Anomalous Hall effect related to the magnetization in pure decagonal Al-Mn phases

An anomalous Hall effect is measured in pure decagonal Al₈₀{Mn}₂₀$ and ${Al}₇₈Mn₂₂. We show that the Hall resistivity ρH is linear with the magnetization M measured for the same fields and temperatures: ρH(H,T)=R₀H+4{π}RSM(H,T). The very dominant term RSM of ρH reveals a strong spin-orbit scattering, which is observed in Al-Mn quasicrystals. RS is found to be temperature independent in the range 6.5--110 K. From our susceptibility, specific-heat, and magnetoresistance data, we deduce that M results from a very low fraction of magnetic moments, which increase drastically with the nominal Mn concentration and that are correlated by Ruderman-Kittel-Kasuya-Yosida interactions. In this respect, the Al-Mn decagonal phase behaves very similarly to previously measured Al-Mn icosahedral and amorphous phases.