Multiple-scattering formalism for correlated systems: A KKR-DMFT approach

We present a charge and self-energy self-consistent computational scheme for correlated systems based on the Korringa-Kohn-Rostoker (KKR) multiple scattering theory with the many-body effects described by the means of dynamical mean field theory (DMFT). The corresponding local multiorbital and energy dependent self-energy is included into the set of radial differential equations for the single-site wave functions. The KKR Green’s function is written in terms of the multiple scattering path operator, the later one being evaluated using the single-site solution for the $t$-matrix that in turn is determined by the wave functions. An appealing feature of this approach is that it allows to consider local quantum and disorder fluctuations on the same footing. Within the coherent potential approximation (CPA) the correlated atoms are placed into a combined effective medium determined by the DMFT self-consistency condition. Results of corresponding calculations for pure Fe, Ni, and ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ alloys are presented.

Figure 1

(Color online) The complex energy contours used within the self-consistent LDA-DMFT approach, combined with the KKR formalism. The solution of the radial equation allows the evalaution of the single-site scattering matrix $t\left(E\right)$ and the scattering path operator ${\tau }_{L,L^{\prime }}^{n{n}^{\prime }}\left(E\right)$ from which the KKR Green’s function is constructed. The projection of the Green’s function is perfomed according to Eq. (22). The impurity Green’s function is then used to solve the many-body problem within the spin-polarized $T$-matrix FLEX solver of the DMFT approach.

Figure 2

Spin-resolved density of states of bcc Fe as calculated within the LDA (dashed line) and the LDA-DMFT (full line) using the KKR method (DMFT parameters, $U=2\mathrm{eV},J=0.9\mathrm{eV},T=400\mathrm{K}$).

Figure 3

Spin-resolved density of states of fcc Ni as calculated in the LDA (dashed line) and the LDA-DMFT (full line) using the KKR method (DMFT parameters, $U=3\mathrm{eV},J=0.9\mathrm{eV},T=400\mathrm{K}$).

Figure 4

Spin magnetic moments of Fe (circles) and Ni (squares) in the ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ alloy calculated using the plain LDA (open symbols) and the LDA-DMFT methods (full symbols).

Figure 5

Left, concentration dependence of the real part of the spin-resolved self-energy for Fe. Only results for $t_{2g}d$ orbitals are shown. Right, same as in the left-hand panel but for Ni.