A meta-GGA perspective on the altermagnetism of RuO2

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 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.