Antiferromagnetic order in the Cd$_6$\textit{R} (\textit{R} $=$ rare earth) quasicrystal approximants

Many theoretical treatments of spins on aperiodic lattices support the notion of long-range antiferromagnetic order. However, to date, there has been no experimental confirmation of long-range magnetic order in quasicrystalline systems. The absence of long-range magnetic order extends to crystalline approximant phases of the icosahedral structures as well. Surprisingly, the 1/1 approximant to the Cd-Mg-R icosahedral phases, Cd$_{6}R$, appears to be an exception to the rule. Here, we report on the results of x-ray resonant magnetic scattering measurements on Cd$_{6}R$ approximants which show that long range antiferromagnetic order is, indeed, realized. For $R \quad =$ Tb and Ho, viewing the structure as a body-centered cubic packing of Tsai clusters, we find that the $R$ ions associated with the icosahedral cluster at the corner of the unit cell are antiferromagnetically correlated with the $R$ ions associated with the icosahedral cluster at the body-center of the unit cell.