Large impact of impurity concentration on spin transport in degenerate n -Ge

Abstract

We experimentally show that the spin relaxation in degenerate $n$-type germanium (${n}^{+}$-Ge) depends strongly on the concentration of the donor impurity (${N}_{\mathrm{d}}$) at low temperatures. From measuring nonlocal spin signals for various lateral spin-valve devices at 8 and 77 K, the spin diffusion length (${\ensuremath{\lambda}}_{\mathrm{Ge}}$) of ${n}^{+}$-Ge can be estimated as a function of carrier concentration ($n$), i.e., ${N}_{\mathrm{d}}\ensuremath{\approx}n$ ($\ensuremath{\sim}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$). We clearly find a large change in ${\ensuremath{\lambda}}_{\mathrm{Ge}}$ from 1.43 to 0.56 $\ensuremath{\mu}\mathrm{m}$ within a relatively narrow range of $n$ at 8 K. The experimental findings are interpreted quantitatively in terms of a recent theory based on donor-driven spin scattering in multivalley conduction bands in Ge.