Bulk Ferromagnetic Icosahedral Quasicrystals without Rapid Quenching.

While ferromagnetism is well understood in periodic and amorphous materials, its critical behavior in quasiperiodic systems has remained elusive. Although ferromagnetic icosahedral quasicrystals (iQCs) have recently been discovered, all known examples have been limited to rapidly quenched, metastable states, precluding annealing, structural refinement, and quantitative studies of magnetic criticality. Here we demonstrate, for the first time, the realization of bulk, annealable ferromagnetic iQCs in compositionally tuned Au-Cu-Al-In-R (R = Gd, Tb, Dy) alloys. Guided by chemical design in multicomponent alloy space, single-phase iQCs are obtained by conventional arc melting and subsequent controlled annealing, resulting in sharp quasiperiodic diffraction and exceptional thermal robustness. Strikingly, while all compounds exhibit clear ferromagnetic order, their magnetic critical behavior differs systematically depending on the rare-earth element. Tb- and Dy-based iQCs display critical exponents close to mean-field values, whereas the Gd-based system exhibits a significantly enhanced critical exponent δ, deviating from mean-field behavior and from both anisotropic counterparts and previously studied approximant crystals. This difference is attributed to stronger spin fluctuations in the isotropic Gd system, which effectively shorten the interaction range, while anisotropy in Tb/Dy suppresses fluctuations and leads to mean-field-like behavior. These results establish that magnetic criticality in quasicrystals is not uniquely determined by quasiperiodic order alone but is governed by the interplay between quasiperiodicity and local spin symmetry. More broadly, they demonstrate that quasiperiodic solids provide a tunable materials platform for accessing nonmean-field critical behavior beyond the constraints of periodic systems.