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Description
Altermagnetism is a topic that has recently been gaining attention, and the RuO$_2$ compound is among the most studied altermagnetic candidates. However, a survey of the available literature on RuO$_2$ properties suggests no consensus on its magnetism. By performing density functional theory (DFT) calculations, we show that the electronic properties of stoichiometric RuO$_2$ are described in terms of a Hubbard U, within DFT+U, smaller than the value required to have magnetism. We further argue that Ru vacancies can actually aid the formation of a magnetic state in RuO$_2$. This, in turn, suggests that a characterization of the amount of Ru vacancies in experimental samples might help resolve the controversy between the different experimental results.
The electronic structure of RuO$_2$ hints at a possibility of realizing a magnetically ordered state upon hole doping, and such a possibility was explored experimentally in Cr-doped RuO$_2$, where it was suggested that this system exhibits the anomalous Hall effect (AHE) due to altermagnetism. Based on our density functional calculations, we revise the results obtained for this system and propose a different interpretation of experimental results. Our calculations suggest that extra holes are bound to the Cr impurity and do not dope the Ru bands, which remain nonmagnetic. Thus, the observed AHE is not due to the altermagnetism but stems entirely from magnetic Cr ions.