Orbitally Driven Spin-Singlet Dimerization in $S=1$ ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$

Using x-ray absorption spectroscopy at the $\mathrm{Ru}\mathrm{\text{−}}{L}_{2,3}$ edge we reveal that the ${\mathrm{Ru}}^{4+}$ ions remain in the $S=1$ spin state across the rare $4d$-orbital ordering transition and spin-gap formation. We find using local spin density $\mathrm{\text{approximation}}+\mathrm{\text{Hubbard}}$ U band structure calculations that the crystal fields in the low-temperature phase are not strong enough to stabilize the $S=0$ state. Instead, we identify a distinct orbital ordering with a significant anisotropy of the antiferromagnetic exchange couplings. We conclude that ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ appears to be a novel material in which the orbital physics drives the formation of spin-singlet dimers in a quasi-two-dimensional $S=1$ system.

Figure 1

The main block of the low-temperature (20 K) triclinic crystal structure of ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ shown in the crystallographic $ab$ plane: the two-dimensional Ru-O network consisting of distorted ${\mathrm{RuO}}_6$ octahedra extends along the $c$ axis (not shown, pointing into paper plane) and $b$ axis with corrugation. The Ru-O bond lengths are marked in units of Å, and those out of the $ab$ plane (not shown) are 2.046 and 2.057 Å for Ru1, and 2.046 and 2.082 Å for Ru2. The spin-singlet dimers are marked by black solid bars. The local orthogonal coordinate system ($xyz$) is used in our band calculations with $z$ parallel to $c$ and $y$ ($x$) along the short (long) Ru1-Ru2 direction. The high-temperature monoclinic structure (not shown) above $T_s=160\mathrm{K}$ has equal Ru-Ru distances along the $x$ and $y$ directions: Ru1 and Ru2 are equivalent.

Figure 2

(a) Experimental $\mathrm{Ru}\mathrm{\text{−}}{L}_{2,3}$ XAS spectra of ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ measured at 220 and 110 K, i.e., above and below $T_s=160\mathrm{K}$. (b) Theoretical simulations for the ${\mathrm{Ru}}^{4+}$ ion in the $S=1$ high-temperature phase at 220 K, $S=1$ low-temperature phase at 110 K, and $S=0$. The inset shows $\mathrm{O}\mathrm{\text{−}}K$ spectra measured at 200 and 85 K from 16.

Figure 3

LDA density of states of the Ru $4d$ orbitals in the high-temperature (HT, upper panel) and low-temperature (LT, middle and lower panels) phases. The insets show a close-up of the $t_{2g}$ ($xy$, $xz$, and $yz$) states in the vicinity of the Fermi level set at 0 eV.

Figure 4

Density of states (DOS) of the ${\mathrm{La}}_4{\mathrm{Ru}}_2{\mathrm{O}}_{10}$ in the antiferromagnetic low-temperature phase calculated using $\mathrm{LSDA}+\mathrm{U}$. (a) Total DOS per formula unit, the $4d$ states of the two inequivalent ${\mathrm{Ru}}^{4+}$ ions, and the $2p$ states of all the ten oxygens; (b) orbitally resolved $4d$ states of Ru1 and (c) of Ru2. The solid (dashed) curves denote the up- (down)-spin channels.