Complex Magnetic Behavior in RuO$_2$ Thin Films: Strain, Surface Effects, and Altermagnetic Signatures

Abstract

RuO$_2$ has been proposed as a prototypical metallic $d$-wave altermagnet, a Néel-ordered compensated antiferromagnetic state exhibiting nonrelativistic momentum-dependent spin splitting; yet, its magnetic ground state remains controversial both theoretically and experimentally. Using comprehensive first-principles calculations, we investigate RuO$_2$ thin films with (110), (100), and (001) orientations, both freestanding and supported on a TiO$_2$ substrate. We show that magnetism in RuO$_2$ thin films is highly fragile, strongly influenced by strain, surface orientation, and atomic relaxation, while also being highly sensitive to the choice of the Brillouin-zone integration scheme. Although tensile strain induces finite magnetic moments, none of the studied systems stabilizes a compensated antiferromagnetic state; hence, an altermagnetic ground state cannot be achieved. Instead, the magnetic response is characterized by pronounced layer- and site-dependent variations and incomplete moment compensation, resembling a ferrimagnetic-like state. Our results reconcile conflicting theoretical and experimental reports and underscore the sensitivity of RuO$_2$ magnetism to structural and methodological details.

Figures (7)

• Figure 1: Different surface orientations of RuO$_2$ thin films considered in this work. For the RuO$_2$(110)/TiO$_2$(110) heterostructure, several film thicknesses were examined; the 5-L configuration is shown as a representative example. Blue and red spheres denote Ru atoms carrying different magnetic moments in the assumed AFM configurations discussed in the main text (labelled Ru$_1$ and Ru$_2$). Ti and O atoms are shown in green and white, respectively.
• Figure 2: Sensitivity of the Ru magnetic moment to k-point sampling in bulk rutile RuO$_2$ under tensile strain. The calculations are performed for bulk RuO$_2$ constructed using the lattice parameters and Wyckoff positions of rutile TiO$_2$, which leads to a tensile strain and stabilizes an AFM state. k-point densities range from 0.05 Å$^{-1}$ (corresponding to a $27 \times 27 \times 42$ Monkhorst–Pack mesh) to 0.30 Å$^{-1}$ (corresponding to a $5 \times 5 \times 8$ mesh). (a) Ru magnetic moment as a function of the Monkhorst–Pack k-point grid calculated using Marzari–Vanderbilt–DeVita–Payne cold smearing for different smearing widths $\sigma$ (in Rydberg). Results obtained with the optimized tetrahedron method, which does not require a smearing parameter, are shown for comparison. (b) Same analysis performed using Fermi–Dirac smearing.
• Figure 3: Magnetic moments of Ru$_1$ and Ru$_2$ as a function of layer index and film thickness. Filled and open symbols denote Ru$_1$ and Ru$_2$, respectively, for RuO$_2$(110) thin films on a TiO$_2$(110) substrate, with thicknesses ranging from 1-L to 7-L. For each thickness, magnetic moments are shown for all Ru layers within the slab. Data corresponding to the same film thickness are connected by lines of the same color to guide the eye.
• Figure 4: Effect of atomic relaxation and induced magnetization on Ru magnetic moments in a 5-L RuO$_2$(110) slab on TiO$_2$(110). Magnetic moments of Ru$_1$ (filled symbols) and Ru$_2$ (open symbols) are shown as a function of the Ru layer index.
• Figure 5: Nonrelativistic band structures of a 5-L RuO$_2$(110) slab on a TiO$_2$(110) substrate. The left panel shows the band structure of the unconstrained magnetic ground state, while the right panel shows the band structure obtained with Ru magnetic moments constrained to enforce a fully compensated AFM configuration. In both cases, the non-relaxed atomic structure is used. Red and blue lines denote spin-up and spin-down bands, respectively.