Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds

Abstract: We reveal that Eu-based Zintl compounds host a hybrid-order topological phase characterized by the coexistence of gapless Dirac surface states and chiral hinge modes. The system exhibits surface-dependent quantum geometry: gapped surfaces display a half-quantized anomalous Hall effect arising from Berry curvature, while the gapless facet hosts unpinned Dirac states whose nonlinear anomalous Hall response originates from the quantum metric.

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