EuA₂X₂ (A: In, Sn; X: Sb, Bi):A Potential Magnetic Topological Material with a Higher-Order TopologicalPhase in Bulk and Monolayer Forms

Magnetic higher-order topological insulators have attracted enormous research attention due to their intriguing hinge or corner modes and quantized magnetoelectric effect. Notably, Zintl compounds are prominent examples of hosting higher-order topological and Axion phases. However, materials that facilitate a higher-order topological phase in three-dimensional (3D) bulk and two-dimensional (2D) monolayer forms are yet to be proposed. In this work, utilizing first-principles calculations, we identify EuA₂X₂ (A: In, Sn; X: Sb, Bi) compounds as promising magnetic topological materials that host higher-order topological states in both 3D and 2D forms, except for the EuIn₂Sb₂ monolayer. Moreover, all the investigated 3D bulk materials exhibit an Axion phase. The higher-order topological and Axion phases were examined by the parity-based topological invariant, Z₄, due to their centrosymmetric nature. Interestingly, the EuSn₂Sb₂ monolayer exhibits a higher-order topological insulating phase with a significant band gap of 0.4 eV in both ferromagnetic (FM) and antiferromagnetic (AFM) configurations. Meanwhile, the FM-EuIn₂Sb₂ monolayer exhibits a Chern topological feature. For brevity, topological surface, edge, and corner states are demonstrated for the 3D bulk and monolayer of EuSn₂Sb₂. The tiny gap in the surface states confirms the presence of a higher-order topological phase in 3D. Similarly, gapped edges and degenerate in-gap corner modes support the higher-order topological nature in the monolayer. Our study reveals the diverse topological phases in Eu-based layered compounds, highlighting their potential for future applications in spintronics and topological devices.