Terahertz spectroscopy of low-energy excitations in $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$

The origin of low-energy excitations in the polycrystalline $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ manganite is explored by terahertz and infrared spectroscopies. The transition from the charge and/or orbital to antiferromagnetic order ($T_{\mathrm{N}}=130-140\mathrm{K}$) is seen as smooth (spread over a temperature range from 50 to 100 K) decrease of free-carrier conductivity with the activation energy change from 86 meV (high temperatures) to 0.52 meV (low temperatures). A broad relaxation is observed at around $10\mathrm{c}{\mathrm{m}}^{-1}$ which we associate with the dynamics of free charge carriers in the presence of random localizing potential. We discover an absorption resonance at $\approx 50\mathrm{c}{\mathrm{m}}^{-1}$ below $T_{\mathrm{N}}$ that is assigned to the formation of hybridized “acoustic phonon-magnon” quasiparticles.

Figure 1

The x-ray-diffraction patterns of $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ at room temperature.

Figure 2

Terahertz-infrared spectra of the reflection coefficient (a), real part of permittivity (b), and ac conductivity (c) of the $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline sample measured at various temperatures as indicated. The solid lines display the results of the least-square fits of the measured spectra of the reflection coefficient together with the directly measured terahertz conductivity and permittivity spectra (dots below $\approx 50\mathrm{c}{\mathrm{m}}^{-1}$) using Eqs. (1, 2, 3). The dashed line in panel (c) corresponds to the frequency squared dispersion of the lowest-frequency infrared phonon “tail.” Panel (d) shows spectral contributions [Eqs. (1)–(3)] separately in the spectra of imaginary permittivity measured at $T=150\mathrm{K}$.

Figure 3

A diagram showing the relationship between the observed phonons’ density of states in the IR spectrum (left) of polycrystalline $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ and the dispersion curves of the hypothetical cubic phase along the three directions in the Brillouin zone (right) [21]. The circles denote phonon modes that are activated in the infrared spectra of the lower-symmetry orthorhombic modification (space group Pnma).

Figure 4

Temperature dependence of the parameters of dispersion mechanisms observed in the THz-IR spectra of the $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ polycrystalline sample and obtained by least-square fitting of the spectra presented in Fig. 2, as described in the text: dc conductivity ${\sigma }_0$ of free charge carriers (a), dielectric contribution $\mathrm{\Delta }{\varepsilon }_{\mathrm{rel}}$ (b) and relaxation frequency ${\gamma }_{\mathrm{rel}}$ (c) of relaxation around $10\mathrm{c}{\mathrm{m}}^{-1}$, dielectric contribution Δε and oscillator strength $f$ (d), and damping constant γ and frequency ${\nu }_0$ of the Lorentzian at $52\mathrm{c}{\mathrm{m}}^{-1}$ (e).

Figure 5

(a, b) Terahertz spectra of real and imaginary parts of dielectric permittivity of polycrystalline $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ measured at different temperatures. Only results of least-square fitting of experimental spectra are shown for clarity. Appearance below $T_{\mathrm{N}}=130-140\mathrm{K}$ of a mode at $52\mathrm{c}{\mathrm{m}}^{-1}$ is clearly seen. (c, d) Temperature dependences of real and imaginary parts of dielectric permittivity of polycrystalline $\mathrm{E}{\mathrm{u}}_{0.42}\mathrm{S}{\mathrm{r}}_{0.58}\mathrm{Mn}{\mathrm{O}}_3$ at a frequency of 1 THz [spectra in panels (a) and (b)]. Kinks are clearly visible demonstrating appearance of the $52\text{−}\mathrm{c}{\mathrm{m}}^{-1}$ underdamped mode in the antiferromagnetically ordered phase.