In typical rare-earth lanthanide compounds, the localized 4-electrons have a weak effect on the electrical conduction, limiting their influence on the Berry curvature and, hence, the intrinsic anomalous Hall effect. A comprehensive study of the magnetic, thermodynamic, and transport properties of single-crystalline NdGaSi, guided by first-principles calculations, reveals a ferromagnetic ground state that induces a splitting of quasi-flat 4 electronic bands and positions them near the Fermi energy. The observation of an extraordinarily large intrinsic anomalous Hall conductivity of 1165 cm implies the direct involvement of localized states in the generation of non-trivial band crossings around the Fermi energy. The angle-resolved photoemission spectroscopy measurements provide direct evidence of non-trivial crossing of the 4-bands with dispersive bands. These results are remarkable when compared to ferrimagnetic NdAlSi, which differs only in a non-magnetic atom (a change in the principal quantum number of the outer orbital) with the same number of valence electrons and does not exhibit any measurable anomalous Hall conductivity.

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