Magnetic skin effect in Pb(Fe _{1/2}$Nb _{1/2}$)O₃

Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of ∼100 μmwhereas usual surface layers only extend over a few unit cells (or ∼nm). We present a muon spectroscopy study of Pb(Fe_{1/2}Nb_{1/2})O₃(PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe³⁺(S=5/2,L ≈ 0) ions, PFN has been characterized as a unique example of a 'cluster spin-glass'. We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm³crystal of PFN. Zero-fieldpositivemuon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe³⁺spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe³⁺relaxation rates as a function of muon implantation depth in our single crystal. Usingnegativemuon elemental analysis, we find small-to-no measurable change in the Fe³⁺/Nb⁵⁺concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics.