Energy Relaxation in the Spin-Polarized Disordered Electron Liquid

Energy relaxation is studied in the spin-polarized disordered electron systems in the diffusive regime. We derive a quantum kinetic equation in which the kernel of the electron-electron collision integral explicitly depends on the electron magnetization. As a consequence, the inelastic scattering rate has a nonmonotonic dependence on the spin polarization of the system.

Figure 1

The diagrammatic illustration of the out-scattering terms in the collision integral: (a) the magnetization-independent spin-conserving scattering and (b) the triplet channel magnetization sensitive scattering with spin-flips. The dashed line denotes the screened $e\mathrm{\text{−}}e$ interaction.

Figure 2

The density plot of ${\tau }_{\mathrm{out}}^{(t)}(0)/{\tau }_{\mathrm{out}}^{(t)}(|\mathbf{m}|)$ as a function of $F_0^{\sigma }$ and $2|\mathbf{m}|/(\nu {\epsilon }_{\uparrow })$ for panel (a), and $2|\mathbf{m}|/(\nu {\epsilon }_{\downarrow })$ for panel (b).