A meta-GGA perspective on the altermagnetism of RuO2

TL;DR

This study probes the stability of altermagnetism in RuO$_2$ across density functional approximations, emphasizing meta-GGA reliability. By comparing LSDA, PBE, r$^2$SCAN-L, and r$^2$SCAN with DFT+$U$, it shows that bulk RuO$_2$ remains nonmagnetic at experimental lattice constants under the higher-rung functionals, while altermagnetism can emerge under lattice expansion, hole doping, or uniaxial strain. The work employs a Landau expansion and an effective Stoner analysis to quantify how the on-site exchange and Ru $4d$ localization evolve with the functional, lattice, and doping, establishing conservative thresholds for altermagnetic onset. The findings provide a practical baseline for interpreting thin-film experiments reporting altermagnetic signals, suggesting that interface-induced distortions and doping can realize altermagnetic states without requiring a magnetic ground state in the bulk.

Abstract

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.

Figures (6)

• Figure 1: Total energy change in fixed spin moment calculations. The energy difference with respect to the nonmagnetic state is given in eV per formula unit. The lines are fourth-order polynomial fits with the constant and odd terms set to zero. The fit results are $a_2(\mathrm{LSDA}) = 0.124\,\mathrm{eV}/\mu_\mathrm{B}^2$, $a_2(\mathrm{PBE}) = 0.076\,\mathrm{eV}/\mu_\mathrm{B}^2$, $a_2(\mathrm{r^2}\text{SCAN-L}) = 0.018\,\mathrm{eV}/\mu_\mathrm{B}^2$.
• Figure 2: Density of states plot for LSDA, PBE, and r$^2$SCAN-L functionals. a) is the full plot, b) is a close-up view around the Fermi energy.
• Figure 3: Local magnetic moments on the Ru site as a function of the Hubbard $+U$ parameter for different exchange-correlation functionals.
• Figure 4: Local magnetic moments on the Ru site as a function of the isotropic lattice scaling parameter for different exchange-correlation functionals.
• Figure 5: Local magnetic moments on the Ru site as a function of uniaxial strain for a) c-axis only scaling, strain including the Poisson ratio, and for the TiO$_2$ lattice parameters; b) for a,b-axis only scaling. All results were obtained with the r$^2$SCAN-L functional.