We present a combined single-crystal x-ray diffuse scattering and ab initio molecular dynamics study of lead telluride, PbTe. Well-known for its thermoelectric and narrow-gap semiconducting properties, PbTe recently achieved further notoriety following the report of an unusual off-centering of the lead atoms, accompanied by a local symmetry breaking, on heating. This observation, which was named emphanisis, ignited considerable controversy regarding the details of the underlying local structure and the appropriate interpretation of the total scattering experiments. In this study, we identify an unusual correlated local dipole formation extending over several unit cells with an associated local reduction of the cubic symmetry in both our x-ray diffuse scattering measurements and our molecular dynamics simulations. Importantly, when averaged spatially or temporally, the most probable positions for the ions are at the centers of their coordination polyhedra. Our results therefore clarify the nature of the local symmetry breaking, and reveal the source of the earlier controversy regarding the existence or absence of off-centering. Finally, we provide an interpretation of the behavior in terms of coupled soft optical and acoustic modes which is linked also to the high thermoelectric performance of PbTe.

Many material properties such as superconductivity, magnetoresistance or magnetoelectricity emerge from the non-linear interactions of spins and lattice/phonons. Hence, an in-depth understanding of spin–phonon coupling is at the heart of these properties. While most examples deal with one magnetic lattice only, the simultaneous presence of multiple magnetic orderings yield potentially unknown properties. We demonstrate a strong spin–phonon coupling in SmFeO₃ that emerges from the interaction of both, iron and samarium spins. We probe this coupling as a remarkably large shift of phonon frequencies and the appearance of new phonons. The spin–phonon coupling is absent for the magnetic ordering of iron alone but emerges with the additional ordering of the samarium spins. Intriguingly, this ordering is not spontaneous but induced by the iron magnetism. Our findings show an emergent phenomenon from the non-linear interaction by multiple orders, which do not need to occur spontaneously. This allows for a conceptually different approach in the search for yet unknown properties.

The phase diagrams of LaMnO₃ perovskites have been intensely studied due to the colossal magnetoresistance (CMR) exhibited by compositions around the $${\frac{3}{8}}^{th}$$3 8 t h doping level. However, phase segregation between ferromagnetic (FM) metallic and antiferromagnetic (AFM) insulating states, which itself is believed to be responsible for the colossal change in resistance under applied magnetic field, has prevented an atomistic-level understanding of the orbital ordered (OO) state at this doping level. Here, through the detailed crystallographic analysis of the phase diagram of a prototype system (AMn $${}_{3}^{A^{\prime} }$$3 A ′ Mn $${}_{4}^{B}$$4 B O₁₂), we show that the superposition of two distinct lattice modes gives rise to a striping of OO Jahn-Teller active Mn³⁺ and charge disordered (CD) Mn^3.5+ layers in a 1:3 ratio. This superposition only gives a cancellation of the Jahn-Teller-like displacements at the critical doping level. This striping of CD Mn^3.5+ with Mn³⁺ provides a natural mechanism though which long range OO can melt, giving way to a conducting state.

A structure and equation of the state of δ-AlOOH has been studied at room temperature, up to 29.35 GPa, by means of single crystal X-ray diffraction in a diamond anvil cell using synchrotron radiation. Above ~10 GPa, we observed a phase transition with symmetry changes from $P{2}_{1}nm$ to $Pnnm$. Pressure-volume data were fitted with the second order Birch-Murnaghan equation of state and showed that, at the phase transition, the bulk modulus (K₀) of the calculated wrt 0 pressure increases from 142(5) to 216(5) GPa.