We performed nuclear magnetic resonance (NMR) and muon spin relaxation ({mu}SR) experiments to identify the magnetic ground state of the frustrated quantum A-site spinel, CuAl2O4. Our results verify that the ground state does not exhibit a long-range magnetic ordering, but a glass-like transition manifests at T*=2.3 K. However, the Gaussian shape and the weak longitudinal field dependence of {mu}SR spectra below T* show that the ground state has dynamic spin fluctuations, distinct from those of conventional spin-glasses.
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