Exploring the Topological Properties of Magnetic Zintl Compounds Eu₅M₂X₆: A First-Principles Study

Topological materials have attracted widespread research interest due to their exceptional surface states and exotic transport properties. Integrating magnetism with topologically nontrivial properties in quantum materials can induce novel phenomena, such as the quantum anomalous Hall effect and the quantum magnetoelectric effect, which are crucial for advancing electronic devices, quantum computing, and spintronics. Here, we explore the topological properties of a subset of stable intrinsic magnetic materials within the Zintl phase family, Eu5M2X6 (M = Ge, Sn, or Pb; X = As, Sb, or Bi). Notably, four materials (Eu5Ge2As6, Eu5Sn2Sb6, Eu5Sn2Bi6, and Eu5Pb2As6) exhibit an axion phase with a nontrivial topological invariant Z4 = 2, suggesting the presence of topological surface states in their AFM configurations. Interestingly, we demonstrate the coexistence of a higher-order topological nature and an axion phase in the out-of-plane AFM configuration. In contrast, the in-plane AFM configuration hosts a gapless Dirac surface state. Moreover, the paramagnetic phase of seven materials exhibits a strong topological character with Z2 = 1. Our study highlights the remarkable tunability of topological phases in Eu5M2X6 materials, enabling precise control over electronic and topological states through magnetic configurations.