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Recent progress in experimental understanding of the A-Mg-R (A = Zn and Mg, R = rare-earth elements) magnetic quasicrystals is reviewed. The A-Mg-R quasicrystals have long been classified as spin-glasses because of their typical spin-freezing behavior at low temperatures. On the other hand, recent neutron diffraction experiments clearly detect strong magnetic diffuse scattering, indicative of significant short-range spin order. After all the data sets obtained by various experimental techniques have been combined, it is proposed that the nature of the spin freezing in magnetic quasicrystals is related to blocking phenomena in superparamagnets rather than to a thermodynamic transition in the canonical spin-glasses.

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