High-temperature terahertz absorption band in rare-earth gallium garnet

In addition to the absorption due to known optical phonons, we found a temperature-dependent absorption band at 2 THz in garnet-type $\mathrm{H}{\mathrm{o}}_3\mathrm{G}{\mathrm{a}}_5{\mathrm{O}}_{12}$, at temperatures in the range of 450–540 K. The optical and electrical properties reveal that the absorption band at 2 THz is not produced by mechanisms related to soft phonons, rattling phonons, impurities, or charge density waves, but rather to polaron conduction. Our analysis of the scattering rates and optical mobility shows that electron transport via the intermediate polaron is significant in this absorption band. Electrical measurements also support the existence of polarons in $\mathrm{H}{\mathrm{o}}_3\mathrm{G}{\mathrm{a}}_5{\mathrm{O}}_{12}$. This paper facilitates a method to investigate charge carrier transport from an optical point of view using terahertz time-domain spectroscopy, which we demonstrate using $\mathrm{H}{\mathrm{o}}_3\mathrm{G}{\mathrm{a}}_5{\mathrm{O}}_{12}$.

Figure 1

(a) Real part ${\varepsilon }^{\prime }\left(\omega \right)$ and (b) imaginary ${\varepsilon }^{\prime \prime }\left(\omega \right)$ parts of complex dielectric functions in HoGG at 77, 300, 500, and 600 K. Red and black circles represent the experimental data in (a) and (b), respectively. Black and yellow lines indicate the parameter fits by Eq. (1) in (a) and (b), respectively. Blue and orange dotted lines are components of phonon A and background absorption in (b), respectively. Green dotted line shows a component of the dielectric relaxation in (b). Red dotted line shows a component of absorption band at 2 THz in (b).

Figure 2

Temperature dependence of (a) resonance frequency $f_{0|\mathrm{ph}-A}$, (b) scattering rate ${\Gamma }_{\mathrm{ph}-A}$, and (c) oscillation strength ${\Omega }_{\mathrm{ph}-A}$ for optical phonon A. A black square indicates experimental data for optical phonon A. Black line in (a) is a parameter fit to the Grüneisen approximation. (d) Temperature dependence of normalized phonon number in background absorption. Black line shows a parameter fit to the Bose-Einstein statistics. (e) Temperature dependence of relaxation time ${\tau }_{\mathrm{rel}}$. Black line shows a parameter fit to the Arrhenius law.

Figure 3

Temperature dependence of (a) oscillation strength Ω, and (b) oscillation frequency $f_0$ of absorption band at 2 THz. The black line in (a) shows a third-order spline interpolation.

Figure 4

Temperature dependence of scattering rate Γ of absorption band at 2 THz. The green dotted line in (a) shows a parameter fit to a CDW model, which is proportional to a square of temperature. The red and blue dotted lines in (a) show parameter fits for an acoustic phonon scattering rate ${\Gamma }_{ac}$ and LO phonon scattering rate ${\Gamma }_{\mathrm{LO}}$. The brown line shows the sum of ${\Gamma }_{ac}$ and ${\Gamma }_{\mathrm{LO}}$. (b) Temperature dependence of the optical mobility ${\mu }_{\mathrm{opt}}$. The black line shows a parameter fit to a polaron conduction model for the mobility, which was assumed that a polaron mass is constant in whole temperature range.

Figure 5

Temperature dependence of the electrical resistivity ρ. The blue, green, and red lines show fits to thermally activated tunnel hopping, polaron conduction, and residual scattering models, respectively. The inset shows the interdigitated electrodes used in the electrical measurements; the geometry of these electrodes is described by $a=0.5\mathrm{mm}$, $b=0.1\mathrm{mm}$, $c=0.1\mathrm{mm}$, $d=0.1\mathrm{mm}$, and $e=9\mathrm{mm}$.