Constraints on magnetism and correlations in RuO$_2$ from lattice dynamics and Mössbauer spectroscopy

Abstract

We provide experimental evidence for the absence of a magnetic moment in bulk RuO$_2$, a candidate altermagnetic material, by using a combination of Mössbauer spectroscopy, nuclear forward scattering, inelastic X-ray and neutron scattering, and density functional theory calculations. Using complementary Mössbauer and nuclear forward scattering we determine the $^{99}$Ru magnetic hyperfine splitting to be negligible. Inelastic X-ray and neutron scattering derived lattice dynamics of RuO$_2$ are compared to density functional theory calculations of varying flavors. Comparisons among theory with experiments indicate that electronic correlations, rather than magnetic order, are key in describing the lattice dynamics.

Figures (4)

• Figure 1: (a) The rutile crystal structure of RuO$_2$ with Ru-atoms in red, and O-atoms in grey. (b) The c-axis projection illustrates the $\left[\mathcal{C}_2 || \mathcal{C}_{4z} t \right]$ symmetry, where Ru$_1$ (spin-up) and Ru$_2$ (spin-down) are associated with RuO$_6$ octahedra oriented differently. The dotted box highlights a unit-cell with a shifted origin that clearly distinguishes Ru$_1$ and Ru$_2$ environments under $\left[\mathcal{C}_{4z} t\right]$ symmetry operation. (c) Representation of the strong distortion in the RuO$_6$ octahedra from two viewing angles. The octahedra consists of 90$^{\circ}$ O-Ru-O bonds along with 77.24$^{\circ}$ and 102.76$^{\circ}$ angle bonds in the plane of the octahedra. The O-atom marked with $\otimes$ shows the 90$^{\circ}$ transformation between the two viewing angles. (d) $^{99}$Ru Mössbauer spectra of RuO$_2$ (data from Ref. stievano1999mossbauer) and (e) nuclear forward scattering data of RuO$_2$ (data from Ref. bessas2014nfs) including the fits with-- (blue) and without-- (red) hyperfine field ($H_{\mathrm{hf}}$). (f) Map of reduced $\chi^2$ as a function of the spin relaxation frequency and hyperfine field ($H_{\mathrm{hf}}$). The red-region ($\chi^2_{\mathrm{red.}} \simeq 1$) represents best fit (dashed lines are a guide to the eye).
• Figure 2: Dynamic structure factor, $S(Q, E)$, of RuO$_2$. (a) The Brillouin zone with high symmetry k-points, drawn next to the $(HKL)$ basis vectors of our IXS experiment. (b) The reciprocal-space map of the $(0KL)$ plane. Green arrows indicate the measured IXS path. Blue and red arrows are the projection of the basis vectors and high-symmetry k-path in the plane. (c) SCAN and (d) DFT+$U$ calculated phonon dispersions. Note the differences in the dispersion of acoustic phonons along $\Gamma-$Z. (e-h) Overlay of the IXS phonons (red circles) on the IXS dynamic structure factor, $S(Q, E)$, computed from SCAN and DFT+$U$ force constants along the $\Gamma-$Z direction for the LA mode reveals that SCAN (NM) is the best model. (i) LA-mode and (j) TA-mode phonons of SCAN (NM) calculation along $\Gamma-$R direction (0, $-$3$\pm\xi$, 1+$\xi$). The error-bars shown in the plot are the FWHM of a Gaussian fit to the IXS constant-Q measurement. Errors of the data points are within the size of the circle. The unit of intensity as shown in the color bar is arbitrary (arb. units).
• Figure 3: Dynamic susceptibility, $\chi"(Q, E)$, for RuO$_2$ powder spectra measured at ARCS (Experiment, in the middle) and the corresponding OCLIMAX calculated $\chi"(Q, E)$ based on DFT force-constants for SCAN (AFM), DFT+$U$=2 (AFM), SCAN (NM), and DFT+$U$=0 (NM). The intensity represents $\chi"(Q, E)$ in arbitrary units. Calculated intensity is shown with the same scaling for all methods.
• Figure 4: Integrated $\chi"(E)$ for RuO$_2$ from the ARCS measurement is represented by black circles. Correspondingly, the simulated Integrated $\chi"(E)$ for SCAN (AFM), SCAN (NM), DFT+$U$=0 (NM), and DFT+$U$=2 (AFM) is plotted. The simulated data is scaled by the same constant to compare with the experiment.