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PbFe$_{1/2}$Nb$_{1/2}$O$_{3}$ (PFN) is a relaxor ferroelectric (T$_{c}$$\sim$ 400 K) consisting of disordered magnetic Fe$^{3+}$ (S=${5\over2}$,L$\approx$0) ions resulting in a low temperature ``cluster glass" phase (W.Kleemann $\textit{et al.}$ Phys. Rev. Lett. ${\bf{105}}$, 257202 (2010)). Weapply neutron scattering to investigate the dynamic magnetism of this phase ina large single crystal which displays a low temperature spin glass transition(T$_{g} \sim$ 15 K), but no observable spatially long-range antiferromagneticorder. The static response in the cluster glass phase (sampled on the timescaleset by our resolution) is found to be characterized by an average magnetic spindirection that lacks any preferred direction. The dynamics that drive thisphase are defined by a magnetic correlation length that gradually increaseswith decreasing temperature. However, below $\sim$ 50 K the spatialcorrelations gradually becoming more short range indicative of increasingdisorder on cooling, thereby unravelling magnetism, until the low temperatureglass phase sets in at T$_{g}$ $\sim$ 15 K. Neutron spectroscopy is used tocharacterize the spin fluctuations in the cluster glass phase and are found tobe defined by a broadband of frequencies on the scale of $\sim$ THz, termedhere ``fast" fluctuations. The frequency bandwidth driving the magneticfluctuations mimics the correlation length and decreases until $\sim$ 50 K, andthen increases again until the glass transition. Through investigating thelow-energy acoustic phonons we find evidence of multiple distinct structuralregions which form the basis of the clusters, generating a significant amountof local disorder. We suggest that random molecular fields originating fromconflicting interactions between clusters is important for the destruction ofmagnetic order and the eventual formation of the cluster glass in PFN.

Fast broadband cluster spin-glass dynamics in PbFe$_{1/2}$Nb$_{1/2}$O$_{3}$