Neel temperature and helical spin order of altermagnetic RuO2

Abstract

The magnetic groundstate of RuO$_2$ remains controversial, with experimental evidence for a nonmagnetic groundstate of ideal bulk material and indications of a magnetic state in strained thin films. Here, I investigate the Néel temperature of the (hypothetical) altermagnetic state of bulk RuO$_2$, stabilized via the DFT$+U$ technique, by mapping on a Heisenberg Hamiltonian. The Néel temperature scales monotonously with the magnetic moment up to the point where a large $+U$ term opens a band gap and turns RuO$_2$ semiconducting. The maximum Néel temperature obtained by this procedure is 408\,K at $U=3$\,eV, and much smaller values for smaller $U$. A reciprocal-space eigenvalue analysis reveals a helimagnetic groundstate of the spin model due to intra-sublattice antiferromagnetic coupling. This situation resembles the isostructural $β$-MnO$_2$, which is a prototype helimagnet. Further comparison with calculations on CrO$_2$ and altermagnetic MnF$_2$ taking $U$ as an adjustable parameter supports the validity of the spin model analysis.

Figures (4)

• Figure 1: a): Local magnetic moment of Ru atoms as a function of the Hubbard $+U$ parameter. b) Neel temperature as a function of $U$, calculated with RPA and classical Monte Carlo simulations. c): Same as b), given as a function of the local magnetic moment.
• Figure 2: Calculations of Néel temperatures and magnetic moments for other rutile-structured materials: a) $\beta$-MnO$_2$, b) MnF$_2$, and c) CrO$_2$. Open symbols denote Monte Carlo results for the Néel temperature, full symbols are RPA results. Horizontal dashed lines indicate experimental Neel temperatures Zhou2018Collins1974Chamberland1977.
• Figure 3: Real-space exchange interaction parameters $J_{ij}$ of RuO$_2$, MnO$_2$, MnF$_2$, and CrO$_2$ with $U$ values chosen such that $T_\mathrm{N}^{RPA}$ is closest to the experimental result. The interactions are resolved as intra-sublattice and inter-sublattice interactions.
• Figure 4: a) Néel temperatures of RuO$_2$ obtained by Monte Carlo simulations on a monolayer (one unit cell), a bilayer (two unit cells), and bulk for comparison at $U =1.5$ eV. b) Mean sublattice magnetization length from Monte Carlo calculations on multilayers of RuO$_2$ with $U=1.5$ eV. Vertical dashed lines represent the expected minima positions according to the reciprocal-space eigenvalue analysis.