A meta-GGA perspective on the altermagnetism of RuO 2

The metallic oxide RuO 2 hosts a fascinating edge case of magnetism: while nonmagnetic in ideal bulk material, density functional theory (DFT) predicts an altermagnetic ground state within the DFT + U method. The magnetic state of strained or doped thin films remains controversial, but evidence for a nontrivial magnetic state is ample. Here, I study the altermagnetic ground state of RuO 2 on a higher rung of Jacob's ladder of density functional approximations, the meta-GGA level including the kinetic energy density and the density Laplacian. While the workhorse functional of solid-state physics is a generalized gradient approximation (GGA), the modern r 2 SCAN-L functional has been established as a general-purpose functional which can replace GGA, while systematically improving solid-state properties without introducing spurious errors like erroneous magnetic ground states. Comparison of local spin-density approximation ( LSDA ) + U , GGA + U , and meta- GGA + U results on RuO 2 shows systematic enhancement of the exchange interaction, leading to a reduction of the onset value of the Hubbard U parameter at different levels of density functional approximation. However, the magnetic ground state, studied at the experimental lattice constants, remains nonmagnetic with r 2 SCAN-L . I demonstrate that altermagnetism is easily formed upon lattice expansion, hole doping, and uniaxial strain on the c axis. The r 2 SCAN-L calculations set conservative thresholds for distortions and doping levels for the onset of altermagnetism in a parameter-free framework.