Altermagnetism in Two Dimensional Ca$_2$RuO$_4$ Perovskite

We propose and characterize a novel two-dimensional material, 2D-CRO, derived from bulk calcium-based ruthenates (CROs) of the Ruddlesden-Popper family, Ca$_{n+1}$Ru$_n$O$_{3n+1}$ ($n = 1$ and $2$). Using density functional theory, we demonstrate that 2D-CRO maintains structural stability down to the monolayer limit, exhibiting a tight interplay between structural and electronic properties. Notably, 2D-CRO displays altermagnetic behavior, characterized by zero net magnetization and strong spin-dependent phenomena, stabilized through dimensionality reduction. This stability is achieved by breaking inversion symmetry along the z-axis, favoring altermagnetic properties even in the absence of van der Waals interactions. Through theoretical models and computational analysis, we explore the altermagnetic behavior of 2D-CRO, both with and without spin-orbit coupling. We identify the spin components that contribute to the altermagnetic character and highlight the potential of 2D-CRO as a promising material for investigating altermagnetic phenomena and topological features.