First-Principles Simulations of Heavy Fermion Cerium Compounds Based on the Kondo Lattice

We propose a new framework for first-principles calculations of heavy-fermion materials. These are described in terms of the Kondo lattice Hamiltonian with the parameters extracted from a realistic density functional based calculation which is then solved using continuous-time quantum Monte Carlo method and dynamical mean field theory. As an example, we show our results for the Néel temperatures of cerium-122 compounds ($\mathrm{Ce}{X}_2{\mathrm{Si}}_2$ with $X=\mathrm{Ru}$, Rh, Pd, Cu, Ag, and Au) where the general trend around the magnetic quantum critical point is successfully reproduced. Our results are organized on a universal Doniach phase diagram in a semiquantitative way.

Figure 1

The hybridization function $\mathrm{Tr}\Im \Delta (ϵ)/14$ between the conduction band and the $4f$ electrons calculated by $\mathrm{LDA}+\mathrm{\text{Hubbard I}}$ for $\mathrm{Ce}{X}_2{\mathrm{Si}}_2$ with $X=\mathrm{Ru}$, Rh, Pd, and Ag. The origin of the energy is set to be the Fermi level.

Figure 2

Determination of Néel temperatures for several settings of the Hund coupling $J_{\mathrm{Hund}}$. We see that the Néel temperature disappears at the point where $J_{\mathrm{Hund}}$ takes the value between 0.96 and 0.98 eV.

Figure 3

Material-specific Doniach phase diagrams for $\mathrm{Ce}{X}_2{\mathrm{Si}}_2$ with (a) $X=\mathrm{Ru}$, Cu, and Rh and with (b) $X=\mathrm{Pd}$, Au, and Ag. The realistic results with $J_{\mathrm{Hund}}=0.94\mathrm{eV}$ are marked with the larger plot symbols.

Figure 4

Universal Doniach phase diagram for the material family of $\mathrm{Ce}{X}_2{\mathrm{Si}}_2$. The horizontal axis is defined as follows: $t\equiv [N_F{J}_K\rho (0)-N_F{J}_K\rho (0){|}_{\mathrm{QCP}}]/N_F{J}_K\rho (0){|}_{\mathrm{QCP}}$. The line is a guide for the eye. We plot ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ with an asterisk mark to note as it apparently has a finite Néel temperature but that just reflects the result that ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ is very close to QCP as can be seen in Fig. 3.