Effects of Eu doping on SmB${}_6$ single crystals

The various phases in Sm${}_{1-x}$Eu${}_x$B${}_6$ are investigated based on magnetic susceptibility, resistivity, and Hall effect measurements. The end compounds are a Kondo insulator (SmB${}_6$) and a polaronic ferromagnet (EuB${}_6$). For $x$ ≈ 0.2, the ground state undergoes a transition from a Kondo insulator to an antiferromagnetic (AF) insulator phase. Further doping induces a transition to an AF metal at $x$ ≈ 0.4. The spin gap is reduced rapidly with the Eu substitution, while there is a charge gap up to $x$ ≈ 0.4. The Hall effect indicates a dramatic decrease in the carrier density at low temperatures ($T$) for the Kondo insulator regime, whereas, the carrier density is almost independent of $T$ in the AF metallic phase.

Figure 1

Phase diagram of Sm${}_{1-x}$Eu${}_x$B${}_6$. Solid diamonds, solid circles, and open triangles correspond to the transport gap, the Néel, and the Curie temperatures, respectively. The vertical dashed line is a guide to the eye for the phase boundary between the AF insulator and the AF metal. The insulating phase for small $x$ originates from the Kondo insulator SmB${}_6$. The inset shows the effective moment for Sm${}_{1-x}$Eu${}_x$B${}_6$.

Figure 2

(a) $T$ dependence of $M/H$ for $x$ $=$ 0.1, 0.15, 0.2, and 0.25, where $H$ $=$ 100 Oe. $M/H$ for SmB${}_6$ is shown in the inset. (b) $T$ dependence of $M/H$ for $x$ $=$ 0.4, 0.6, and 0.95, where $H$ $=$ 100 Oe. The inset displays $M/H$ for EuB${}_6$.

Figure 3

(a) The magnetic susceptibility data between 40 and 150 K for $x$ $=$ 0.0. The solid curve is a fit curve to $\chi \left(T\right)=(C/T)\exp (-{\Delta }_s/k_{B}T)$ $+$ ${\chi }_0$. (b) Effective Curie constant $T\chi$($T$) for $x$ $=$ 0.1 as a function of temperature.

Figure 4

(a) $T$ dependence of the resistivity for $x$ $=$ 0.0, 0.1, 0.2, and 0.3. The inset displays $\rho$/$\rho$ (300 K) for $x$ $=$ 0.3, 0.4, 0.6, and 0.8. (b) Thermal activation of $\rho$ ($T$) for $x$ ≤ 0.3. The transport gaps are shown in the inset.

Figure 5

(a) The Hall coefficient for SmB${}_6$ vs 1/$T$. $E_{\mathrm{p}}$ and $E_{\mathrm{g}}$ indicate the intragap bound-state binding energy and charge gap, respectively.[27] The inset displays the Hall resistivity for selected $T$. (b) Carrier density as a function of $T$ for $x$ ≤ 0.4.