Orbital-Driven Electronic Structure Changes and the Resulting Optical Anisotropy of the Quasi-Two-Dimensional Spin Gap Compound ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$

We investigated the electronic response of the quasi-two-dimensional spin gap compound ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ using optical spectroscopy. We observed the drastic changes in the optical spectra as the temperature decreased, resulting in anisotropy in the electronic structure of the spin-singlet ground state. Using the orbital-dependent hopping analysis, we found that orbital ordering plays a crucial role in forming the spin gap state in the non-one-dimensional material.

Figure 1

The crystal structure of ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ in the crystallographic (a) $ab$ plane and (b) $bc$ plane. The large red and small blue dots denote La and O ions, respectively. The shaded octahedra are at the lower positions on the $a$ axis. Note that the zigzag chains (along the red line) are formed along the $b$ axis. (c),(d), and (e) display the $d_{xy}$, $d_{yz}$, and $d_{zx}$ orbitals on the lattice, respectively. The local lattice distortion results in lengthening and shortening of the Ru-Ru bonds along the zigzag chains, resulting in lattice dimerization. The $x$ ($y$) direction is chosen parallel to the direction of the long (short) Ru-Ru bonds.

Figure 2

(a) $T$-dependent optical conductivity spectra ${\sigma }_b(\omega )$ along the $b$ axis. The interatomic $d\mathrm{\text{−}}d$ transitions are labeled as ${\alpha }_b$ and ${\beta }_b$. The blue dotted lines represent the contributions of the peaks ${\alpha }_b$, ${\beta }_b$, and the charge transfer excitation peak in the Lorentz oscillator fit. The inset shows the phonon spectra between 0.05 and 0.09 eV across the structural transition temperature. (b) and (c) show the spin and orbital configurations of the neighboring $t_{2g}$ orbitals in the suggested LT phase with $S=0$ (Ref. 5) and $S=1$ (Ref. 9), respectively. The possible optical transition is indicated by the dashed arrow.

Figure 3

$T$-dependent (a) ${\sigma }_b(\omega )$ and (b) ${\sigma }_c(\omega )$. The interatomic $d\mathrm{\text{−}}d$ transition between the neighboring $d_{zx}$ ($d_{xy/yz}$) orbital is labeled as the peak $\alpha$ ($\beta$). The thin dotted lines represent the contributions from the charge transfer excitation of each spectrum. The inset in (b) shows the total spectral weights of the interatomic $d\mathrm{\text{−}}d$ transitions, i.e., the contributions from both of the peaks $\alpha$ and $\beta$, ${\mathrm{SW}}^{\alpha +\beta }$. The solid squares and open circles indicate the $T$-dependent ${\mathrm{SW}}^{\alpha +\beta }$ along the $b$ and $c$ axes, respectively. (c) $T$- and polarization-dependent changes of the SW of the peaks $\alpha$ and $\beta$, obtained from the Lorentz oscillator model fit. The inset shows the ratio of ${\mathrm{SW}}_b^{\beta }$ to ${\mathrm{SW}}_c^{\beta }$, which represents the optical anisotropy in peak $\beta$ in the $bc$ plane.