Probing the spin-glass freezing transition in Cu1−xMnx alloy by spin current

In this study, we used the thermally driven spin current to investigate the spin frustrations and spin fluctuations in spin-glass (SG) $\mathrm{C}{\mathrm{u}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{n}}_x$ alloys. Tuning the $\mathrm{C}{\mathrm{u}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{n}}_x$ composition results in a transition of the alloys from the SG state to the antiferromagnetic state; these states have different spin-freezing temperatures $({T}_f)$. Most spins randomly freeze at temperatures lower than the ${T}_f$ of the alloy. For each alloy composition, we obtained a temperature-dependent inverse spin Hall voltage with a peak at ${T}_p$. Crucially, ${T}_p$ had nearly identical composition dependence as that of ${T}_f,$, with ${T}_p$ being nine times larger than ${T}_f$. Similar behavior was captured using the SG insulator, amorphous ${\mathrm{Y}}₃\mathrm{F}{\mathrm{e}}₅{\mathrm{O}}₁₂$. These results indicated that the maximum spin fluctuation in both conducting and insulating SGs occurred at temperatures considerably higher than the ${T}_f$ of each. In addition, we demonstrated the importance of the effective number of valence electrons in tailoring the spin Hall angle in binary alloys.