Demonstration of the spin solar cell and spin photodiode effect

Spin injection and extraction are at the core of semiconductor spintronics. Electrical injection is one method of choice for the creation of a sizeable spin polarization in a semiconductor, requiring especially tailored tunnel or Schottky barriers. Alternatively, optical orientation can be used to generate spins in semiconductors with significant spin-orbit interaction, if optical selection rules are obeyed, typically by using circularly polarized light at a well-defined wavelength. Here we introduce a novel concept for spin injection/extraction that combines the principle of a solar cell with the creation of spin accumulation. We demonstrate that efficient optical spin injection can be achieved with unpolarized light by illuminating a p-n junction where the p-type region consists of a ferromagnet. The discovered mechanism opens the window for the optical generation of a sizeable spin accumulation also in semiconductors without direct band gap such as Si or Ge.


Supplementary information
Demonstration of the spin solar cell and spin photodiode effect  fields, the spin accumulation is almost zero at the laser spot position since the spins that are accumulated are subsequently drifting away. The Kerr rotation in this state therefore can be used as a reference signal for the case when no spin accumulation is present at the laser spot. We investigated the influence of the electric field on spin accumulation in detail in a previous publication [19].
In addition to this modulation, the measurements are performed in remanence after saturating the magne- observed which correspond to electrical spin injection and extraction. However, the signal from this effect changes sign when the modulation voltage is reversed and therefore cannot be responsible for the observed Kerr rotation in (d). The position-dependent photo-current along the channel (black) was measured separately in closed circuit.
In addition, other effects like thermal spin injection due to electrical Joule heating may appear which have to be considered. First of all, it is easy to prove that no spin accumulation is generated by the relatively large voltage applied along the n-GaAs channel for the modulation of the spin solar cell effect, since the Kerr rotation signal disappears when the absorbed laser power is reduced to a probe beam (corresponding to an absorbed laser power of 5 µW/µm 2 ). Thus, thermal spin injection due to Joule heating can be ruled out.
Supplementary Figure S2. Since the observed Kerr rotation is only visible when the laser spot is at the contact region (see (d)), the spin accumulation must be created by the laser light itself. In addition the signal fits to the observed photo-current distribution that is measured when short-circuiting the junction (see black curve in (d)). Furthermore, the electrical detection of the spin accumulation on Sample B (see Fig. 3 in the main text) directly proves the equivalence of optically and electrically induced spin accumulation since the same non-local signals are observed for the same corresponding values of photo-current and electrically applied current.
Also, a temperature gradient due to the incident laser light has to be considered which could give rise to thermo-electric spin injection/extraction. In our experiment the laser beam of 1 µm diameter (FWHM) is oriented parallel to the sample plane and hits the sample at the cleaved edge consisting of 150 nm Au, 50 nm (Ga.Mn)As, a 1 µm thick n-GaAs layer and the semi-insulating GaAs substrate as illustrated in (a).
The heat generated by light absorption will be carried away at the top by lateral heat conduction mainly through the Au layer, by radiation from the surface and by vertical heat conduction into the substrate. ). If we tentatively assume that this voltage is mainly of thermo-electric origin, then using a Seebeck coefficient of 0.5 µV/K for GaAs/(Ga.Mn)As given by Naydenova et al. [28] a temperature difference across the junction of nearly 2 · 10 5 K would be required to generate the observed voltage. Thus, a thermo-electric origin of (photo)voltage and (photo)current can be ruled out, and this should also be true for a conceivable spin accumulation related to the spin Seebeck effect.
The influence of the absorbed laser power on the n-GaAs is shown in Supplementary Fig. S3. Altogether, this clearly shows that the observed signal unambiguously corresponds to laser-induced spin extraction -the spin solar cell effect.
In addition to the laser-induced spin extraction process also the spin-dependent reflection of optically pumped electrons (proximity effect) could be expected [29]. Since the proximity effect does not depend on doping density we tested the spin solar cell effect on a reference tunnel diode with a larger doping density (n = 7 · 10 16 cm −3 ) and hence a much smaller photo-voltaic effect where no significant spin polarization was observed.
Altogether, due to the excellent agreement of the optically induced signal and the photo-current with electrical spin injection (see Fig. 2 and Fig. 3 in the main text), we conclude that the spin solar cell effect must be the dominant mechanism in our device. Kerr-spectra for various laser intensities (absorbed power density) taken at the diffusion side next to the contact (see inset) while directly extracting spins electrically. With increasing laser power the Kerr spectrum is influenced by the additional optically generated electrons that increase the electron density in the GaAs conduction band. Therefore a quantitative dependence of the spin accumulation on laser power via the Kerr rotation is not trivial. The Kerr spectra were determined in a reference experiment on Sample A where the spin accumulation was created by direct electrical spin extraction (V b = 9 V, see inset). The spectra were observed on the diffusion side a few µm away from the (Ga,Mn)As contact in order to rule out any influence of the laser light on the contact resistance. The data clearly shows a shift to shorter wavelengths with increasing laser intensity. A shift of 1 nm corresponds to about 2 meV shift of the absorption edge or a 1 meV shift of the Fermi energy in the conduction band. Compared to the photo-voltaic effect, the increase of the Fermi energy in the n-GaAs conduction band by the optically generated electrons of a few meV is negligible. In fact, the Fermi energy increase is balanced across the whole p-n-junction in equilibrium. The additionally generated electrons and holes therefore act as an increased doping density in the p-n-junction and hence illumination will solely result in a narrower tunnel barrier. For the lowest laser power no spin solar cell effect could be observed. However, a well defined Kerr spectrum is visible as shown by the red curve so that this laser intensity can be used as a probe for spin accumulation where any other effects due to laser illumination can be ruled out.  The offset-voltage which occurs in the non-local voltage signal also for electrical spin injection may originate on the one hand from a small nonuniform current that passes the detecting contact, which can be shown in 2D simulations [19], or from thermo-electric effects due to a small temperature gradient [30]. that should be more reliable since DNP is eliminated in this measurement technique due to the fast periodic reversal of the magnetization direction [19], [33]. Details about DNP in n-GaAs, which is also responsible for the peak at zero magnetic field in the spin-valve signal (see Supplementary Fig. S5 right) are already discussed in several publications [34][35][36][37][38]. Illustration of the spin photodiode effect via the Kerr spectra for various laser intensities and an applied bias voltage of -10 V. The inset shows the maximum Kerr rotation of each spectrum versus the absorbed laser power. The estimation of the absorbed laser power density is given in Supplementary Fig. S10.
In contrast to the reference Kerr spectra shown in Supplementary Fig. S3 a reduced wavelength shift of the spectrum with increasing power density is observed. Only for the largest laser intensity the zero-crossing of the spectrum is slightly shifted to lower wavelengths by 0.5 nm. This confirms that now the spin accumulation is generated when the negative bias is applied, which also broadens the band bending in the n-GaAs and shifts the optically excited electrons away. Thus the increase of the absorption edge is less visible in this geometry. The almost linear laser power dependence of the spin photodiode effect is directly shown in the inset, where the maximum Kerr rotation is plotted as a function of laser power.
The spin photodiode effect was already proposed and calculated for a similar case, where the p-side of a nonmagnetic p-n-junction was proposed to be illuminated with circularly polarized light [16]. By applying a negative voltage to the junction, it acts as a spin photodiode, converting light into a spin-polarized charge current. In principle the effect should also be present without a negative bias, since some of the optically excited spins in the (Ga,Mn)As should reach the GaAs channel by diffusion. However, the effect seems to be rather small without negative bias since its manifestation is not observed when detecting the spin solar cell effect (see Fig. 3 in the main text). In order to calculate the absorbed laser power the transmitted light is normalized to the spot size area of 1 µm diameter. The power density is then calculated by assuming that 50% of the laser intensity is located within the full width half maximum (FWHM) of the two-dimensional Gaussian spot profile (see Supplementary Fig. S11).
The external magnetic field is included in the Lamor frequency ω 0 . Since the Hanle measurements were performed on the diffusion side, no electron drift is assumed (κ = 0).
A constant spin diffusion length of 6 µm is used for all curves, extracted from linescans along the GaAs channel. In addition, to take into account the width of the contact and hence all possible injection-detection distances, the fitting function is numerically integrated over the contact width.