  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.
