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Muon spin relaxation ($\mu$SR) measurements were carried out onSrDy$_2$O$_4$, a frustrated magnet featuring short range magnetic correlationsat low temperatures. Zero-field muon spin depolarization measurementsdemonstrate that fast magnetic fluctuations are present from $T=300$ K down to20 mK. The coexistence of short range magnetic correlations and fluctuations at$T=20$ mK indicates that SrDy$_2$O$_4$ features a spin liquid ground state.Large longitudinal fields affect weakly the muon spin depolarization, alsosuggesting the presence of fast fluctuations. For a longitudinal field of$\mu_0H=2$ T, a non-relaxing asymmetry contribution appears below $T=6$ K,indicating considerable slowing down of the magnetic fluctuations asfield-induced magnetically-ordered phases are approached.

Evidence for spin liquid ground state in SrDy$_2$O$_4$ frustrated magnet probed by muSR