Evidence of a spin-glass transition in the quasicrystal ${\mathrm{Al}}_{73}$${\mathrm{Mn}}_{21}$${\mathrm{Si}}_6$

We give a definite answer to the question whether or not the quasicrystal i-${\mathrm{Al}}_{73}$ ${\mathrm{Mn}}_{21}$ ${\mathrm{Si}}_6$ is a true three-dimensional spin glass by measuring the linear (${\mathrm{\chi }}_{\mathrm{ac}}$ and ${\mathrm{\chi }}_{\mathrm{dc}}$) and dc nonlinear susceptibilities [${\mathit{A}}_3$(T),. . .]. We show that the magnetic correlations expand over large distances with decreasing T and that ${\mathit{A}}_3$(T) diverges following the spin-glass transition scaling law with finite ${\mathit{T}}_{\mathit{c}}$. From ${\mathit{A}}_3$ and ${\mathrm{\chi }}_{\mathrm{dc}}$ we deduce separately and in the H=0 field limit the number (1.3% of the Mn concentration) and the moment (large, 7.5${\mathrm{\mu }}_{\mathit{B}}$) of the magnetic entities, which can be attributed to Mn clusters.