Fast broadband cluster spin-glass dynamics in PbFe1/2Nb1/2O3

PbFe1/2Nb1/2O3 (PFN) is a relaxor ferroelectric (Tc∼400K) consisting of magnetic Fe3+ (S=52, L≈0) ions disordered throughout the lattice and hosts a spin-glass phase at low temperatures built from spatially isolated clusters of Fe3+ ions, termed a “cluster glass” [Kleemann et al., Phys. Rev. Lett. 105, 257202 (2010)]. We apply neutron scattering to investigate the magnetism and dynamics of this phase in a large single crystal which displays a low-temperature spin-glass transition (Tg∼15K, found with magnetization), but no observable macroscopic and spatially long-range antiferromagnetic order. The static response in the low-temperature cluster-glass phase (sampled on the timescale set by our resolution) is found to be characterized by an average magnetic spin direction that lacks any preferred direction. The dynamics that drive this phase are defined by a magnetic correlation length that gradually increases with decreasing temperature. However, below ∼50K the opposite is found with spatial correlations gradually becoming more short ranged, indicative of increasing disorder on cooling, thereby unraveling magnetism, until the low-temperature glass phase sets in at Tg∼15K. Neutron spectroscopy is used to characterize the spin fluctuations in the cluster-glass phase and are found to be defined by a broadband of frequencies on the scale of terahertz, termed here “fast” fluctuations. The frequency bandwidth driving the magnetic fluctuations mimics the correlation length and decreases until ∼50K, and then increases again until the glass transition. Through investigating the low-energy acoustic phonons we find evidence of multiple distinct structural regions which form the basis of the clusters, generating a significant amount of local disorder. We suggest that random molecular fields originating from conflicting interactions between clusters is important for the destruction of magnetic order and the eventual formation of the cluster glass in PFN.