Temperature-independent spin relaxation in heavily doped $n$-type germanium

We experimentally study the spin relaxation mechanism in heavily doped $n$-type germanium (Ge) layers by electrically detecting pure spin current transport. The spin diffusion length (${\lambda }_{\mathrm{Ge}}$) in heavily doped $n$-type Ge layers at 125 K is less than $0.7\mu \mathrm{m}$, much shorter than that expected in the recent study by Dushenko et al. We find that the spin relaxation time ${\tau }_{\mathrm{s}}$ is independent of temperature in the range of 8 to 125 K, which can be interpreted by the recent theory by Song et al. This study clarifies that the spin-relaxation mechanism at low temperatures in degenerate Ge is dominated by extrinsic scattering with impurities.

Figure 1

(a) Schematic illustration of the fabricated $n^{+}$-Ge based LSV. (b) $I\text{−}{V}_{\mathrm{int}}$ characteristics at various temperatures for spin injector and detector. (c) Nonlocal magnetoresistance curve and (d) Hanle-effect curves for the parallel and antiparallel magnetization configurations at 8 K at $I=-1.0$ mA.

Figure 2

(a) Temperature-dependent $|\mathrm{\Delta }{R}_{\mathrm{NL}}|$ for the LSVs with $d=0.3$, 0.4, 1.0, and $1.9\mu \mathrm{m}$. (b) $d$ dependencies of $|\mathrm{\Delta }{R}_{\mathrm{NL}}|$ at various temperatures.

Figure 3

Temperature dependencies of (a) ${\lambda }_{\mathrm{Ge}}$ and (b) ${\tau }_{\mathrm{s}}$, estimated by $d$ dependencies (red) and Hanle-effect curves (blue) of NL spin signals. The inset of Fig. 3 shows the temperature dependence of $D$, estimated from Eq. (4) in Ref. [37] (red squares) and nonlocal Hanle-effect curves (blue squares).