Nonmagnetic Ground State in ${\mathrm{RuO}}_2$ Revealed by Muon Spin Rotation

The magnetic ground state of single crystalline ${\mathrm{RuO}}_2$ was investigated by the muon spin rotation and relaxation ($\mu \mathrm{SR}$) experiment. The spin precession signal due to the spontaneous internal magnetic field $B_{\mathrm{loc}}$, which is expected in the magnetically ordered phase, was not observed in the temperature range 5–400 K. Muon sites were evaluated by first-principles calculations using dilute hydrogen simulating muon as pseudohydrogen, and $B_{\mathrm{loc}}$ was simulated for the antiferromagnetic structures with a Ru magnetic moment $|{\mathit{m}}_{\mathrm{Ru}}|\approx 0.05{\mu }_{\mathrm{B}}$ suggested from diffraction experiments. As a result, the possibility was ruled out that muons are localized at sites where $B_{\mathrm{loc}}$ accidentally cancels. Conversely, assuming that the slow relaxation observed in $\mu \mathrm{SR}$ spectra was part of the precession signal, the upper limit for the magnitude of $|{\mathit{m}}_{\mathrm{Ru}}|$ was estimated to be $4.8(2)\times {10}^{-4}{\mu }_{\mathrm{B}}$, which is significantly less than $0.05{\mu }_{\mathrm{B}}$. These results indicate that the antiferromagnetic order, as reported, is unlikely to exist in the bulk crystal.

Figure 1

(a) Examples of ZF-$\mu \mathrm{SR}$ spectra at typical temperatures, and (b) magnetic field dependence of LF-$\mu \mathrm{SR}$ spectra at 5 K observed in single-crystalline ${\mathrm{RuO}}_2$. Solid curves represent the least-square fit by Eq. (1). Inset: the spontaneous spin precession signal expected in the presence of the presumed AFM order (see text).

Figure 2

Temperature dependence of (a) the initial polarization and (b) relaxation rate obtained by the analysis using Eq. (1). The dashed line in (b) is the result of a curve fit using Eq. (2).

Figure 3

Local atomic configurations of hydrogen defect in ${\mathrm{RuO}}_2$ obtained by DFT calculations with lattice relaxation in $3\times 3\times 3$ superlattice. Site1: the lowest energy site (forming OH bond). Site2 (light blue): the $c$-channel center ($4d$) site. The structure was displayed using vesta [45].

Figure 4

The total energy $\mathrm{\Delta }{E}_{\mathrm{tot}}(\mathit{r})$ and internal magnetic field $B_{\mathrm{loc}}(\mathit{r})$ along the $\mathit{r}=(0,0.5,z)$ axis (corresponding to the $c$-channel center) calculated in the $2\times 2\times 3$ superlattice of ${\mathrm{RuO}}_2$. The solid and dashed lines showing $B_{\mathrm{loc}}(\mathit{r})$ (mapped on the right axis) are for the cases where the Ru moment ${\mathit{m}}_{\mathrm{Ru}}$ is either parallel to (001) (the $c$ axis) or it is tilted 20° toward the (110) plane, respectively [6]. The horizontal dashed line is the Mu zero-point energy.