Boson peak in overdoped manganites La${}_{1-x}$Ca${}_x$MnO${}_3$

In the charge-ordered phase of strongly doped manganites La${}_{1-x}$Ca${}_x$MnO${}_3$ ($x\ge 0.5$) absorption lines appear in the terahertz spectral range for commensurate $x$ values right below the charge-ordering temperature. They are connected to acoustic phonons that become optically active by folding of the Brillouin zone. At lower temperatures a strongly asymmetric extra absorption band develops at frequencies corresponding to the position of the lowest-energy van Hove singularity in the reduced Brillouin zone. The band is assigned to the boson peak, i.e., to the excess of lattice vibrational states over the standard Debye contribution. The folded phonons and the boson peak do not show up for incommensurate calcium contents when no distinct Brillouin zone folding exists.

Figure 1

Temperature dependence of the optical properties of La${}_{0.33}$Ca${}_{0.67}$MnO${}_3$ ceramic sample in the THz range. In the low-frequency part of (a) the dielectric permittivity ${\epsilon }^{\prime }\left(\nu \right)$ and (b) the optical conductivity $\sigma \left(\nu \right),$ the charge order transition at $T_{\mathrm{CO}}=240$ K is seen as a dramatic change due to the opening of the energy gap in the far infrared. The arrows indicate the vibrational acoustic modes at 50 cm${}^{-1}$ that become infrared active by Brillouin zone folding due to charge ordering. The inset in panel (a) exhibits the temperature evolution of the THz conductivity measured on a thin epitaxial La${}_{0.33}$Ca${}_{0.67}$MnO${}_3$ film. In the lower panel the inset demonstrates that it is not possible to fit the low-frequency asymmetrical band by a Lorentzian curve (dashed line).

Figure 2

Development of the low-temperature terahertz conductivity of La${}_{1-x}$Ca${}_x$MnO${}_3$ ceramics for different $x$. Close to $x=2/3$ an asymmetric band develops around $20–30$ cm${}^{-1}$, that disappears again upon further doping. The charge-order activated folded modes are indicated by the arrow. Spectrum for $x=0.75$ was taken on a pellet pressed of a powder.[16] The dielectric permittivity ${\epsilon }^{\prime }\left(\nu \right)$ is displayed in the inset for the same compositions.

Figure 3

Explanation of the observed conductivity spectra (that is proportional to absorption) by the vibrational density of states. (a) Optical conductivity of La${}_{0.33}$Ca${}_{0.67}$MnO${}_3$ at two different temperatures. The dashed line corresponds to a $\sigma \left(\nu \right)\propto {\nu }^2$ behavior. (b) Energy dispersion of lattice vibrations calculated for CaMnO${}_3$. For commensurate doping $x=2/3$ the Brillouin zone is folded to one third and the acoustic phonons become optical active around 50 cm${}^{-1}$. In the case of disorder as in polycrystalline samples, a broad distribution with a maximum in the density of states around 25 cm${}^{-1}$ occurs, called the boson peak.

Figure 4

Phonon modes of La${}_{1-x}$Ca${}_x$MnO${}_3$ for different $x=0.5$, $2/3$, 0.9, and 1. While for $x<0.87$ three broad bands are observed that shift to lower frequencies as $x$ increases, above $x=0.87$ the absorption features change to a typical phonon spectrum.