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.