Physical properties of ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals

We study the magnetic susceptibility, electrical resistivity, Hall effect, and heat capacity of single crystals of ${\mathrm{Sm}}_x{\mathrm{B}}_6$ for $x=1,0.94,0.8,$ and 0.75. Remarkably, the overall properties of the crystals do not qualitatively depend on the density of vacancies. The topological surface states are seen at low temperatures in the electrical transport properties as the bulk conductivity freezes out. Even a large number of Sm vacancies does not close the hybridization gap. The linear term in the specific heat $\gamma$, of unclear origin, remains large but decreases gradually with $x$. The shoulder in the density of states, brought by the hybridized $4f$ states and observed in the susceptibility and the specific heat, does not move but decreases its height with decreasing $x$. The specific heat also displays a weak Schottky anomaly at about 1.5 K for all $x$, except for the $x$ = 0.75 sample. This Schottky anomaly is only slightly field dependent and of unknown origin.

Figure 1

Magnetic susceptibility vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals, measured using a SQUID magnetometer. In the inset we plot the fraction of ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ ions for crystals with different contents of vacancies.

Figure 2

Resistivity of ${\mathrm{Sm}}_x{\mathrm{B}}_6$ for as-grown single crystals vs temperature. The lower inset shows the bulk resistivity vs inverse temperature for the same crystals. The upper inset is the actual image of the transport geometry used in measurements.

Figure 3

Hall coefficient $R_H$ vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals. In the inset we plot the absolute value of $R_H$ vs $1/T$ for the same samples. The dashed lines show $|R_H|\propto exp(E_A/k_{B}T)$ variation.

Figure 4

Hall mobility vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals.

Figure 5

Hall coefficient vs $\rho \chi$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals in the 180 $\lesssim T\lesssim$ 350 K temperature range. In the lower inset we plot the electron concentration values ($=1/e{R}_o$) as a function of $x$. The upper inset shows the determination of $R_o$ for the $x=0.94$ and $x=0.75$ samples.

Figure 6

$C_p/T$ vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals. The inset shows $C_p/T$ vs $T$ for the $x=0.94$ sample at three different magnetic fields.

Figure 7

Low-temperature $C_p/T$ vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals. The inset shows the electronic specific heat coefficient vs $x$.

Figure 8

Low-temperature $C_p/T$ vs $T$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals at various magnetic fields.

Figure 9

Low-temperature excess heat capacity $\mathrm{\Delta }C=C_p-C_{el}$ for ${\mathrm{Sm}}_x{\mathrm{B}}_6$ single crystals in various magnetic fields.