We describe the development of an atom-based Monte Carlo simulation model which gives rise to a nanoscale polar domain structure as envisaged to occur in $\mathrm{Pb}\left({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$ (PZN) and similar relaxor ferroelectric materials. Individual domains are essentially thin platelike domains normal to each of the six $⟨110⟩$ directions. Calculated diffuse scattering patterns have been obtained from the simulations, and these are in good agreement with observed neutron scattering data. Nanoscale domain formation is driven by the need for the Pb atoms to satisfy their valence requirements; within a planar domain, the Pb atoms are displaced in a concerted fashion away from the center of their 12-fold coordination polyhedra with an in-plane displacement along $⟨110⟩$ towards one of the coordinating O atoms. The $B$-site cations Zn and Nb display a strong tendency to alternate in the $⟨100⟩$ directions but complete order is frustrated by the 2:1 stoichiometry. No diffraction evidence has been found that this $B$-site ordering is directly linked to the nanoscale polar domain ordering. Such a linkage cannot be completely ruled out, but if it does exist, its effect on the diffraction pattern must be quite subtle. The $B$-site ordering does play an indirect role in establishing the average cell dimension, which in turn dictates the magnitude of the Pb displacements. The effect of applying an external electric field is modeled, and the results are found to be consistent with experiment.

The perovskite-based oxide ${\mathrm{Y}}_{0.33}{\mathrm{Sr}}_{0.67}{\mathrm{CoO}}_{2.79}$ has been magnetically and structurally characterized. The material shows a unit cell of $2\times 2\times 4$ simple perovskite cubes with space group $I4/mmm.\mathrm{}$ This is a different structure to that observed in the much-studied $(\mathrm{L}\mathrm{a},\mathrm{S}\mathrm{r}){\mathrm{CoO}}_3$ oxides. Oxygen stoichiometry is established through thermogravimetric analysis and correlated with ac and dc magnetic measurements and magnetic neutron diffraction. Hysteresis with field and temperature is observed in the dc magnetization measurements, yet the absence of an imaginary component in the ac susceptibility suggests a time-independent cause for these effects such as the presence of independently ordering ferromagnetic regions due to compositional inhomogeneities within the (single-phase) sample. Rietveld magnetic refinements suggest that the Co moments are arranged antiferromagnetically below 320 K, with the ferromagnetic regions existing within the long-range ordered antiferromagnetic matrix. The staggered moments are (anti)parallel with the c axis and of magnitude $2{\mu }_B,$ a moment most typical of intermediate spin ${\mathrm{Co}}^{3+}.$ The material does not enter a spin glass or cluster glass phase, but appears to undergo a broad spin-state transition below 100 K.

MnPS₃ is a layered honeycomb lattice antiferromagnet with the spins aligned perpendicular to the layers at low temperature. Structurally it is monoclinic, with an unusual combination of magnetic and crystallographic symmetries, and so offers a rare insight into the behaviour of low-dimensional magnetism. Here the effect of magnetic dilution by Zn substitution on the magnetic structure is explored using neutron diffraction and magnetometry. The composition dependencies of T_N and the spin flop field are found. The critical concentration for long-range order is estimated to be 45% Mn. The first neighbour exchange is found to be independent of composition. It appears that dilution induces a moment component in the plane, and gives rise to a complex phase diagram in which a reordering temperature is apparent.