Orbital Ordering Transition in ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ Observed with Resonant X-Ray Diffraction

Resonant x-ray diffraction performed at the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ absorption edges of Ru has been used to investigate the magnetic and orbital ordering in ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ single crystals. A large resonant enhancement due to electric dipole $2p\to 4d$ transitions is observed at the wave-vector characteristic of antiferromagnetic ordering. Besides the previously known antiferromagnetic phase transition at $T_{\mathrm{N}}=110\mathrm{K}$, an additional phase transition, between two paramagnetic phases, is observed around 260 K. Based on the polarization and azimuthal angle dependence of the diffraction signal, this transition can be attributed to orbital ordering of the Ru $t_{2g}$ electrons. The propagation vector of the orbital order is inconsistent with some theoretical predictions for the orbital state of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$.

Figure 1

Energy dependence of the scattered intensity of the (100)-reflection around the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ absorption edges at a sample temperature of 20 K ($\psi =0°$). The energy profiles are not corrected for absorption. The inset shows the $L_{\mathrm{II}}$ resonance in more detail, together with the absorption coefficient $\mu$ (right scale), calculated from fluorescence measurements.

Figure 2

Polarization dependence of the scattered intensity at the (100) position at $\psi =0°$. Data are shown for the $\sigma \mathrm{\text{−}}{\pi }^{\prime }$ (full bullets) and $\sigma \mathrm{\text{−}}{\sigma }^{\prime }$ (empty bullets) polarization channels. The solid line is the result of a fit to a Lorentzian profile. The inset shows a schematic view of the experimental configuration.

Figure 3

Temperature dependence of the integrated intensity of the (100) peak as determined from $h$ scans, at (a) $L_{\mathrm{II}}$, both without analyzer and in $\sigma \mathrm{\text{−}}{\pi }^{\prime }$ geometry (scaled), as well as (b) at $L_{\mathrm{II}}{}^{\prime }$. In (a), the measurements with and without polarization analyzer were taken on two different samples. The horizontal error bars reflect uncertainties about the thermal coupling between sample, cold finger, and temperature sensors. In (b), because of the strong contribution from the $L_{\mathrm{II}}$ resonance peak, the integrated intensity at $L_{\mathrm{II}}{}^{\prime }$ could be reliably determined from $h$ scans only above 90 K. The intensity at $T=10\mathrm{K}$ has therefore been determined from energy scans (panel c). In (b) the temperature dependence of the (110) peak at $L_{\mathrm{II}}$ is also shown. (c) Variation of the intensity of the (100) peak with energy around the $L_{\mathrm{II}}$ edge for selected temperatures. All scans were corrected for absorption.

Figure 4

(a) Azimuthal angle ($\psi$) dependence of the scattered intensity of the (110) peak for both $\sigma \mathrm{\text{−}}{\pi }^{\prime }$ (full bullets) and $\sigma \mathrm{\text{−}}{\sigma }^{\prime }$ (empty bullets) polarization channels at $T=13\mathrm{K}$. The solid lines are simulations of the scattered intensity induced by the tilting of the ${\mathrm{RuO}}_6$ octahedra. (b) Energy dependence of the (110) peak intensity at $\psi =0°$ without analyzer for different temperatures. The data were corrected for absorption.