Evolution of phonon Raman spectra with orbital ordering in spinel MnV${}_2$O${}_4$

We investigated Raman scattering of spinel MnV${}_2$O${}_4$, for which orbital ordering of V $t_{2g}$ states below $T_c=57$ K was proposed. Several peaks evolve in the Raman spectra below $T_c$, and they show a peculiar polarization dependence, which cannot be explained only by a group theory analysis. We found that it can be explained by considering Mott excitations in the presence of orbital ordering as the dominant intermediate states in the Raman process. This result gives the evidence of orbital ordering in this compound from the viewpoint of electronic structure.

Figure 1

(a)(b) Schematic pictures of the orbital ordering in MnV${}_2$O${}_4$ below 57 K, where the orbital occupation of (a) the first electron and (b) the second electron in the V ions are illustrated. (c) Optical conductivity spectrum of MnV${}_2$O${}_4$ at 300 K. The arrow shows the energy of the incident light for Raman scattering. (d) Magnetization of the sample attached to a glass plate and copper plate as a function of magnetic field applied perpendicular to the plate.

Figure 2

(a)(b) Raman scattering spectra at various polarization configurations at 5 K (a) for the sample attached to a glass plate (on the $ab$ plane) and (b) for that to a copper plate (on the $ac$ plane). The irreducible representation of each mode is based on $I{4}_1/amd$.

Figure 3

Raman scattering spectra at various temperatures in the (a) $XY$ and (b) $X^{\prime }{Y}^{\prime }$ polarization configurations on the $ab$ plane. (c) Temperature dependence of the integrated intensity for the modes at 178 cm${}^{-1}$, 479 cm${}^{-1}$, and 585 cm${}^{-1}$.

Figure 4

(a)(b) Mott excitations as the intermediate states allowed in the (a) $X^{\prime }{Y}^{\prime }$ and (b) $XY$ polarization configuration. (c) The calculated and experimentally observed Raman spectra at 5 K in the $X^{\prime }{Y}^{\prime }$ and $XY$ polarization configurations. The arrows show the position of the two $B_g$ modes having negligible intensities in the calculation.

Figure 5

(a) An example of the Mott excitation allowed for ${\epsilon }_L\parallel \left[110\right]$ and ${\epsilon }_S\parallel \left[1\overline{1}0\right]$. (b) The shift of the equilibrium positions of the oxygen ions associated with the Mott excitation shown in (a) ($f_i^{\eta }$). (c)(d) The shift of the oxygen ions for $B_g$ mode (c) at 590 cm${}^{-1}$ and (d) at 495 cm${}^{-1}$ ($T_{ik}$).

Figure 6

(a) An example of the Mott excitation allowed for ${\epsilon }_L\parallel \left[100\right]$ and ${\epsilon }_S\parallel \left[010\right]$. (b) The shift of the equilibrium positions of the oxygen ions associated with the Mott excitation shown in (a) ($f_i^{\eta }$). (c)(d) The shift of the oxygen ions for $B_g$ mode (c) at 590 cm${}^{-1}$ and (d) at 495 cm${}^{-1}$ ($T_{ik}$).