  We report results of a muon spin relaxation ($\mu$SR) study of
YFe$_2$Al$_{10}$, a quasi-2D nearly-ferromagnetic metal in which unconventional
quantum critical behavior is observed. No static Fe$^{2+}$ magnetism, with or
without long-range order, is found down to<EMAIL_ADDRESS>The dynamic muon spin
relaxation rate~$\lambda$ exhibits power-law divergences in temperature and
magnetic field, the latter for fields that are too weak to affect the
electronic spin dynamics directly. We attribute this to the proportionality of
$\lambda(\omega_\mu,T)$ to the dynamic structure factor~$S(\omega_\mu,T)$,
where $\omega_\mu \approx 10^5$--$10^7~\mathrm{s}^{-1}$ is the muon Zeeman
frequency. These results suggest critical divergences of $S(\omega_\mu,T)$ in
both temperature and frequency. Power-law scaling and a 2D dissipative quantum
XY (2D-DQXY) model both yield forms for $S(\omega,T)$ that agree with neutron
scattering data ($\omega \approx 10^{12}~\mathrm{s}^{-1}$). Extrapolation to
$\mu$SR frequencies agrees semi-quantitatively with the observed temperature
dependence of $\lambda(\omega_\mu,T)$, but predicts frequency independence for
$\omega_\mu \ll T$ in extreme disagreement with experiment. We conclude that
the quantum critical spin dynamics of YFe$_2$Al$_{10}$ are not well understood
at low frequencies.
