Spin Photodetector: Conversion of Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect

Recent developments in optical and material science have led to remarkable industrial applications, such as optical data recording and optical communication. The scope of the conventional optical technology can be extended by exploring simple and effective methods for detecting light circular polarization; light circular polarization carries single-photon information, making it essential in future optical technology, including quantum cryptography and quantum communication.


Spin current and inverse spin Hall effect
A spin current is a flow of electron spins in a solid. One of the driving forces for a spin current is a gradient of the difference in the spin-dependent electrochemical potential   for spin up ( = ↑) and spin down ( = ↓). Here,   =   c  e, where   c is the chemical potential. A current density for spin channel is expressed as where   is the electrical conductivity for spin up ( = ↑) and spin down ( = ↓) channel.
Here, a charge current, a flow of electron charge, is the sum of the current for  = ↑ and ↓ as j c j ↑ j ↓ : This flow is schematically illustrated in Fig. 2(a). This flow carries electron charge while the flow of spins is cancelled. In contrast, the opposite flow of j ↑ and j ↓ , j s j ↑ j ↓ , or carries electron spins without a charge current. This is a spin current. In nonmagnetic materials, a spin current is expressed as j s  (  N /2e) ↑  ↓ ), since the electrical conductivity is spin-independent:  ↑  ↓ = N /2.
Since charge  is a conserved quantity, the continuity equation of charge is described as c ·. In contrast, spins are not conserved; a spin current decays typically in a length scale of nm to m. Therefore, the continuity equation of spins are written as where M z is the z component of magnetization. z is defined as the quantization axis. Here, represents spin relaxation. n  is the equilibrium carrier density with spin and  ' is the scattering time of an electron from spin state from  to '.
Note that the detailed balance principle imposes that N ↑ / ↑↓ = N ↓ / ↓↑ , so that in equilibrium no net spin scattering takes place, where N  denotes the spin dependent density of states at the Fermi energy. This indicates that, in general, in a ferromagnet,  ↑↓ and  ↓↑ are not the same. In the equilibrium condition, d/dt=dM z /dt = 0, using the continuity equations, one finds the spin-diffusion equations: The spin relaxation time  sf is given by 1/ sf = 1/ ↑↓ + 1/ ↓↑ . By solving the diffusion equations, one can obtain the spatial variation of spin currents generated by  ↑  ↓. A spin current generated by  ↑  ↓ decays as e  /x . Thus a spin current play a key role only in a system with the scale of . A spin current can be detected electrically using the inverse spin Hall effect (ISHE), conversion of a spin current into an electric field [see Fig. 3(a)]. The ISHE has the same symmetry as that of the relativistic transformation of magnetic moment into electric polarization, which is derived from the Lorentz transformation, as follows. Consider a magnet with the magnetic moment M moving at a constant velocity v along the z axis with respect to an observer [see Fig. 3 (b)]. This motion of the magnet is a flow of angular momentum, meaning an existence of a "spin current". In the observer's coordinate system, the Lorentz transformation converts a part of this magnetic moment M into an electric dipole moment P' as where c and  0 are the light velocity and the electric constant, respectively. This indicates that electric polarization perpendicular to the direction of the magnetic-moment velocity is induced.
This electric-polarization generation can also be regarded as the spin-current version of Ampere's law as follows. As shown in Fig. 4(a), when a charge current j c flows, a circular magnetic field H is induced around the charge current, according to Ampere's law: rotH = j c . If a hypothetical magnetic monopole flows, a circular electric field E is expected to be induced around the monopole current j m according to rotE = j m [see Fig. 4(b)], from the electromagnetic duality. Although this monopole has never been observed in reality, a spin current can be regarded as a pair of the hypothetical monopole currents flowing in the opposite directions along the spin current spatial direction. Therefore, a spin current may generate an electric field and this field is the superposition of the two electric fields induced by this pair of the monopole current, as shown in Fig. 4(c). This spin-currentinduced electric field is identical to the field induced by the dipole moment described by Eq. (8).
In this way, electromagnetism and relativity predict that a spin current generates an electric field. According to Eq. (8), however, this electric field is too weak in a vacuum to be detected in reality. In a solid with strong spin-orbit interaction, in contrast, a similar but strong conversion between spin currents and electric fields appears, which is the ISHE.
In a solid, existence of a spin current can be modelled as that two electrons with opposite spins travel in opposite directions along the spin-current spatial direction j s , as shown in Fig. 3(a). Here,  denotes the spin polarization vector of the spin current. The spin-orbit interaction bends these two electrons in the same direction and induces an electromotive force E ISHE transverse to j s and , which is the ISHE. The relation among j s , E ISHE , and  is therefore given by (Saitoh, 2006) where D ISHE is the ISHE efficiency. This equation is similar to Eq. (8) but this effect may be enhanced by the strong spin-orbit interaction in solids.
The ISHE was recently observed using a spin-pumping method operated by ferromagnetic resonance (FMR) and by a non-local method in metallic nanostructures (Saitoh, 2006;Valenzuela, 2006;Kimura, 2007). Since the ISHE enables the electric detection of a spin current, it will be useful for exploring spin currents in condensed matter.

Photoinduced inverse spin Hall effect: Experiment
The combination of the optical generation of spin-polarized carriers and the ISHE enables direct conversion of light-polarization information into electric voltage in a Pt/GaAs interface (Ando, 2010). Figure 5(a) shows a schematic illustration of the Pt/GaAs sample.
Here, the thickness of the Pt layer is 5 nm. The Pt layer was sputtered on a Si-doped GaAs substrate with a doping concentration of N D = 4.7 × 10 18 cm  3 . The surface of the GaAs layer was cleaned by chemical etching immediately before the sputtering. Two electrodes are attached to the ends of the Pt layer as shown in Fig. 5(a). During the measurement, circularly polarized light with a wavelength of  = 670 nm and a power of I i = 10 mW was illuminated to the Pt/GaAs sample as shown in Fig. 5(a). In the GaAs layer, electrons with a spin polarization  along the light propagation direction are excited to the conduction band by the circularly polarized light due to the optical selection rule. Here, note that hole spin polarization plays a minor role in this setup, since it relaxes in ~ 100 fs, which is much faster than the relaxation time of ~ 35 ps for electron spin polarization (Hilton, 2002;Kimel, 2001). This spin polarization of electrons then travels into the Pt layer across the interface as a pure spin current. The injected spin current is converted into an electric voltage by the ISHE in the Pt layer due to the strong spin-orbit interaction in Pt (Ando, 2008). Here, note that the angle of the light illumination to the normal axis of the film plane is set at  0 = 65° to obtain the photoinduced ISHE signal, since the electric voltage due to the photoinduced ISHE is proportional to j s sin 0 because of the relation E ISHE  j s × , where the spin polarization  is directed along the light propagation direction. The difference in the generated voltage between illumination with right circularly polarized (RCP) and left circularly polarized (LCP) light, V R V L , was measured by a polarization-lock-in technique using a photoelastic modulator operated at 50 kHz. The difference in the intensities between RCP and LCP light incident on the sample was confirmed to be vanishingly small. All the measurements were performed at room temperature at zero applied bias across the junction.
www.intechopen.com In-plane light illumination angle  dependence of V R V L for the Pt/GaAs sample is shown in Fig. 5(b), where the in-plane angle  is defined in Fig. 5(a). Figure 5(b) shows that V R V L varies systematically by changing the illumination angle . Notable is that this variation is well reproduced using a function proportional to cos, as expected for the photoinduced ISHE. The relation of the ISHE, E ISHE  j s × , indicates that the electric voltage due to the photoinduced ISHE is proportional to |j s × | x  cos, since  and j s are directed along the light propagation direction and the z axis, respectively. Here, |j s × | x denotes the x component of j s ×  [see Fig. 5(a)]. This electromotive force was found to be disappeared in a Cu/GaAs system, where the Pt layer is replaced by Cu with very weak ISHE, supporting that ISHE is responsible for the observed electric voltage.  The observed electric voltage signal depends strongly on the ellipticity of the illuminated light polarization. Here, the ellipticity A is defined as the ratio of the minor to major radiuses of the elliptically polarized light. Figure 6(a) shows the illuminated-light ellipticity A dependence of V R V L . As shown in Fig. 6(a), the V R V L signal increases with the ellipticity A of the illuminated light. This supports that this signal is induced by the photoinduced ISHE, since the angular momentum component of a photon along the light propagation direction is zero (maximized) when A = 0 (1).

Photoinduced inverse spin Hall effect: Theory
The A dependence of V R V L shown in Fig. 6(a) demonstrates that the electric voltage observed in the Pt/GaAs junction is induced by the circularly polarized light illumination. However, the variation of the electric voltage with respect to A is not straightforward to understand; the V R V L signal is not linear to A. In the following, we discuss in detail on the experimental result by calculating the polarization of the light injected into the GaAs layer.  . Using Eqs. (11) and (12) with the parameters shown in Table 2, the transmittance T s(p) and the transmission coefficient  s(p) for the Pt/GaAs system are obtained as shown in Table 3. The calculated transmission coefficients  s(p) show that the transmission of the s and p polarized light is different. This indicates that the ellipticity of the illuminated to the sample is changed during the propagation of the film. The relation between the ellipticity A GaAs of the light injected into the GaAs layer and the ellipticity A of the illuminated light is shown in Fig. 6(b). Here, A GaAs is obtained using p s GaAs . From the value of the ellipticity A, the degree of circular polarization P circ , the difference in the numbers between RCP and LCP photons, can be written as, where I + and I -are the intensities of the RCP and LCP light, respectively. The degree of circular polarization GaAs circ P of the light injected into the GaAs layer is shown in Fig. 6(d), which is obtained from the ellipticity shown in Fig. 6 polarization. This is consistent with the prediction of the photoinduced ISHE. Thus both the light illumination angle and light ellipticity dependence of the electric voltage support that the electric voltage is induced by the ISHE driven by photoinduced spin-polarized carriers. Table 2. The parameters used in the calculation. n 0 , n 1 , and n 2 are the complex refractive indices for air, Pt, and GaAs, respectively (Adachi, 1993;Ordal, 1983).  0 is the incident angle of the illumination to the normal axis of the film plane. d 1 is the thickness of the Pt layer and  is the wavelength of the light. illumination, the output signal V R V L is proportional to the degree of circular polarization P circ of the illuminated light outside the sample. This indicates that the photoinduced ISHE can be used as a spin photodetector: the direct conversion of circular polarization information into electric voltage. This function is demonstrated experimentally in Fig. 8, in which V R V L is proportional to the degree of circular polarization of the illuminated light outside the sample.

Conclusion
The photoinduced inverse spin Hall effect provides a simple way for detecting light circular polarization through a spin current. This phenomenon enables the direct conversion of light-polarization information into electric voltage in a Pt/GaAs junction. This technique will be useful both in spintronics and photonics, promising significant advances in optical technology.