Spin-degenerate bulk bands and topological surface states associated with Dirac nodal lines in RuO2

Altermagnets are a novel platform to realize exotic electromagnetic properties distinct from those of conventional ferromagnets and antiferromagnets. We report results of micro-focused angle-resolved photoemission spectroscopy (ARPES) on RuO2, in which its altermagnetic nature has been under fierce debate in connection with crystal-orientation-dependent spintronic functionalities. By elucidating the band structure of the (100), (110) and (101) surfaces of a bulk single crystal using micro-ARPES, we found that, irrespective of the surface orientation, the experimental band structures show a good agreement with the bulk-band calculations for the nonmagnetic phase, but display a severe disagreement with those for the antiferromagnetic phase. Moreover, spin-resolved ARPES signifies a negligible spin polarization in the bulk bands, suggesting the absence of antiferromagnetism and altermagnetic spin splitting. In addition, we identified a nearly flat surface band and a dispersive one near the Fermi level at the (100)/(110) and (101) surfaces, respectively. Our first-principles calculations and analysis of Berry phase attribute these states to the topological surface bands emerging from the bulk Dirac nodal lines around the Fermi level. Our results indicate that such topological surface/interface states must be considered to understand the spintronic functionalities of RuO2, and may provide new insights into its catalytic characteristics.

💡 Research Summary

This paper addresses two long‑standing questions concerning ruthenium dioxide (RuO₂): (i) whether it truly exhibits altermagnetism—a recently proposed class of collinear antiferromagnets that display momentum‑dependent spin splitting without relying on spin‑orbit coupling, and (ii) what microscopic electronic structures underlie the pronounced crystal‑orientation‑dependent spintronic phenomena reported in previous transport studies. To answer these, the authors performed a comprehensive micro‑focused angle‑resolved photoemission spectroscopy (micro‑ARPES) study on a high‑quality bulk single crystal of RuO₂, cleaving three distinct crystallographic surfaces—(100), (110), and (101)—and complemented the measurements with spin‑resolved ARPES (SARPES). First‑principles density‑functional theory (DFT) calculations were carried out for both a non‑magnetic (NM) phase and an antiferromagnetic (AF) phase (the latter stabilized by an on‑site Coulomb term U = 2 eV).

The ARPES intensity maps for all three surfaces reveal Fermi‑surface (FS) pockets (labeled α, β, γ) that match the NM calculation remarkably well. In contrast, the AF calculation predicts only tiny pockets centered at Γ and Z, which are absent in the experiment. Systematic variation of U confirms that the discrepancy is not an artifact of the chosen interaction strength. Band‑dispersion cuts along high‑symmetry directions further demonstrate that the experimentally observed bulk bands (designated B1, B2) follow the NM band structure, including a Dirac‑like crossing associated with a bulk Dirac nodal line (DNL1). The AF calculation, however, shows substantial spin‑splitting and band‑doubling that are not observed.

Spin‑resolved measurements at k‑points where altermagnetic splitting is theoretically maximal show essentially zero spin polarization within experimental uncertainty, directly ruling out the presence of altermagnetic spin splitting in the bulk. This result, together with the excellent agreement with NM DFT, establishes that RuO₂ is spin‑degenerate in its bulk electronic structure.

In addition to bulk states, the authors identify surface‑derived bands that are not reproduced by either bulk calculation. On the (100) and (110) surfaces a nearly flat band resides at the Fermi level, while on the (101) surface a more dispersive surface band appears. Photon‑energy independence and slab‑Green’s‑function calculations confirm their surface origin. Berry‑phase analysis shows that these surface bands emerge from the bulk Dirac nodal lines, i.e., they are topological surface states protected by the nodal‑line topology. The effective mass of these surface states varies strongly with surface orientation, suggesting that they could dominate transport and spin‑charge conversion in thin‑film or interface geometries.

The study also emphasizes the importance of crystal quality. The RuO₂ crystals used exhibit a residual‑resistivity ratio (RRR) of 400, far exceeding values reported in earlier ARPES works (typically 20–200). This high quality yields sharper spectral features, enabling reliable identification of subtle surface states and accurate spin polarization measurements.

Overall, the work provides decisive experimental evidence that RuO₂ does not host altermagnetic order; instead, its remarkable spintronic responses must be attributed to topological surface/interface states derived from Dirac nodal lines. These findings reshape the interpretation of previous anomalous Hall, anomalous Nernst, and spin‑charge conversion experiments, and they open a pathway for exploiting nodal‑line‑derived surface states in spintronic devices and catalytic applications.