Pb(Fe$_{0.5}$Nb$_{0.5}$)O$_3$ (PFN), one of the few relaxor multiferroic systems, has a $G$-type antiferromagnetic transition at $T_N$ = 143 K and a ferroelectric transition at $T_C$ = 385 K. By using high-resolution neutron-diffraction experiments a
nd a total scattering technique, we paint a comprehensive picture of the long- and short-range structures of PFN: (i) a clear sign of short-range structural correlation above $T_C$, (ii) no sign of the negative thermal expansion behavior reported in a previous study, and (iii) clearest evidence thus far of magnetoelectric coupling below $T_N$. We conclude that at the heart of the unusual relaxor multiferroic behavior lies the disorder between Fe$^{3+}$ and Nb$^{5+}$ atoms. We argue that this disorder gives rise to short-range structural correlations arising from O disorder in addition to Pb displacement.
SrRuO3 is a ferromagnetic metal with several unusual physical properties such as zero thermal expansion below Tc, so-called Invar behavior. Another anomalous feature is that the a-axis lattice constant is larger than the b-axis lattice constant, a cl
ear deviation from the predictions of the Glazer structural description with rigid RuO6 octahedron motion. Using high resolution neutron diffraction techniques, we show how these two structural anomalies arise from the irregular in-plane deformation, i.e. plastic behavior of the RuO6 octahedron, a weak band Jahn-Teller distortion. We further demonstrate that the ferromagnetic instability of SrRuO3 is related to the temperature-induced localization of Ru 4d bands.
How the magnetoelectric coupling actually occurs on a microscopic level in multiferroic BiFeO3 is not well known. By using the high-resolution single crystal neutron diffraction techniques, we have determined the electric polarization of each individ
ual elements of BiFeO3, and concluded that the magnetostrictive coupling suppresses the electric polarization at the Fe site below TN. This negative magnetoelectric coupling appears to outweigh the spin current contributions arising from the cycloid spin structure, which should produce a positive magnetoelectric coupling.
