupling $J=0.54, {rm eV}$ we reproduce the lattice parameter, magnetic moment, and bulk modulus of bcc iron. For these parameters, bcc is the ground-state lattice structure at ambient pressure up to a pressure of $p_{rm c}=41, {rm GPa}$ where a transition to the non-magnetic hcp structure is predicted, in qualitative agreement with experiment ($p_{rm c}^{rm exp}=10ldots 15, {rm GPa}$). The calculated bandstructure for bcc iron is in good agreement with ARPES measurements. The agreement improves when we perturbatively include the spin-orbit coupling.
The ground states of Na$_x$CoO$_2$ ($0.0<x<1.0$) is studied by the LDA+Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated {it ab-initio}. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as: (1) Stoner magnetic metal for $x>0.6$ due to $a_{1g}$ van-Hove singularity near band top; (2) correlated non-magnetic metal without $e_g^{prime}$ pockets for $0.3<x<0.6$; (3) $e_g^{prime}$ pockets appear for $x<0.3$, and additional magnetic instability involves. Experimental quasi-particle properties is well explained, and the $a_{1g}$-$e_g^{prime}$ anti-crossing is attributed to spin-orbital coupling.
We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasi-particle bands of LaOFeAs. The Fe3d--As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parameterized by the Hubbard interaction U and an average Hunds-rule interaction J. We reproduce the experimentally observed small ordered magnetic moment over a large region of (U,J) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasi-particles.
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