Separated transport relaxation scales and interband scattering in thin films of ${\mathrm{SrRuO}}_3$, ${\mathrm{CaRuO}}_3$, and ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

The anomalous charge transport observed in some strongly correlated metals raises questions as to the universal applicability of Landau Fermi-liquid theory. The coherence temperature $T_{\text{FL}}$ for normal metals is usually taken to be the temperature below which $T^2$ is observed in the resistivity. Below this temperature, a Fermi liquid with well-defined quasiparticles is expected. However, metallic ruthenates in the Ruddlesden-Popper family frequently show non-Drude low-energy optical conductivity and unusual $\omega /T$ scaling, despite the frequent observation of $T^2$ dc resistivity. Herein we report time-domain THz spectroscopy measurements of several different high-quality metallic ruthenate thin films and show that the optical conductivity can be interpreted in more conventional terms. In all materials, the conductivity has a two Lorentzian line shape at low temperature and a crossover to a one Drude peak line shape at higher temperatures. The two component low-temperature conductivity is indicative of two well-separated current relaxation rates for different conduction channels. In ${\mathrm{SrRuO}}_3$ and ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, both relaxation rates scale as $T^2$, while in ${\mathrm{CaRuO}}_3$ the slow relaxation rate shows $T^2$, and the fast relaxation rate generates a constant background in conductivity. We discuss three particular possibilities for the separation of rates: (a) strongly energy-dependent inelastic scattering; (b) an almost conserved pseudomomentum operator that overlaps with the current, giving rise to the narrower Drude peak; and (c) the presence of multiple conduction channels that undergoes a crossover to stronger interband scattering at higher temperatures. None of these scenarios requires the existence of exotic quasiparticles. However, the interpretation in terms of multiple conduction channels in particular is consistent with the existence of multiple Fermi surfaces in these compounds and with the expected relative weakness of ${\omega }^2$ dependent effects in the scattering as compared to $T^2$ dependent effects in the usual Fermi-liquid treatment. The results may give insight into the possible significance of Hund's coupling in determining interband coupling in these materials. Our results also show a route towards understanding the violation of Matthiessen's rule in this class of materials and deviations from the “Gurzhi” scaling relations in Fermi liquids.

Figure 1

dc resistivity as a function of temperature for the ${\mathrm{SrRuO}}_3$ film for electric field along the $\left[\overline{1}10\right]$ direction. Inset: Resistivity minus residual resistivity as a function of $T^2$ up to 1000 ${\mathrm{K}}^2$. The black dashed line is the linear fit. This figure is adapted from Ref. [22].

Figure 2

(a), (b) 5-K conductivity of a ${\mathrm{SrRuO}}_3$ thin-film sample for $E$//$\left[\overline{1}10\right]$. (a) Real and imaginary part of the complex conductivity, plotted with dc conductivity and a single Drude fitting. (b) The same data as in (a) with two Drude fitting, which is improved compared to that in (a). (c), (d) Complex conductivity at 15 and 25 K, plotted with two Drude fitting sharing the same legend as in (b). (e), (f) Complex conductivity at 35 and 60 K, which can be fit with a single Drude term. (g) Scattering rates for the two phenomenological Drude terms plotted against temperature. The narrow Drude term is fitted with the highest scattering rate that is compatible with the data. (h) The spectral weights of the two Drude terms where they can be resolved separately and the total spectral weight. This figure is adapted from Ref. [22].

Figure 3

dc resistivity as a function of temperature for the ${\mathrm{CaRuO}}_3$ film for the two orthogonal crystallographic directions. Inset: Resistivity minus residual resistivity as a function of $T^{1.5}$. $T^{1.5}$ fits to the data in the temperature range of 4–30 K are shown as black dashed lines.

Figure 4

(a) Real and imaginary THz conductivity of the ${\mathrm{CaRuO}}_3$ thin film with dc values of 5-K data. The black dashed lines show a single Drude term modeling. (b) The same data as in (a), but plotted with a one-Drude-plus-a-constant-term fitting. (c) The same 5-K data as (a) plotted with a logarithmic vertical axis. The two terms in (a) are separately plotted (as indicated by blue and green shaded areas) to show how they contribute to conductivity. (d) Real and imaginary conductivity at 5 K for two orthogonal crystal axes and the corresponding one-Drude-plus-a-constant-term fitting. (e)–(g) Real and imaginary parts of the complex conductivity with dc values for various temperatures as in the annotation of each graph, plotted with the one-Drude-plus-a-constant-term fitting. (h) Single Drude fitting for the data at 100 K. Above 60 K, the conductivity is flat in the measurement range.

Figure 5

(a) Scattering rates of the narrow Drude peak from two Drude modeling as a function of temperature, for the two in-plane directions in the ${\mathrm{CaRuO}}_3$ thin film. The dashed black lines are quadratic fits to the data below 40 K, and extended to higher temperatures. (b) Spectral weight of the narrow Drude peak as a function of temperature. (c) The wide Drude term (incoherent background) part of the conductivity against temperature.

Figure 6

(a) dc resistivity as a function of temperature for the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ film. The data are geometric means of the $\left[\overline{1}10\right]$ and [001] directions of the ${\mathrm{NdGO}}_3$ substrate. Inset: Resistivity minus residual resistivity as a function of temperature squared. Fits to the data in the temperature range 2–32 K are shown as black lines. (b) Real and (c) imaginary parts of the THz conductivity ${\sigma }_{1,2}$ from 3 to 250 K. The markers at zero frequency are dc conductivity. (d) Two Drude fit of dc plus THz data at 3 K. dc conductivity and real and imaginary parts of the optical conductivity are fitted simultaneously. For all THz data, $E//\left[\overline{1}10\right]$.

Figure 7

(a)–(d) Real and imaginary THz conductivity of the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ thin film with dc conductivity at (a) 8 K, (b) 16 K, (c) 40 K, and (d) 50 K. Fitting is presented in dashed lines. For data $\le 40$ K, two Drude terms are required. The 50-K data can be approached by a single Drude model. Green and blue shades correspond to a narrow and wide Drude term, respectively. (e) Spectral weight and (f) scattering rates of the two Drude terms as a function of temperature. The black dashed lines in (f) are quadratic fitting.

Figure 8

(a)–(c) Real part of the complex THz resistivity ${\rho }_1\left(\omega \right)$ at different temperatures for the ${\mathrm{SrRuO}}_3$, ${\mathrm{CaRuO}}_3$, and ${\mathrm{SrRuO}}_3$ thin films, respectively. $E$//$\left[\overline{1}10\right]$ for all the three samples. Quadratic fitting in (b) is presented with black dashed lines. (d) Simulated ${\rho }_1\left(\omega \right)$ by inverting the two Drude conductivities. The scattering rates ${\gamma }_1$ and ${\gamma }_2$ (in a.u.) for the two Drude terms are (0.2, 0.6), (0.2, 1.2), and (0.6, 1.2) for the three modeled curves black, blue, and red, respectively. The spectral weights for the two Drude terms are set to be equal and identical for the three situations.