Altermagnetism, characterized by its ferromagnetism-like spin-splitting band structure and antiferromagnetism-like magnetic order, has garnered considerable attention recently. Although hole doping may promote magnetism in the debated altermagnet (AM) candidate ${\mathrm{RuO}}_2$, the evolution of its electronic and magnetic properties under hole doping remains poorly understood. Based on first-principles calculations, we employ quantum oscillations to study hole-doped ${\mathrm{RuO}}_2$. We find that hole doping can enhance spin splitting and reconstruct the Fermi surface in ${\mathrm{RuO}}_2$, which is revealed by the angle-dependent quantum oscillation frequency. By tracking a pair of closed Fermi-surface pockets, we identify a meaningful correlation between the magnetic moment of Ru and a quantum-oscillation-based signature of spin splitting. This correlation follows a quasilinear trend over a broad doping range, which can be captured by a minimal two-dimensional $d$-wave AM model. In addition, the hole-doped ${\mathrm{RuO}}_2$ exhibits a transition from a nonmagnetic to an AM state via an intermediate state. The quasilinear correlation through quantum oscillation and the distinct quantum oscillation frequency of the stable AM state can serve as useful signatures for identifying the AM state in ${\mathrm{RuO}}_2$. Our results provide a comprehensive framework for understanding hole-doped ${\mathrm{RuO}}_2$, offering insights into AM transitions and their identification.

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• Altermagnetism
• Electrical properties
• Oxides
• Density functional calculations