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 N\'eel temperature of the (hypothetical) altermagnetic state of bulk RuO$_2$, stabilized via the DFT$+U$ technique, by mapping on a Heisenberg Hamiltonian. The N\'eel 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 N\'eel 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 $\beta$-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.