Absence of magnetic order in RuO$_2$: insights from $\mu$SR spectroscopy and neutron diffraction

Altermagnets are a novel class of magnetic materials besides ferro- and antiferromagnets, where the interplay of lattice and spin symmetries produces a magnetic order that is staggered both in coordinate as well as momentum space. The metallic rutile oxide RuO$_2$, long believed to be a textbook Pauli paramagnet, recently emerged as a workhorse altermagnet when resonant X-ray and neutron scattering studies reported nonzero magnetic moments and long-range collinear order. While experiments on thin films seem consistent with altermagnetic behavior, the origin and size of magnetic moments in RuO$_2$ still remain controversial. Here we show that RuO$_2$ is nonmagnetic, regardless if as bulk or thin film. Employing muon spin spectroscopy as a highly sensitive probe of local magnetic moments complemented by density functional theory, we find at most $1.4 \times 10^{-4} $ $\mu_B$/Ru in bulk RuO$_2$ and at most $7.5 \times 10^{-4}$ $\mu_B$/Ru in epitaxial films. In their essence, these moments reflect the detection limit of our spectrometers and are orders of magnitude smaller than previously reported neutron results, i.e., the moments previously assumed to rationalize altermagnetic behavior. Our own neutron diffraction measurements on RuO$_2$ single crystals identify multiple scattering as a likely source for this discrepancy.