Magnetism trends in doped Ce-Cu intermetallics in the vicinity of quantum criticality: Realistic Kondo lattice models based on dynamical mean-field theory

The quantum critical point (QCP) in the archetypical heavy-fermion compound ${\mathrm{CeCu}}_6$ doped by Au is described, accounting for the localized $4f$ electron of Ce, using realistic electronic structure calculations combined with dynamical mean-field theory. Magnetism trends in $\mathrm{Ce}{\left({\mathrm{Cu}}_{1-\epsilon }{\mathrm{Au}}_{\epsilon }\right)}_6$ ($0<\epsilon \ll 1$) are compared with those in Co-doped ${\mathrm{CeCu}}_5$, which resides on the nonferromagnetic side of the composition space of one of the earliest rare-earth permanent magnet compounds, $\mathrm{Ce}{(\mathrm{Co},\mathrm{Cu})}_5$. The construction of a realistic Doniach phase diagram shows that the system crosses over a magnetic quantum critical point in the Kondo lattice in $0.2<x<0.4$ of $\mathrm{Ce}{\left({\mathrm{Cu}}_{1-x}{\mathrm{Co}}_x\right)}_5$. Comparison between Au-doped ${\mathrm{CeCu}}_6$ and Co-doped ${\mathrm{CeCu}}_5$ reveals that the swept region in the vicinity of QCP for the latter thoroughly covers that of the former. The implications of these trends on the coercivity of the bulk rare-earth permanent magnets are discussed.

Figure 1

Realistic Doniach phase diagram for the target compounds with a rescaled horizontal axis to measure an effective distance to the magnetic quantum critical point for each target compound. There are the antiferromagnetic (AFM) phase and the Kondo-screened paramagnetic (PM) phase. It is seen that Co-doped ${\mathrm{CeCu}}_5$ moves from the magnetic side towards the Kondo-screened phase crossing the QCP, while Au-doped ${\mathrm{CeCu}}_6$ moves in the opposite direction. Arrows are a guide for the eye.

Figure 2

Calculated hybridization function for the target compounds within $\mathrm{LDA}+\mathrm{Hubbard}-\mathrm{I}$.

Figure 3

Schematic picture for local-level splitting caused by spin-orbit interaction and crystal fields.

Figure 4

Calculated temperature dependence of the reciprocal of staggered magnetic susceptibility for ${\mathrm{CeCu}}_6$, the reference compound. The data with $\alpha =1.135$, specified with an asterisk, correspond to the realistic data point.

Figure 5

Realistic Doniach phase diagram for the target compounds with the bare energy scale of the Kondo couplings.