Electrical transport properties of single-crystal ${\mathbf{CaB}}_{\mathbf{6}},{\mathbf{SrB}}_{\mathbf{6}}$, and ${\mathbf{BaB}}_{\mathbf{6}}$

The electrical resistivity and Hall effect of alkaline-earth-metal hexaboride single crystals are measured as a function of temperature, hydrostatic pressure, and magnetic field. The transport properties vary weakly with the external parameters and are modeled in terms of intrinsic variable-valence defects. These defects can stay either in (1) delocalized shallow levels or in (2) localized levels resonant with the conduction band, which can be neutral or negatively charged. Satisfactory agreement is obtained for electronic transport properties in a broad temperature and pressure range, although fitting the magnetoresistance is less straightforward and a combination of various mechanisms is needed to explain the field and temperature dependences.

Figure 1

Variation of electrical resistivity with temperature for $E_A{\mathrm{B}}_6(E_A=\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})$ single crystals.

Figure 2

The difference between the conductivity and its extrapolated zero-temperature value is plotted vs temperature for some of the $E_A{\mathrm{B}}_6$ single crystals. Below approximately 5 K, the power-law dependence has exponent 1/2.

Figure 3

Variation of Hall resistivity with temperature for $E_A{\mathrm{B}}_6(E_A=\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})$ single crystals.

Figure 4

Hall coefficient dependence on hydrostatic pressure for ${\mathrm{BaB}}_6$ (upper panel) and ${\mathrm{SrB}}_6$ (lower panel) single crystals at two different temperatures. The solid lines are fits to experimental data points using the variable-valence defects model. The insets show how the resistivity for the above crystals varies with pressure.

Figure 5

Hall electron concentration vs temperature for various $E_A{\mathrm{B}}_6$ single-crystal samples. The solid lines are fits to experimental data points using the variable-valence defects model.

Figure 6

Fitting parameters $E_1$ (circles) and $E_2$ (squares) vs electron concentration in $E_A{\mathrm{B}}_6$ single crystals. $U_{eff}=E_2-2E_1$ is the energy of on-site repulsion (rhombus). The solid and dotted lines are to guide the eye.

Figure 7

Temperature variation of the Hall mobility for $E_A{\mathrm{B}}_6$ single crystals. The inset shows how the mobility changes with pressure for two samples.

Figure 8

Low-temperature magnetoresistance for $E_A{\mathrm{B}}_6$ single crystals in different localization regimes. The low-field region is shown in the inset.

Figure 9

Low-temperature magnetoconductance for ${\mathrm{CaB}}_6$ single crystals in the weakly localized regime. The inset shows magnetoresistance as a function of the square of the magnetic field for the crystals in strongly localized and critical regimes.