Fermi surface investigation of the filled skutterudite ${\mathrm{LaRu}}_4{\mathrm{As}}_{12}$

Of all stoichiometric filled-skutterudite superconductors, ${\mathrm{LaRu}}_4{\mathrm{As}}_{12}$ has the highest critical field and temperature. Here we report on a detailed Fermi-surface investigation of ${\mathrm{LaRu}}_4{\mathrm{As}}_{12}$ by means of de Haas–van Alphen measurements and density-functional-theory calculations. We find evidence for a nearly spherical and a multiply connected Fermi-surface sheet. The different effective masses and mass enhancements for the two sheets support two-band superconductivity, which was inferred from previous specific-heat measurements. Furthermore, quantum oscillations persist as well in the superconducting phase. We use two models to describe the additional damping, yielding energy gaps differing by a factor of 5.

Figure 1

Raw torque signal near $B\parallel a$. Black and red curves represent up- and down-sweep of the magnetic field, respectively. Lower inset: Zoom into the high-field region showing quantum oscillations. The torque oscillations shown here are relatively small due to the small angle between magnetic field and the [100] direction. Upper inset: Unit cell for ${\mathrm{LaRu}}_4{\mathrm{As}}_{12}$. Blue: La, red: Ru, grey: As; created using Ref. [30].

Figure 2

Inset: Torque signal after subtraction of a second-order background polynomial. Main panel: Corresponding frequency spectrum obtained by Fourier transformation.

Figure 3

Angular dependence of experimental (large symbols) and calculated dHvA frequencies (lines: fplo code; small, open symbols: kansai code). Left panel: Rotation from $B\parallel \left[100\right]$ to $B\parallel \left[010\right]$. Note that the dHvA frequencies are not symmetric around the [110] axis because the $Im\overline{3}$ structure does not possess any corresponding symmetry element. Right panel: Rotation from $B\parallel \left[100\right]$ to $B\parallel \left[011\right]$.

Figure 4

Influence of $y$ and $z$ atomic positions. (a) Calculated band structure (using the LDA exchange functional) for the positions measured by Braun and Jeitschko [2] (red), Shirotani et al. (private communication in Ref. [25]) (blue), and optimized by fplo (green). (b) Corresponding DOS. For clarity, the graph only shows a narrow region around $E_F$.

Figure 5

(a) Calculated band structure of ${\mathrm{LaRu}}_4{\mathrm{As}}_{12}$ along high-symmetry lines of the BZ. Bands 175 (magenta) and 176 (green) cross $E_F$. (b) Calculated DOS near $E_F$. Shaded areas mark the contributions of Ru-$4d$ (orange) and As-$4p$ states (cyan). (c) Calculated FS of band 175. (d)–(f) Calculated FS of band 176, shown from different perspectives: (d) identical to the sketch in (a), (e) parallel to the [110] axis, and (f) parallel to the [111] axis. All results in this figure were obtained using the fplo code.

Figure 6

Temperature-dependent amplitudes, taken at ${\mathrm{\Theta }}_{0\overline{1}1}=5^{\circ }$, with fit lines determined by use of the Lifshitz-Kosevich formula.

Figure 7

Field dependence of dHvA signals at ${\mathrm{\Theta }}_{001}={42}^{\circ }$. The blue curve shows the torque signal after subtraction of a nonoscillatory background. Black symbols represent a Dingle plot of the amplitudes for $\delta =1.216$ kT, the red line shows a linear fit to the data above the superconducting phase. $B_{c2}$ was determined by the onset of the peak effect. To reduce interference from smaller frequencies, we averaged over four periods per data point.

Figure 8

Field dependence of the oscillation amplitude reduction within the superconducting phase. Symbols indicate dHvA oscillation amplitudes rescaled by $R_D$ and $R_T$. Lines are fits of different theoretical models to the data (see text).