Realization of Kondo chain in ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$

We revisited the anisotropy of the heavy-fermion material ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$ by measuring the electrical resistivity and magnetic susceptibility along all the principal $\mathbf{a},\mathbf{b}$, and $\mathbf{c}$ axes. Resistivity along the $\mathbf{c}$ axis $\left({\rho }_c\right)$ shows clear Kondo coherence below about 17 K, while both ${\rho }_a$ and ${\rho }_b$ remain incoherent down to 2 K. The magnetic anisotropy is well understood within the theoretical frame of crystalline electric field effect in combination with magnetic exchange interactions. We found the anisotropy ratio of these magnetic exchange interactions $|J_{\text{ex}}^c/J_{\text{ex}}^{a,b}|$ reaches a large value of 4–5. We, therefore, firmly demonstrate that ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$ is a quasi-one-dimensional heavy-fermion compound both electrically and magnetically, and thus provide a realistic example of Kondo chain.

Figure 1

Schematic diagrams of Kondo effects. (a) A local moment (red) immerses in a metal (blue) forming a Kondo singlet. The spin of the local moment is screened by the conduction electrons and forms a resonance (white haze). (b) A dense lattice of local moments in a metal, without Kondo coupling. (c) Appearance of Kondo coherence for a multidimensional dense lattice, leading to heavy-fermion narrow band. (d) A Kondo chain may appear when Kondo coherence is of a one-dimensional characteristic.

Figure 2

Temperature dependence of electrical resistivity of ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$ for current applied along the $\mathbf{a},\mathbf{b}$, and $\mathbf{c}$ axes, respectively. Coherent Kondo scattering behavior is only seen in ${\rho }_c$ for $T$ below 17 K. Inset shows $\rho \left(T\right)$ in a semi-logarithmic frame.

Figure 3

(a) Temperature dependent magnetic susceptibilities of ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$ measured for external field $\mathbf{B}$ parallel to the $\mathbf{a},\mathbf{b}$, and $\mathbf{c}$ axes, respectively. All the measurements were made under $B=0.1\mathrm{T}$ in zero-field cooling protocol. The inset shows Curie-Weiss behavior of ${\chi }_{\text{avg}}\left(T\right)$, where ${\chi }_{\text{avg}}=({\chi }_a+{\chi }_b+{\chi }_c)/3$ is the powder-average susceptibility. (b) Inverse susceptibilities as a function of temperature. The symbols stand for experimental data, while the solid lines are theoretically calculated results based on CEF theory.

Figure 4

(a) Sketch of CEF splitting of ${\mathrm{CeCo}}_2{\mathrm{Ga}}_8$, as well as the contours of $4f$ charge density for each doublet. The calculations were based on the parameters listed in Table 1. (b) Isothermal field dependence of magnetization at 2 K. The symbols denote experimental data, and the solid lines signify simulated ones based on CEF theory without magnetic exchange interactions. The colors are red $\left(\mathbf{a}\right)$, blue $\left(\mathbf{b}\right)$, and green $\left(\mathbf{c}\right)$. (c) Calculated CEF resistivity (left) and specific heat (right) as functions of temperature.