Terahertz conductivity of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$

We investigate the optical conductivity of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ across the ferromagnetic to paramagnetic transition that occurs at $x=0.8$. The thin films were grown by metalorganic aerosol deposition with $0\le x\le 1$ onto ${\mathrm{NdGaO}}_3$ substrates. We performed terahertz frequency domain spectroscopy in a frequency range from 3 to $40 {\mathrm{cm}}^{-1}$ (100 GHz to 1.4 THz) and at temperatures ranging from 5 to 300 K, measuring transmittivity and phase shift through the films. From this we obtained the real and imaginary parts of the optical conductivity. The end-members, ferromagnetic ${\mathrm{SrRuO}}_3$ and paramagnetic ${\mathrm{CaRuO}}_3$, show a strongly frequency dependent metallic response at temperatures below 20 K. Due to the high quality of these samples we can access pronounced intrinsic electronic contributions to the optical scattering rate, which at 1.4 THz exceeds the residual scattering rate by more than a factor of three. Deviations from a Drude response start at about 0.7 THz for both end-members in a remarkably similar way. For the intermediate members a higher residual scattering originating in the compositional disorder leads to a featureless optical response instead. The relevance of low-lying interband transitions is addressed by a calculation of the optical conductivity within density functional theory in the local-density approximation.

Figure 1

Resistivity values, obtained from low-frequency optical data (symbols) and four-point dc measurements (lines). Optical relative resistivity data were calculated from low-frequency (between 4 and $5 {\mathrm{cm}}^{-1}$) THz data by normalizing to the 300 K value; dc data were normalized to the 280 K value. Inset: Phase diagram of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$. Circles represent Curie temperatures of differently doped thin-film samples [20]; squares indicate the doping levels that were investigated in this optical study.

Figure 2

(a) Transmittivity and (b) phase data of ${\mathrm{CaRuO}}_3$ on ${\mathrm{NdGaO}}_3$ and bare ${\mathrm{NdGaO}}_3$ substrate at 300 and 5 K. Open circles correspond to substrate data; solid squares correspond to thin-film samples. The inset in (a) shows that multiple reflections in a dielectric substrate lead to Fabry-Pérot oscillations in the raw data.

Figure 3

Real and imaginary parts of the optical conductivity of the four studied ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ compositions at various temperatures between 300 and 5 K [33, 35].

Figure 4

${\sigma }_1\left(\omega \right)$ of ${\mathrm{SrRuO}}_3$ for low temperatures. The dotted lines at 5, 20, and 40 K are Drude fits following Eq. (1) with ${\sigma }_{\mathrm{dc}}$ values fixed from dc measurements. All points were taken into account for the 20 and 40 K fits; the 5 K fit includes only frequencies below $30 {\mathrm{cm}}^{-1}$ due to the non-Drude-like plateau at higher frequencies. Insets (a) and (b) show ${\rho }_1$ and ${\rho }_2$ for corresponding temperatures, respectively.

Figure 5

Frequency-dependent ${\rho }_1$, proportional to the scattering rate $\mathrm{\Gamma }$, at 300, 250, 200, 150, 100, 60, 40, 20, 10, and 5 K. Colors and symbols are as in Fig. 3.

Figure 6

Real part ${\rho }_1$ of complex resistivity, proportional to the scattering rate $\mathrm{\Gamma }$, of ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ at 5 K. The dashed guides indicate the value of the dc value, 1/${\sigma }_{\mathrm{dc}}$. The dotted line indicates the best FL-like fit to the entire data range.

Figure 7

${\rho }_1$, proportional to the scattering rate $\mathrm{\Gamma }$, from extended Drude analysis at frequency $7 {\mathrm{cm}}^{-1}$ for the four different compositions ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ as a function of temperature (main plot) and as a function of Ca content $x$ (inset).

Figure 8

${\sigma }_1$ spectra of ${\mathrm{CaRuO}}_3$ for low temperatures with tentative Drude fits. Due to the high-frequency plateau, the fits do not work at lowest temperatures. Inset: Scattering rates for corresponding temperatures.

Figure 9

(a) Optical conductivity in the LDA approximation with static impurity scattering $1/{\tau }_D=0.008$ eV for ${\mathrm{CaRuO}}_3$ and for ${\mathrm{SrRuO}}_3$ compared to the Drude optical conductivity. For ${\mathrm{SrRuO}}_3$, besides ferromagnetic calculation in an orthorhombic structure, the paramagnetic result in the orthorhombic and cubic structure are also shown. (b) The corresponding optical scattering rates, normalized to the dc value.

Figure 10

$\omega /T$ scaling plots for ${\mathrm{SrRuO}}_3$ and ${\mathrm{CaRuO}}_3$ following Refs. [7, 8].