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Pb(Fe$_{0.5}$Nb$_{0.5}$)O$_3$ (PFN), one of the few relaxor multiferroicsystems, has a $G$-type antiferromagnetic transition at $T_N$ = 143 K and aferroelectric transition at $T_C$ = 385 K. By using high-resolutionneutron-diffraction experiments and a total scattering technique, we paint acomprehensive picture of the long- and short-range structures of PFN: (i) aclear sign of short-range structural correlation above $T_C$, (ii) no sign ofthe negative thermal expansion behavior reported in a previous study, and (iii)clearest evidence thus far of magnetoelectric coupling below $T_N$. We concludethat at the heart of the unusual relaxor multiferroic behavior lies thedisorder between Fe$^{3+}$ and Nb$^{5+}$ atoms. We argue that this disordergives rise to short-range structural correlations arising from O disorder inaddition to Pb displacement.

High-resolution structure studies and magnetoelectric coupling of relaxor multiferroic Pb(Fe$_{0.5}$Nb$_{0.5}$)O$_3$