At present, the research on two-dimensional (2D) ferromagnets is mainly concentrated in the field of van der Waals materials, while the successful preparation of strain-free freestanding 2D perovskite films provides a great opportunity for the design of 2D ferromagnets beyond van der Waals materials. Perovskite oxide SrRuO<sub>3</sub>, as a typical perovskite itinerant ferromagnet, has broad application prospects in many fields. In this paper, the lattice dynamics, ground-state structure, electronic and magnetic properties of its perovskite monolayer with formula Sr<sub>2</sub>RuO<sub>4</sub>, as well as the effect of external electric field, are studied by combining first-principles calculation, symmetry analysis and Monte Carlo simulation. The influence of the Hubbard parameter <i>U</i> is also revealed. The results indicate that the ground-state structure under all <i>U</i> values is the structural phase (space group <inline-formula><tex-math id="M2">\begin{document}$P4/mbm$\end{document}</tex-math></inline-formula>) generated by octahedral rotation distortion. Similar to the SrRuO<sub>3</sub> bulk, the ground-state phase of the Sr<sub>2</sub>RuO<sub>4</sub> monolayer exhibits ferromagnetism, which is independent of the <i>U</i> value and thus robust. Density functional theory calculation with Hubbard parameter <i>U</i> predicts the ground-state phase of the monolayer to be a ferromagnetic half metal with out-of-plane easy-magnetization axis, while excluding the <i>U</i> parameter predicts the ground-state phase to be a ferromagnetic metallic state. The ferromagnetism mainly originates from the strong ferromagnetic exchange interaction between the nearest neighbor spin pairs. The simulated Curie temperature of the Sr<sub>2</sub>RuO<sub>4</sub> monolayer is 177 K, which is close to the value (150 K) of its bulk phase. The out-of-plane electric field does not change the ground-state structure and ferromagnetism of the Sr<sub>2</sub>RuO<sub>4</sub> monolayer, but can significantly modulate its electronic and magnetic properties. When an external electric field exceeding 0.3 V/Å is applied, the system undergoes a transition from a ferromagnetic half-metal state to a ferromagnetic metallic state. This work indicates the potential application of Sr<sub>2</sub>RuO<sub>4</sub> monolayer in low-dimensional spintrnic devices, and provides a reference for the development of perovskite-based 2D ferromagnets and the realization of controlling 2D magnetism by electric field.
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