Structural origin of resonant diffraction in RuO$_2$

Abstract

We report Ru L$_3$-edge resonant X-ray diffraction studies on single crystal and (001) epitaxial films of RuO$_2$. We investigate the distinct $\mathbf{Q} = (100)$ and $(001)$ reflections as a function of incident energy, azimuthal angle, and temperature. The results show that the observed resonant diffraction in RuO$_2$ is fully consistent with a resonant charge anisotropy signal of structural origin permitted by the parent (non-magnetic) rutile $P4_2/mnm$ space group. These results significantly constrain the magnetic contribution to the resonant diffraction signal and indicate the unlikely existence of $\mathbf{k} = 0$ antiferromagnetic order in RuO$_2$.

Figures (4)

• Figure 1: (a) Crystal structure of RuO$_2$ along the $c$-axis. (b) Forbidden reflections for the $P4_2/mnm$ space group in the $(h0l)$ plane. (c) Scattering geometry for RXD experiments. (d) $H$ scans at $\mathbf{Q} = (100)$ in bulk RuO$_2$ for different $\psi$ in the $\sigma\pi'$ channel at $T = 300$ K. (e) $\psi$ dependence of $\mathbf{Q} = (100)$ in the same condition. Dashed lines in (d) are pseudo-Voigt fits. Dashed line in (e) is a fit to the theoretical $\psi$ dependence for both the $c$-axis AFM and ATS contributions (see text).
• Figure 2: $\psi$ dependence of $\mathbf{Q} = (001)$ in bulk RuO$_2$ in the $\sigma\sigma'$ (blue) and $\sigma\pi'$ (orange) channels at (a) $T = 300$ K and (b) $T = 9$ K. (c) $L$ scans of $\mathbf{Q} = (001)$ at $\psi = 45^\circ$ and $T = 9/300$ K. Inset: integrated $\sigma\sigma'$ and $\sigma\pi'$ intensity vs. $T$ at the same condition. (d) $L$ scans in $\sigma\sigma'$ and $\sigma\pi'$ channels at $T = 9$ K for $\psi = 0^\circ$ and $\psi = 45^\circ$. Dashed lines in (a)/(b) are fits to the theoretical $\psi$ dependence for ATS scattering considering the extinction ratio of the analyzer (see text). Black lines in (c)/(d) are pseudo-Voigt fits.
• Figure 3: (a) $\theta$ scans at $\mathbf{Q} = (001)$ in the $\sigma\sigma'$ channel vs. $E_i$ at $\psi = 45^\circ$ and $T = 6.5$ K, expressed as the deviation from the nominal Bragg angle ($\delta\theta$). (b) Integrated $\theta$ scans vs. $E_i$ for $\sigma\sigma'$ (blue) and $\sigma\pi'$ (orange). Black line: non-magnetic FDMNES simulation of the (001) resonance profile, accounting for self-absorption. (c) Peak width vs. $E_i$, compared to the FY XAS ($\mu$ exp., black dots) and the FDMNES calculated XAS ($\mu$ calc., black line). $\mu$ -- arbitrary units. (d) Resonance spectra at $\mathbf{Q} = (0.9975, 0, 0)$ in the $\sigma\pi'$ channel at $T = 45/340$ K (blue/red) in comparison to the non-magnetic FDMNES calculation excluding self-absorption.
• Figure 4: (a) $\psi$ dependence of the (001) reflection in an epitaxial (001) RuO$_2$/TiO$_2$ film at $T = 300$ K. (b) Energy scans at $(001)$ in the $\sigma\sigma'$ (blue) and $\sigma\pi'$ (orange) polarizations at $\psi = 45^\circ$. $\theta$ scans of the (001) reflection in both polarizations at (c) $T = 300$ K and (d) $T = 6.5$ K at $\psi = 45^\circ$. (e) $T$ dependence of each polarization channel ($I_{\sigma\sigma'} + I_{\sigma\pi'}$ -- without analyzer).