Soft vibrational mode associated with incommensurate orbital order in multiferroic ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$

We report inelastic light scattering measurements of lattice dynamics related to the incommensurate orbital order in ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$. Below the ordering temperature $T_{\mathrm{o}}\approx 250\mathrm{K}$, we observe extra phonon peaks as a result of Brillouin zone folding, as well as a soft vibrational mode with a power-law $T$-dependent energy, $\Omega ={\Omega }_0{(1-T/T_{\mathrm{o}})}^{1/2}$. This temperature dependence demonstrates the second-order nature of the transition at $T_{\mathrm{o}}$, and it indicates that the soft mode can be regarded as the amplitude excitation of the composite order parameter. Our result strongly suggests that the lattice degrees of freedom are actively involved in the orbital-ordering mechanism.

Figure 1

(a) The crystal structure of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ with hexagonal (solid lines) and pseudocubic (dashed lines) unit cells. Ca and Mn1 ions are shown in yellow and red spheres, respectively. Mn2 (green) and Mn3 (blue) ions are shown within oxygen octahedra. Oxygen atoms are not shown. (b) A Mn1-Mn2 chain along the hexagonal $c$ axis. Arrows indicate the local $xyz$ coordinate system for the definition of orbital states (see text).

Figure 2

Powder x-ray diffraction data of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ obtained at room temperature (measurement and simulation).

Figure 3

dc resistivity of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ measured by a two-probe method on a single crystal.

Figure 4

Specific heat of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$. Small variations above 150 K are measurement artifacts related to the thermal properties of the sample mounting we used.

Figure 5

(a) Polarized Raman spectra obtained at $300\mathrm{K}$, offset for clarity. Peaks are located at 209.4, 427.3, 473.7, and $610.2{\mathrm{cm}}^{-1}$ in the $A_g$ spectrum, and at 180.3, 309.8, 397.8, 496.9, 594.6, and $647.2{\mathrm{cm}}^{-1}$ in the $E_g$ spectrum. (b) $A_g$ spectra at selected temperatures, offset for clarity. (c) Color representation of the $A_g$ Raman susceptibility. Dashed line indicates $T_{\mathrm{o}}=250$ K. White arrow indicates $T_{\mathrm{N}}1=90\mathrm{K}$, below which the peak at $411.3{\mathrm{cm}}^{-1}$ gains extra intensity. (d) Positions of prominent phonon peaks near 480 and $610{\mathrm{cm}}^{-1}$ as functions of temperature.

Figure 6

Polarized Raman spectra obtained at 10 K. The measurements are performed on natural facets (NF) parallel to the pseudocubic $\left\{110\right\}$ planes. Note that the measurements presented in Fig. 7 are performed on different and much larger NF that are parallel to the pseudocubic $\left\{100\right\}$ planes. The $A_g$ and $E_g$ spectra are offset for clarity. The soft mode at $\sim 80{\mathrm{cm}}^{-1}$ is absent from the $E_g$ spectrum.

Figure 7

(a) Low-energy Raman spectra at selected temperatures between 10 K and 300 K, offset for clarity. A temperature-independent background contribution due to the optical set up is inferred from the full data set (see text) and displayed at the bottom. (b) Color representation of the temperature-dependent Raman susceptibility.

Figure 8

Temperature dependence of the soft-mode energy (a), energy width (b), and Raman-susceptibility amplitude (c). Dashed line in (a) is a power-law fit to the data, resulting in ${\Omega }_0=81.2\pm 1.2{\mathrm{cm}}^{-1}\text{and}{T}_{\mathrm{o}}=249.4\pm 2.1\mathrm{K}$.