RKKY signatures as a probe for intrinsic magnetism and AI/QAH phase discrimination in MnBi$_2$Te$_4$ films

Abstract

We present a systematic study of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in MnBi$_2$Te$_4$ films under both dark and illuminated conditions. In the dark, the intrinsic magnetism of MnBi$_2$Te$_4$ is shown to yield a stronger anisotropic RKKY spin model compared to nonmagnetic topological insulators, providing a clear signature for differentiating these systems. Furthermore, key band properties -- such as energy gap, band degeneracy/splitting, and topological deformations of the Fermi surface -- imprint distinct signatures on the RKKY interaction, enabling clear discrimination between axion insulators (AI) and quantum anomalous Hall (QAH) insulators in even- and odd-septuple-layer (SL) films. This discrimination manifests in multiple ways: through the Fermi-energy dependence or spatial oscillations of the interaction for impurities on the same surface, or via the presence versus absence of spin-frustrated terms for those on different surfaces. Under off-resonant circularly polarized light, additional phase-transition-related fingerprints also emerge to distinguish these two phases, such as sign reversals of spin-frustrated terms in even-SL films versus chirality-selective double-dip structures of collinear RKKY components in odd-SL films. Overall, this work establishes RKKY interactions as a sensitive magnetic probe for distinguishing between AI phase (even-SL) and QAH phase (odd-SL), thereby complementing conventional electrical measurements while providing new insights into the influence of intrinsic magnetism on the surface-state band structure.