Moir\'e-assisted charge instability in ultrathin RuO$_2$

Abstract

Ruthenium dioxide (RuO$_2$) has been in the focus of contemporary condensed matter research as a prototypical candidate material for altermagnetism. In the face of daunting evidence for bulk magnetic order despite promising theoretical predictions, it naturally suggests the focus on thin films where Coulomb interactions are dimensionally quenched and may yield a more strongly correlated environment prone to magnetic ordering. Here, we combine scanning tunneling microscopy (STM), density functional theory (DFT), and density matrix renormalization group (DMRG) methods to investigate atomically ordered ultrathin RuO$_2$(110) grown on Ru(0001). Contrary to predictions of magnetic order, we observe a nonmagnetic charge density wave (CDW) instability that is driven by Fermi surface nesting within the flat-band surface state, and stabilized by the incommensurate moir\'e stacking with the substrate. We further identify a nonmagnetic and metastable 2 $\times$ 2 surface reconstruction that breaks in-plane mirror symmetry and can be reversibly toggled via STM tip manipulation. Our spin-polarized STM measurements find no sign of any magnetic instability at the RuO$_2$ surface. As much as our findings refute proposals for either bulk or surface magnetism in RuO$_2$, we establish ultrathin RuO$_2$(110) as an intriguing platform for exploring Moir\'e-assisted electronic surface order.