Correlation effects in the total energy, the bulk modulus, and the lattice constant of a transition metal: Combined local-density approximation and dynamical mean-field theory applied to Ni and Mn

I. Di Marco, J. Minár, S. Chadov, M. I. Katsnelson, H. Ebert, and A. I. Lichtenstein

Phys. Rev. B 79, 115111 – Published 16 March 2009

Abstract

We present an accurate implementation of total-energy calculations into the local-density approximation plus dynamical mean-field theory $(LDA + DMFT)$ method. The electronic structure problem is solved through the full-potential linear muffin-tin orbital and Korringa-Kohn-Rostoker methods with a perturbative solver for the effective impurity suitable for moderately correlated systems. We have tested the method in detail for the case of Ni, and investigated the sensitivity of the results to the computational scheme and to the complete self-consistency. It is demonstrated that the $LDA + DMFT$ method can resolve a long-standing controversy between the LDA/generalized gradient approximation density-functional approach and experiment for equilibrium lattice constant and bulk modulus of Mn.

Received 27 September 2008

DOI:https://doi.org/10.1103/PhysRevB.79.115111

Authors & Affiliations

I. Di Marco^1,*, J. Minár², S. Chadov^2,3, M. I. Katsnelson¹, H. Ebert², and A. I. Lichtenstein⁴

¹Institute for Molecules and Materials, Radboud University of Nijmegen, NL-6525 ED Nijmegen, The Netherlands
²Department Chemie und Biochemie, Physikalische Chemie, Ludwig-Maximilians Universität München, D-81377 München, Germany
³Institut für Anorganische und Analytische Chemie, Johannes-Gutenberg Universität Mainz, 55128 Mainz, Germany
⁴Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany

^*dimarco@science.ru.nl

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Vol. 79, Iss. 11 — 15 March 2009

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Images

Figure 1
(Color online) Schematic representation of the iterative procedure to follow in the $LDA + DMFT$ scheme. As a first step the DFT-LDA problem is solved and a ground-state electron density $ρ (r)$ is obtained. From $ρ (r)$ we can extract the matrix elements of the single-particle LDA Hamiltonian, and then build the one-electron Green’s function $G (k, i ω_{n})$ at the Matsubara frequencies $i ω_{n}$ . Now the basic DMFT cycle starts: the Green’s function $G (k, i ω_{n})$ is projected onto the correlated orbitals, defining the bath Green’s function $G_{0}^{- 1} (R, i ω_{n})$ of the Anderson impurity model by means of Eq. (11). The solution of the local problem through one of the available solvers leads to a self-energy function $Σ_{R} (i ω_{n})$ . After a back projection to the LDA basis set, a new one-electron Green’s function $G (k, i ω_{n})$ and a new chemical potential $μ$ are calculated. The procedure is repeated iteratively until convergence in the self-energy and the chemical potential. Once the convergence of the basic DMFT cycle has been reached, a new electron density $ρ (r)$ can be calculated from $G (k, i ω_{n})$ . This is the fully self-consistent cycle and should be continued until convergence in $ρ (r)$ .Reuse & Permissions
Figure 2
(Color online) Illustration of the $KKR + DMFT$ scheme: blue semicircle is the complex energy path used by KKR to calculate the Green’s function. After the bath Green’s function $G$ is obtained, it is analytically continued onto the imaginary axis (vertical red line) to calculate the self-energy via the SPTF impurity solver. The latter is analytically extrapolated back to the semicircle.Reuse & Permissions
Figure 3
(Color online) Energy vs lattice-constant curves for fcc Ni in the DFT-LDA scheme and in the $LDA + DMFT$ scheme based on the FP-LMTO (top) and FP-KKR methods (bottom). The zero of the energy of each curve is set to its own minimum value $E_{0}$ and three chosen values of $U$ are presented $(T = 400 K)$ . The experimental value of the lattice constant is indicated by the arrow.Reuse & Permissions
Figure 4
(Color online) Energy versus lattice-constant curves for $γ -Mn$ in the DFT-LDA scheme and in the $LDA + DMFT$ scheme based on the FP-LMTO method. The zero of the energy of each curve is set to its own minimum value $E_{0}$ and two chosen values of $U$ are presented $(T = 400 K)$ . The lattice constant that corresponds to the experimental atomic volume is indicated by the arrow. In the inset we can observe the total energy for $LDA + DMFT$ simulation at $U = 2.6 eV$ (big points) as function of the atomic volume compared to the standard Birch-Murnaghan equation of state (solid line).Reuse & Permissions
Figure 5
(Color online) Local magnetic moment $μ$ and Galitskii-Migdal contribution to the total energy $⟨ {\hat{H}}_{U} ⟩$ as function of the lattice constant for $γ -Mn$ . While it is not observable from the picture the magnetic moment of the $LDA + DMFT$ simulation is increased with respect to its bare LDA value. For $U = 2.6 eV$ the increase in the magnetic moment is about $0.02 μ_{B}$ while for $U = 3.0 eV$ it is about $0.03 μ_{B}$ . Interestingly no magnetic moment is created if the starting Kohn-Sham densities is nonmagnetic.Reuse & Permissions

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