AC Susceptibility and Electron Spin Resonance Studies of Spin Dynamics in n Ba${}_3$NbFe${}_3$Si${}_2$O${}_{14}$: A Geometrically Frustrated Lattice

We report ac susceptibility and high-frequency electron spin resonance (ESR) measurements on the geometrically frustrated compound Ba${}_3$NbFe${}_3$Si${}_2$O${}_{14}$ with the N'{e}el temperature $T_N=27K$. An unusually large frequency-dependence of ac susceptibility in the temperature range of 20 - 100 K reveals a spin-glass-like behavior, signalling the presence of frustration related slow magnetic fluctuations. ESR experiments show a multi-step magnetic and spin chirality ordering process. For temperatures above 30 K, the weak temperature dependence of the ESR linewidth $\Delta H_{pp}\propto T^{-p}$with$p=0.8$ evidences the development of short-range correlated spin clusters. The critical broadening with $p=1.8$, persisting down to 14 K, indicates the coexistence of the short-range ordered spin clusters within a helically ordered state. Below 9.5 K, the anomalously large decrease of the linewidth reveals the stabilization of a long-range ordered state with one chirality.