Abstract
We find a linear relation between the conductivity $\ensuremath{\sigma}$ and the Mn spin concentration x in pure AlPdMn single grains of high structural quality. We associate the vanishing concentration of Mn spins (down to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ moments) to local defects in the Mn atoms local environments. Both $\ensuremath{\sigma}$ and x are set by the nominal composition and can be reversibly tuned by careful heat treatments. We deduce that low $\ensuremath{\sigma}$ characteristics of perfect AlPdMn quasicrystals can only be observed for concentrations of magnetic Mn lower than $x<5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},$ i.e., for defects more than about $30 \mathrm{\AA{}}$ apart. In addition, we show that a Kondo-like effect explains the low-temperature $\ensuremath{\sigma}$ upturn, also linear with x.
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