Half-Heusler alloys are leading candidate materials for large scale thermoelectric power generation. In the past decade, substantial improvements have been made to the established n-types based on X_IVNiSn, and exciting new p-types based on X_VFeSb and ZrCoBi have been discovered. This has been achieved through careful experimental work and by increased fundamental insight. In particular, advances in materials synthesis and compositional optimisation guided by empirical modelling have been key to extracting more performance from half-Heuslers alloys. This review summarises recent progress for the main classes of half-Heusler alloys, including their fundamental electronic and thermal properties, processing, and thermoelectric performance. It also incorporates some of the expanding body of work focused on translating materials performance (zT > 1 at 773 K is now routinely possible) into generator devices.

The structures and thermoelectric properties of the ${\left({\mathrm{Bi}}_2\right)}_m{\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_n$ homologous series, derived from stacking hexagonal ${\mathrm{Bi}}_2$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ blocks, are reported. The end members of this series are metallic Bi and semiconducting ${\mathrm{Bi}}_2{\mathrm{Te}}_3$; nine members of the series have been studied. The structures form an infinitely adaptive series and a unified structural description based on a modulated structure approach is presented. The as-synthesized samples have thermopowers $\left(S\right)$ that vary from $n$ type for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ to $p$ type for phases rich in ${\mathrm{Bi}}_2$ blocks but with some ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ blocks present, to $n$ type again for Bi metal. The thermoelectric power factor $(S^2∕\rho )$ is highest for Bi metal ($43\mu \mathrm{W}∕{\mathrm{K}}^2\mathrm{cm}$ at $130\mathrm{K}$), followed by ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ ($20\mu \mathrm{W}∕{\mathrm{K}}^2\mathrm{cm}$ at $270\mathrm{K}$), while ${\mathrm{Bi}}_2\mathrm{Te}$ $(m:n=5:2)$ and ${\mathrm{Bi}}_7{\mathrm{Te}}_3$ $(m:n=15:6)$ have $9\mu \mathrm{W}∕{\mathrm{K}}^2\mathrm{cm}$ (at $240\mathrm{K}$) and $11\mu \mathrm{W}∕{\mathrm{K}}^2\mathrm{cm}$ (at $270\mathrm{K}$), respectively. The results of doping studies with Sb and Se into ${\mathrm{Bi}}_2\mathrm{Te}$ are reported.

We report on the unconventional magnetism in the cubic B-site ordered double perovskite Ba2YMoO6, using ac and dc magnetic susceptibility, heat capacity and muon spin rotation. No magnetic order is observed down to 2~K while the Weiss temperature is $\sim${}-160\,\,K. This is ascribed to the geometric frustration in the lattice of edge-sharing tetrahedra with orbitally degenerate Mo5+ s=1/2 spins. Our experimental results point to a gradual freezing of the spins into a disordered pattern of spin singlets, quenching the orbital degeneracy while leaving the global cubic symmetry unaffected, and providing a rare example of a valence bond glass.

Half-Heusler thermoelectrics first attracted interest in the late-1990s and are currently undergoing a renaissance. This has been driven by improved synthesis, processing and characterisation methods, leading to increases in the thermoelectric figure of merit and the observation of novel phenomena such as carrier filtering in nanocomposite samples. The difficulty in extracting good thermoelectric performance is at first glance surprising given the relative simplicity of the ideal crystal structure with only site occupancies and lattice parameter as crystallographic variables. However, the observed thermoelectric properties are found to depend sensitively on sample processing. Recent work has shown that prepared ingots can contain a range of inhomogeneities, including interstitials, nano- and micron sized Heusler inclusions and multiple half-Heusler phases. For this reason, the prepared materials are far more complex than initially appreciated and this may offer opportunities to enhance the thermoelectric figure of merit.

We have investigated the magnetoelectric coupling in the lone pair containing piezoelectric ferrimagnet ${\text{Cu}}_2{\text{OSeO}}_3$. Significant magnetocapacitance develops in the magnetically ordered state $\left(T_c=60\text{K}\right)$. We find critical behavior near $T_c$ and a divergence near the metamagnetic transition at 500 Oe. High-resolution x-ray and neutron powder diffraction measurements show that ${\text{Cu}}_2{\text{OSeO}}_3$ is metrically cubic down to 10 K but that the ferrimagnetic ordering reduces the symmetry to rhombohedral $R3$. The metric cubic lattice dimensions exclude a magnetoelectric coupling mechanism involving spontaneous lattice strain, and this is unique among magnetoelectric and multiferroic materials.