Magnetic properties of the electride compound Y$_2$C were investigated by muon spin rotation and magnetic susceptibility on two samples with different form (poly- and single-crystalline), to examine the theoretically-predicted Stoner ferromagnetism for the electride bands. There was no evidence of static magnetic order in both samples even at temperatures down to 0.024 K. For the poly-crystalline sample, the presence of a paramagnetic moment at Y sites was inferred from the Curie-Weiss behavior of the muon Knight shift and susceptibility, whereas no such tendency was observed in the single-crystalline sample. These observations suggest that the electronic ground state of Y$_2$C is at the limit between weak-to-strong electronic correlation, where onsite Coulomb repulsion is sensitive to a local modulation of the electronic state or a shift in the Fermi level due to the presence of defects/impurities.
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