Abstract: In the thirty years since the discovery of quasi-crystals by Dan Shechtman, there has been tremendous progress in our understanding of the structure of quasi-crystals and aperiodic systems in  general. Indeed, the question first asked by Per Bak soon after Shechtman’s discovery, ​“Where are the atoms?”, can largely be answered for at least one class of quasi-crystals, the i‐YbCd5.7 icosahedral phase.

Progress in our understanding of the consequences of aperiodicity for physical phenomena such as the electronic, magnetic, and optical properties has lagged somewhat but we have recently seen a surge of activity and new results. On the magnetism front, the discovery of a& new family of magnetic quasi-crystals and their closely related crystalline approximants, has allowed for a direct comparison of the impact of aperiodicity on magnetic interactions in compounds that have similar local structures. Examples of stable binary icosahedral quasi-crystals are quite rare and, before the discovery of icosahedral quasi-crystals in the i‐R‐Cd system (R = Gd to Tm, Y), there were& no known examples that featured localized magnetic moments. Local‐moment‐bearing binary quasi-crystals represent the compositionally simplest system for the study of magnetic interactions in aperiodic compounds and, therefore, the new R‐Cd quasi-crystal family will play a key role in these studies, offering non‐magnetic, Y, Heisenberg‐like, Gd, and non‐Heisenberg (CEF split) Tb to Tm members, in addition to the structural and compositional simplicity of a binary phase.

Furthermore, the existence of a corresponding set of cubic approximants, RCd6, to the icosahedral phase allows for direct comparisons between the low‐temperature magnetic states of crystalline and quasi-crystalline phases with fundamentally similar local structures. RCd6 may be described as a body‐centered cubic packing of the same clusters of atoms as found in the newly discovered icosahedral phase. Using X‐ray resonant magnetic scattering and neutron diffraction, we have shown that the RCd6 approximants manifest long‐range magnetic order at low temperatures, whereas the related icosahedral phase exhibits only spin‐glass‐like freezing at low temperatures. To understand the reason for the absence of long‐range magnetic ordering in the quasi-crystalline phase, we have investigated both the elastic and inelastic neutron scattering measurements of i‐Tb‐Cd. Our results to date will be described and discussed.