Correlated electronic structure with uncorrelated disorder

A. Östlin, L. Vitos, and L. Chioncel

Phys. Rev. B 98, 235135 – Published 17 December 2018

Abstract

We introduce a computational scheme for calculating the electronic structure of random alloys that includes electronic correlations within the framework of the combined density functional and dynamical mean-field theory. By making use of the particularly simple parametrization of the electron Green's function within the linearized muffin-tin orbitals method, we show that it is possible to greatly simplify the embedding of the self-energy. This in turn facilitates the implementation of the coherent potential approximation, which is used to model the substitutional disorder. The computational technique is tested on the Cu-Pd binary alloy system, and for disordered Mn-Ni interchange in the half-metallic NiMnSb.

Received 23 July 2018
Revised 11 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.235135

Physics Subject Headings (PhySH)

First-principles calculations

Disordered alloys Half-metals Random & disordered media Strongly correlated systems

Coherent potential approximation Density functional theory Dynamical mean field theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Östlin¹, L. Vitos^2,3,4, and L. Chioncel^5,1

¹Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
²Department of Materials Science and Engineering, Applied Materials Physics, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
³Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
⁴Research Institute for Solid State Physics and Optics, Wigner Research Center for Physics, P.O. Box 49, H-1525 Budapest, Hungary
⁵Augsburg Center for Innovative Technologies, University of Augsburg, D-86135 Augsburg, Germany

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Vol. 98, Iss. 23 — 15 December 2018

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Images

Figure 1
Schematic flow diagram of the main DMFT-CPA loop, as implemented within the $z MTO$ +DMFT formalism [36]. Inputs are the alloy component–dependent potential parameters $C^{i}, Δ^{i}$ , and $γ^{i}$ , taken from a LDA-level self-consistent EMTO-CPA calculation. For each Matsubara frequency along the imaginary energy axis, the CPA equations are solved self-consistently. The alloy impurity Green's functions are supplied to the DMFT impurity problem, which is solved self-consistently, giving alloy component self-energies as output. These self-energies in turn modify the potential parameters which is the key for the combined self-consistency of CPA and DMFT equations. To make the scheme charge self-consistent, the change in the density due to correlation, $Δ n (r)$ , can be added to the EMTO-CPA charge density $n (r)$ , and then the Kohn-Sham equations are iterated until convergence.
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Figure 2
(a) Partial density of states of Pd in the ${Cu}_{0.75} {Pd}_{0.25}$ alloy, as a function of Coulomb interaction $U$ . Inset: Experimental photoemission data taken from Ref. [61]. (b) Real parts (solid lines) and imaginary parts (dashed lines) of the Pd self-energy along the real-energy axis, for $U = 3$ eV and $J = 0.9$ eV. The $t_{2 g}$ states are shown with blue boxes and the $e_{g}$ states with red disks. The insets in (b) are the real and imaginary parts of the $t_{2 g}$ self-energy for different concentrations of palladium running from $x = 1.0$ (blue) until $x = 0.1$ (orange).
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Figure 3
(a) Fermi surface (Bloch spectral function) for the ${Cu}_{0.60} {Pd}_{0.40}$ alloy with $U = 4 eV$ . (b) Difference of spectra between $U = 4$ eV and $U = 0$ . The color maps indicate the spectral weight in arbitrary units.
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Figure 4
Imaginary part of the effective medium $\tilde{P} (E)$ along the real-energy axis. (a) $\tilde{P} (E)$ for several values of the Coulomb parameters and for a fixed concentration ${Cu}_{0.3} {Pd}_{0.7}$ . Red lines correspond to the LDA solution ( $U = 0$ ). $t_{2 g}$ states are shown with solid lines and $e_{g}$ states are shown with dashed lines. (b) $\tilde{P} (E)$ for several values of the concentration $x$ and fixed Coulomb $U = 3$ eV and Hund's coupling $J = 0.9$ eV. The concentration ranges from pure Cu ( $x = 0$ , orange line) to pure Pd ( $x = 1$ , blue line). Only the $t_{2 g}$ orbital is shown.
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Figure 5
(a) Spin-resolved spectral function around the Fermi level for NiMnSb with Mn-Ni interchange, from $0 %$ (no disorder, light-blue solid line) to $0.1 %$ (dark-blue dashed line), $0.5 %$ (green dash-dotted line). The red solid line corresponds to $U = 0$ and no disorder. (b) Same as in (a), but for the larger degrees of disorder $1 %$ (dark-blue dashed line), and $5 %$ (green dash-dotted line).
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Figure 6
(a) Self-energy along the real axis for the $d - t_{2 g}$ states of Mn, at a Mn-Ni interchange disorder of $5 %$ . Dark-blue lines correspond to Mn on the Mn site, and red lines correspond to Mn on the Ni site. Dashed lines with triangles pointing down correspond to the spin-down channel, while solid lines with triangles pointing up correspond to the spin-up channel. The Mn self-energy for NiMnSb without disorder (light blue) has been plotted for comparison. (b) Same as in (a), but for the Mn $d - e_{g}$ states. The inset in (b) shows the NQP states in the $e_{g}$ spin-down channel for different disorder concentrations.
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