  A spin-triplet superconducting state mediated by ferromagnetic (FM) spin
fluctuations has been suggested to occur in the newly discovered heavy-fermion
superconductor UTe$_2$. However, the recent neutron scattering measurements
revealed the presence of antiferromagnetic (AFM) spin fluctuations in UTe$_2$.
Here, we report the $^{125}$Te nuclear magnetic resonance (NMR) studies of a
single-crystal UTe$_2$, suggesting the coexistence of FM and AFM spin
fluctuations in UTe$_2$. Owing to the two different Te sites in the compound,
we conclude that the FM spin fluctuations are dominant within ladders and the
AFM spin fluctuations originate from the inter-ladder magnetic coupling.
Although AFM spin fluctuations exist in the system, the FM spin fluctuations in
the ladders may play an important role in the appearance of the spin-triplet
superconducting state of UTe$_2$.
