Fig. 5: Schematic temperature dependence of the SH conductivity ferromagnets in the T regimes I and II with nonzero TC. | npj Quantum Materials

Fig. 5: Schematic temperature dependence of the SH conductivity ferromagnets in the T regimes I and II with nonzero TC.

From: Critical enhancement of the spin Hall effect by spin fluctuations

Fig. 5

The side-jump contribution \({\sigma }_{{{{\rm{FM,SH}}}}}^{{{{\rm{side}}}}\,{{{\rm{jump}}}}}\) is shown in a and the skew-scattering contribution \({\sigma }_{{{{\rm{FM,SH}}}}}^{{{{\rm{skew}}}}\,{{{\rm{scatt.}}}}}\) is shown in b. The carrier lifetime is modeled as \({\tau }_{{{{\bf{k}}}}}^{-1}={r}_{{{{\rm{dis}}}}}+{r}_{{{{\rm{ee}}}}}{T}^{2}+{r}_{{{{\rm{sf}}}}}{T}^{3}/| T-{T}_{{{{\rm{C}}}}}|\), with rdis, ree, and rsf terms representing the disorder and impurity effects, electron-electron interaction, and the FM SF, respectively. rsf is varied with fixing rdis = ree = 1. Shaded areas indicate where the current treatment breaks down, requiring the self-consistent treatment.

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