Rutile ${\mathrm{RuO}}_2$ has recently attracted great interest, as its magnetic ground state remains controversial. Experimental studies have reported either nonmagnetic (NM) or altermagnetic (AM) ground states in different crystalline samples of ${\mathrm{RuO}}_2$, highlighting the need for a reasonable explanation to resolve this contradiction. In this study, density functional theory calculations are performed to reveal the correlation-sensitive and strain-dependent magnetism of bulk ${\mathrm{RuO}}_2$. On one hand, multiple AM phases with different magnitudes of the spin magnetic moment are identified for ${\mathrm{RuO}}_2$ by employing Hubbard's $U$ parameter as a perturbation probe. On the other hand, when appropriate strains that significantly change the crystal cell volume are applied, the ground state of ${\mathrm{RuO}}_2$ is suggested to undergo transitions between the NM state (with no spin splitting) and the magnetic states (with spin splitting in the band structure). These findings not only demonstrate intriguing physics in $4d$-electron-correlated ${\mathrm{RuO}}_2$, but also retain its potential for spintronic applications.

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• Altermagnetism
• Magnetic order
• Transition metal oxides
• DFT+U
• Strain engineering