Optical study of ${\mathrm{MgTi}}_2{\mathrm{O}}_4$: Evidence for an orbital-Peierls state

Dimension reduction due to the orbital ordering has recently been proposed to explain the exotic charge, magnetic, and structural transitions in some three-dimensional transitional metal oxides. We present optical measurement on a spinel compound ${\mathrm{MgTi}}_2{\mathrm{O}}_4$ which undergoes a sharp metal-insulator transition at $240\mathrm{K}$, and show that the spectral change across the transition can be well understood from the proposed picture of one-dimensional Peierls transition driven by the ordering of $d_{yz}$ and $d_{zx}$ orbitals. We further elaborate that the orbital-driven instability picture applies also very well to the optical data of another spinel ${\mathrm{CuIr}}_2{\mathrm{S}}_4$ reported earlier.

Figure 1

The dc resistivity and specific heat vs temperature for ${\mathrm{MgTi}}_2{\mathrm{O}}_4$.

Figure 2

Optical reflectance and conductivity spectra for ${\mathrm{MgTi}}_2{\mathrm{O}}_4$ at $320\mathrm{K}$.

Figure 3

(Color online) The temperature dependence of the reflectance and conductivity spectra in the frequency range of $0–8000{\mathrm{cm}}^{-1}$. The black dots are corresponding dc conductivity values. The inset is an expanded plot of the low frequency region.

Figure 4

(Color online) An expanded plot of the low-frequency optical conductivity spectra at different temperatures.

Figure 5

(Color online) (a) Orbital ordering of ${\mathrm{MgTi}}_2{\mathrm{O}}_4$ at low $T$. The $B$-site ions (blue dots) are arranged in chains through corner-sharing tetrahedra. The short (pink), intermediate (black), and long (yellow) bonds together with $d_{yz}$ and $d_{zx}$ orbitals along the chains (four directions $[0,1,1]$, $[0,1,-1]$, $[1,0,1]$, and $[1,0,-1]$) are displayed. (b) Schematic diagram of the electronic states above and below the MIT temperature. At high $T$, the $3d^1$ electron of ${\mathrm{Ti}}^{3+}$ ion occupies the $t_{2g}$ bands with equal distribution on the $d_{xy}$, $d_{yz}$, and $d_{zx}$ orbitals. The $e_g$ bands are at higher energy. The two arrows indicate the two interband transitions. Below $T_{MIT}$, the Ti $3d^1$ electron occupies the $d_{yz}$ and $d_{zx}$ orbitals, leading to two quarterly filled 1D $d_{yz}$ and $d_{zx}$ bands, which were further split into lower and upper subbands due to Peierls instability. Then the lower subbands are fully occupied, the upper subbands, being mixed with $d_{xy}$ band, are empty, and a gap forms between them.

Figure 6

(a) The optical conductivity of ${\mathrm{CuIr}}_2{\mathrm{S}}_4$ at $300\mathrm{K}$ and $20\mathrm{K}$ taken from Ref. 8. (b) Schematic diagram of the electronic states above and below the MIT temperature. At high temperature, the 5.5 $d$ electron of ${\mathrm{Ir}}^{3.5+}$ ion occupies the $t_{2g}$ bands with equal probability on the $d_{xy}$, $d_{yz}$, and $d_{zx}$ orbitals. Arrow A indicates an interband transition from occupied $t_{2g}$ to empty $e_g$ states. Below $T_{MIT}$, the structure distortion splits the $t_{2g}$ bands. The doubly degenerate $d_{yz}$ and $d_{zx}$ orbitals are fully occupied, however, the 1D band along the $d_{xy}$ chain becomes quarterly filled, which was further split due to Peierls instability. As a result, new states above the Fermi level (i.e., upper subband of the split $d_{xy}$ band) were created. Arrow B indicates a new interband transition from occupied $t_{2g}$ to those new states.