We report results of a muon spin relaxation ($\mu \mathrm{SR}$) study of ${\mathrm{YFe}}_2{\mathrm{Al}}_{10}$, a quasi-two-dimensional (2D) nearly ferromagnetic metal in which unconventional quantum critical behavior is observed. No static ${\mathrm{Fe}}^{2+}$ magnetism, with or without long-range order, is found down to 19 mK. 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 model both yield forms for $S(\omega ,T)$ that agree with neutron scattering data ($\omega \approx {10}^{12}{\mathrm{s}}^{-1}$). Extrapolation to $\mu \mathrm{SR}$ frequencies agrees semiquantitatively 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 ${\mathrm{YFe}}_2{\mathrm{Al}}_{10}$ is not well understood at low frequencies.

• Received 8 January 2018
• Revised 28 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.155110