Bandlike electrical transport in $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ manganites

The conductivity and dielectric permittivity spectra of polycrystalline manganites $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ with $x=0.3$, 0.4, and 0.5 have been measured in a broad frequency range ($5–3000\mathrm{c}{\mathrm{m}}^{-1}$) down to low temperatures. From the dispersion analysis the existence of a Drude component can be established that is associated with small polarons coherently moving within a band several meV wide. The temperature-dependent conductivity shows an activated behavior with an activation energy of approximately 165 meV above 170 K and 4.8 meV below 120 K. The change in the activation energy is assigned to the onset of magnetic order at 120 K. In all three samples an absorption band is discovered at $40–60\mathrm{c}{\mathrm{m}}^{-1}$ that is associated with the transition between Stark-split $\mathrm{P}{\mathrm{r}}^{3+}$ electron states which gain optical activity due to coupling to acoustical phonons.

Figure 1

X-ray powder diffraction pattern for $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ ($\mathrm{Cu}K\alpha$). (a) Profile of Rietveld refinements of $\mathrm{P}{\mathrm{r}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. The observed (circles), calculated (solid line), and difference (bottom line) profiles are shown. The vertical bars show the peak positions of the reflexes. (b) The diffraction patterns of $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ with $x=0.3$, 0.35, 0.4, 0.45, and 0.5 are indexed in the orthorhombic space group Pnma. (c) High-resolution x-ray powder diffraction of $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ in the ${47}^{\circ }<2\theta <{48}^{\circ }$ region. (d) The lattice parameters and the unit cell volume of the $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ solid solution samples. The values of the lattice parameter $b$ were divided by a factor $2^{1/2}$. Symbols represent experimental data. The error bars are smaller than the symbol size in all cases.

Figure 2

Spectra of the (a) reflection coefficient and (b) real and (b) imaginary parts of the dielectric permittivity and of (d) the conductivity of the $\mathrm{P}{\mathrm{r}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline sample measured at various temperatures. Solid lines show the results of the least-squares fits of the measured infrared reflectivity spectra, together with the directly measured terahertz spectra (dots below $60\mathrm{c}{\mathrm{m}}^{-1}$) using expressions (1, 2, 3) (see the text). The dashed line in (d) corresponds to the frequency squared dispersion of the lowest-frequency infrared phonon “tail.”

Figure 3

Same as Fig. 2, for the $\mathrm{P}{\mathrm{r}}_{0.6}\mathrm{C}{\mathrm{a}}_{0.4}\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline sample with spectral contributions [expressions (1, 2, 3)] shown separately.

Figure 4

Same as Fig. 2, for the $\mathrm{P}{\mathrm{r}}_{0.5}\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline sample.

Figure 5

Room-temperature infrared conductivity spectra of $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline samples obtained by a Kramers-Kronig analysis of the reflectivity spectra. The onset of absorption due to polaronic excitation is shown with an oval.

Figure 6

(a) Arrhenius plot of the dc conductivity of $\mathrm{P}{\mathrm{r}}_{1-x}\mathrm{C}{\mathrm{a}}_x\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline samples obtained by least-squares fitting of the spectra presented in Figs. 2, 3, 4, as described in the text. The values of ${\sigma }_0$ correspond to the Drude term (2), whose spectral contribution is shown separately in Fig. 3. The dashed lines show ranges (indicated with numbers; $h$ is the Planck's constant, $c$ is the speed of light) of activation energies describing the variations of conductivity at high ($E_a^h$) and low ($E_a^l$) temperatures. (b), (c) Temperature dependences of the parameters of the Debye relaxator term (1) [the spectral contribution is shown separately for $x=0.4$ in Fig. 3] and the dielectric contribution $\mathrm{\Delta }{\varepsilon }_{\mathrm{rel}}$ and ${\gamma }_{\mathrm{rel}}$ obtained by least-squares fitting of the spectra presented in Figs. 2, 3, 4, as described in the text.