Spin-to-charge conversion for hot photoexcited electrons in germanium

We investigate the spin-to-charge conversion in highly doped germanium as a function of the kinetic energy of the carriers. Spin-polarized electrons are optically generated in the Ge conduction band, and their kinetic energy is varied by changing the photon energy in the 0.7–2.2 eV range. The spin detection scheme relies on spin-dependent scattering inside Ge, which yields an inverse spin-Hall electromotive force. The detected signal shows a sign inversion for $h\nu \approx 1\mathrm{eV}$ which can be related to an interplay between the spin relaxation of high-energy electrons photoexcited from the heavy-hole and light-hole bands and that of low-energy electrons promoted from the split-off band. The inferred spin-Hall angle increases by about 3 orders of magnitude within the analyzed photon energy range. Since, for increasing photon energies, the phonon contribution to spin scattering exceeds that of impurities, our result indicates that the spin-to-charge conversion mediated by phonons is much more efficient than the one mediated by impurities.

Figure 1

(a) Sketch of the sample. A single crystalline Ge stripe of dimensions $d_x\times d_y\times d_z=1\times 20\times 1\mu {\mathrm{m}}^3$ lies on top of ${\mathrm{SiO}}_2/\mathrm{Si}$. Two Au/Ti pads deposited onto the stripe allow measuring the photoinduced ISHE signal $\mathrm{\Delta }{V}_{\mathrm{ISHE}}$. (b) Experimental geometry: $\vartheta$ and $\phi$ are the polar and azimuthal angles of the incident light, respectively.

Figure 2

ISHE signal measured in the $n$-doped sample $\left(h\nu =1.97\mathrm{eV}\right)$ as a function of (a) $\phi$ [see Fig. 1], with optical power absorbed by Ge $W=246\mu \mathrm{W}$ and degree of circular polarization $\mathrm{DCP}=100\%$; (b) DCP, with $W=246\mu \mathrm{W}$ and $\phi =0^{\circ }$; and (c) $W$ for $\mathrm{DCP}=100\%$ and $\phi =0^{\circ }$. (d) ISHE signal in $p$-doped (red circles) and $n$-doped (blue squares) samples as a function of the incident photon energy. Each data point represents the average value of ten acquisitions with an integration time of 200 s. The bars account for the fluctuations of the data to twice their standard deviation. The vertical gray dashed line marks the onset of SO transitions, $h\nu =E_{\mathrm{dg}}+{\mathrm{\Delta }}_0=1.04\mathrm{eV}$.

Figure 3

Relaxation times of spin-polarized electrons in Ge (for further information see Sec. 3b and the appendices). Triangles pointing upwards (downwards) refer to $n$- $(p$-) doped samples, and stars refer to both. The vertical lines separate different regimes, as discussed in the text. (a) Impurity (green) and phonon (red) momentum relaxation times. (b) Energy (blue) and spin (red) lifetimes.

Figure 4

(a) Spin-polarization spectra at the generation time $t=0$ (blue dotted line) and after 0.5 ps (orange dashed line) and 2 ps (green solid line). (b) Total average spin current density (gray solid line) and partial contributions originated by electrons excited from the HH (blue dash-dotted line), LH (orange dotted line), and SO (green dashed line) bands. The vertical dashed red line highlights the onset of transitions from SO states.

Figure 5

Estimated spin-to-charge conversion parameter $\gamma$ as a function of photon energy for $n$-doped (blue squares) and $p$-doped Ge (red circles). Dashed lines are guides for the eye. The inset shows the ratio ${\gamma }_p/{\gamma }_n$ between the spin-to-charge conversion parameters for $n$- and $p$-doped Ge. In the inset, the band marks the expected ratio within an atomic picture, with $m$ ranging between 2 and 4.

Figure 6

Average spin current density inside a Ge stripe (dashed line) and spin current density injected into Pt in a Pt/Ge junction (solid line).

Figure 7

Phonon momentum scattering time for electrons in (a) $L$, (b) $\mathrm{\Gamma }$, and (c) $\mathrm{\Delta }$ valleys. (d) Sketch of the leading phonon-scattering processes occurring in the Ge CB. (e) Valley occupation probability as a function of the kinetic energy.