Manipulating spin-polarized photocurrents in 2D transition metal dichalcogenides

Significance

Monolayer group VI transition metal dichalcogenides (TMDs) feature a massive Dirac fermion system with strong spin–valley locking. It provides a route to manipulate quantum states via the interplay of spin and valley degrees of freedom. Here we report that the spin polarization and spin–valley lifetime of free carriers are electrically detected via a spin–valve-like structure in monolayer TMDs. The long spin–valley lifetime (∼10² ns) of free carriers is electrically probed, contrasting to that of excitons (∼10¹–10² ps) probed by optical spectroscopy. It demonstrates the potential application of 2D TMDs in nonmagnetic semiconductor-based spintronics.

Abstract

Manipulating spin polarization of electrons in nonmagnetic semiconductors by means of electric fields or optical fields is an essential theme of the conceptual nonmagnetic semiconductor-based spintronics. Here we experimentally demonstrate an electric method of detecting spin polarization in monolayer transition metal dichalcogenides (TMDs) generated by circularly polarized optical pumping. The spin-polarized photocurrent is achieved through the valley-dependent optical selection rules and the spin–valley locking in monolayer WS₂, and electrically detected by a lateral spin–valve structure with ferromagnetic contacts. The demonstrated long spin–valley lifetime, the unique valley-contrasted physics, and the spin–valley locking make monolayer WS₂ an unprecedented candidate for semiconductor-based spintronics.

A longtime focus in nonmagnetic semiconductor spintronics research is to explore methods to generate and manipulate spin of electrons by means of electric fields or optical fields instead of magnetic fields, enabling scalable and integrated devices (1). The present efforts follow two distinct paths. One uses spin Hall effect or optical pumping in III-V semiconductors which feature a significant spin–orbit coupling in a form of Dresselhaus and/or Rashba terms (2–4); the other focuses on spin transport [usually generated by spin injection from ferromagnetic (FM) electrodes] in semiconductor structures made of silicon (5), carbon nanotube (6), graphene (7), etc. which have long spin-coherence length due to weak spin–orbit coupling. The emergence of atomic two-dimensional group VI transition metal dichalcogenides (TMDs) MX₂ (M = Mo, W; X = S, Se), featuring nonzero but contrasting Berry curvatures at inequivalent $K$ and K′ (equivalent to $-K$) valleys and unique spin–valley locking, provides an alternative pathway toward spintronics (8).

Valleys refer to the energy extremes around the high symmetry points of the Brillouin zone, either a “valley” in the conduction band or a “hill” in the valence band. Owing to their hexagonal lattices, the family of TMDs has degenerate but inequivalent $K$($K\prime$) valleys well separated in the first Brillouin zone. This gives electrons an extra valley degree of freedom, in addition to charge and spin. In monolayer TMDs the inversion symmetry breaking of crystal structures gives rise to nonzero but contrasting Berry curvatures at $K$ and $K\prime$ valley which are a characteristic of the Bloch bands and could be recognized as a form of orbital magnetic moment of Bloch electrons (9–11). These contrasting Berry curvatures of electrons (holes) at $K$($K\prime$) valleys lead to contrasting response to certain stimulus (9–19). One example is the valley Hall effect: An electric field would drive the electrons at different valleys ($K$ and $K\prime$) toward opposite transverse directions, in a similar way as in spin Hall effect (10, 20). A more pronounced manifestation is valley-dependent circular optical selection rules in $K$ and $K\prime$ valleys. Namely, the interband optical transitions at $K$($K\prime$) only couple with circularly polarized light of σ+(σ−) helicity. Consequently the valley polarization could be realized by the polarization field of optical excitations (10–13). On the other side, the band edge at $K$($K\prime$) valleys mainly constructed from d orbits of the heavy metal atoms inherits the strong spin–orbit coupling (SOC) of atomic orbits. And, the Zeeman-like SOC originating from $D_{3h}^1$ symmetry of monolayer TMDs lifts the out-of-plane spin degeneracy of the band edges at $K$ and $K\prime$ valleys by a significant amount, around 0.16 and 0.45 eV in the valence bands of molybdenum dichalcogenides and tungsten dichalcogenides, respectively, and about 1 order of magnitude smaller in conduction bands (10, 21–27). Owing to the presence of time-reversal symmetry $\left(K\leftrightarrow -K\right)$, the spin splitting has opposite sign between $K$ and $K\prime$ valleys at monolayer TMDs as illustrated in Fig. 1A. The Kramer doublet, spin-up state $S_z=\hslash /2$ at $K$ valley $|K\uparrow \rangle$, and spin-down state $S_z=-\left(\hslash /2\right)$ at $K\prime$ valley$|K\prime \downarrow \rangle$, are separated from the other doublet $|K\downarrow \rangle$ and $|K\prime \uparrow \rangle$ by the SOC energy. This strong SOC and the explicit inversion symmetry breaking lock the spin and valley degrees of freedom in monolayer TMDs and this interplay leads to sophisticated consequences. First the spin and valley relaxation are dramatically squelched due to the simultaneously requirements of spin flip and momentum conservation. The intrinsic mirror symmetry with respect to out-of-plane direction further suppresses spin relaxation via the D’yakonov–Perel’ mechanism, which usually plays an important role for spin relaxation in III-V semiconductors (28). Subsequently the valley and spin polarization are expected to be robust against low-energy perturbation (10, 29). Second, the spin–valley locking offers a versatile measure to manipulate spin degree of freedom via control of valley degree of freedom or vice versa (8, 30–32). This could lead to an integrated and complementary approach of valleytronics and spintronics in monolayer TMDs.

Fig. 1.

(A) Schematics of valley-dependent optical selection rules at K and K′ valleys in the momentum space of monolayer TMDs and spin–valley locking, and the proposed mechanism of the spin-resolved photocurrent measurement with the ferromagnetic electrodes. The spin-splitting at conduction band (∼0.03 eV) and valence band (∼0.45 eV) are disproportionally sketched for clarity. (B) Schematic of monolayer WS₂ devices for spin-polarized photocurrent measurements. (Inset) Optical image of the representative devices.

Here we report an experimental demonstration of spin polarization via valley-dependent optical selection rules in monolayer WS₂. The valley polarization is realized by controlling the polarization field of interband optical excitations and the spin polarization is simultaneously generated via spin–valley locking in monolayer WS₂. The spin polarization is electrically detected by the lateral spin–valve structure consisting of a tunneling barrier of Al₂O₃ and superlattice-structured cobalt–palladium (Co/Pd) ferromagnetic electrodes with perpendicular magnetization anisotropy (PMA). A high spin polarization of diffusive photocurrents is observed and a micrometer-size spin-free path and spin lifetime of free carriers in the range of 10¹∼10² ns are estimated.

Methods

The photocurrent measurements were conducted on a 5-µm-channel field-effect transistor (FET) structure of mechanically exfoliated monolayer WS₂ on a silicon substrate capped with 300-nm oxide. To overcome the conductance mismatch for efficient spin filtering, an ultrathin Al₂O₃ (1.2 nm) was deposited between the monolayer and ferromagnetic electrodes, which are made of 20 periods of alternating Co (4.5 Å)/Pd(15 Å) layers deposited with a deposition rate of 1 Å/min (Co) and 0.25 Å/min (Pd) in a metal molecular beam epitaxy system. Owing to the intrinsic mirror symmetry ($D_{3h}^1)$ with respect to the plane of metal atoms, the spin projection is along the out-of-plane direction and S_Z is a good quantum number in monolayer WS₂. To electrically detect the spin polarization along the $z$ direction, a spin analyzer with PMA is the key, which is realized with a superlattice of ultrathin Co (4.5 Å)/Pd (15 Å) multilayers (33). The in situ polar magnetooptic Kerr effect spectroscopy (MOKE) demonstrates a clear ferro-magnetization along the $\overrightarrow{z}$ direction with a coercive force around 30 Oe, as shown in Fig. 2B (SI Appendix). Standard electric characterization as shown in Fig. 2A shows a slightly n-type FET behavior in all of the devices, which might be induced from the defects, vacancy, and/or substrate effects. The source–drain conductance is at a tens of nanosiemens level at maximum within the back-gate bias range of $V_G=\pm 80\hspace{0.5em}\text{V}$, showing the Fermi level falls deep in the band gap.

Fig. 2.

Transport characteristics (A) $I_{ds}-V_G$ curve and standard I–V characteristic of the device at 10 K. (B) Polar MOKE measurement of Co/Pd layered FM electrodes at 10 K with external magnetic field perpendicular to the sample surface. The magnetic hysteresis loop clearly shows a ferromagnetic behavior with PMA.

Results and Discussion

The photocurrent was generated at a source–drain bias under the near-resonance excitation of 2.09 eV. The source–drain current was fed to a preamplifier with input impedance of 100 KΩ close to the sample side. The laser was focused through a 50× objective lens onto a spot of 1 µm and the excitation power was kept below 150 µW. The photocurrents and the circular dichroism were monitored simultaneously with a photoelastic modulator (50 KHz) and two sets of lock-in amplifiers which extract both the photocurrents and the difference between two helicities. So, the potential effects due to sample inhomogeneity were minimized.

The drain current rises by 1–3 orders of magnitude when the near-resonance excitation scans across the monolayer, similar to the reported photocurrent experiments on multilayer WS₂ (34). As demonstrated in Fig. 3B, the scanning photocurrent distributes inhomogeneously across the channel, concentrating around charge traps/defects and electrode contacts where local electric fields are strong enough to disassociate excitons, quasiparticles of Coulomb-bounded electron–hole pairs, into free carriers. To generate significant photocurrents with a minimum background electric current (dark current), a gate $V_G=-80\hspace{0.5em}\text{V}$ pulls the FET to the “off” state and a source–drain bias $V_{DS}=-5\hspace{0.5em}\text{V}$ is applied to accelerate the photocarriers. Once the FM electrodes are ferro-magnetized by the external magnetic field, the photocurrent shows a distinct pattern of optical-polarization responses at zero magnetic field as demonstrated in Fig. 3 C and D. For the excitation close to the electrode–TMD contacts, the strength of the photocurrent exhibits a strong dependence on the combination of the FM electrode magnetization and the polarization of optical excitations. Depending on the magnetization of FM electrodes, the photocurrent at the same location shows a clear circular dichroism for the circularly polarized optical excitations with opposite helicities. Namely under one magnetization direction, for example, along positive $\overrightarrow{z}$ $\left(M\uparrow \right)$, the excitation with polarization of ${\sigma }^{+}$ induces higher photocurrent than that of ${\sigma }^{-}$. If the FM magnetization is reversed, the photocurrent difference (${\sigma }^{+}-{\sigma }^{-})$ between opposite helicities also switches the sign. The nonzero photocurrent difference shows a clear dependence on the magnetization of FM electrodes as shown in Fig. 4B, which is consistent with the magnetization of the FM electrodes demonstrated in the MOKE measurements. The photocurrent difference has a clear spatial distribution pattern: It generally rises upon the excitation spot being close to FM electrodes and it vanishes when the excitation is far away from the FM electrodes. This scenario is well understood with the valley-dependent circular optical selection rules and the spin–valley locking in monolayer WS₂. The excitation of ${\sigma }^{+}({\sigma }^{-}\hspace{0.17em})$ selectively pumps the excitons at $K$(K′) valley and the electrons are fully spin-polarized to $S_z=\hslash /2$ ($S_z=-\left(\hslash /2\right)$) due to spin–valley locking. If local electric fields break the excitons into free carriers, these free carriers are accelerated by the source–drain bias to generate photocurrents while the spin polarization remains. If the spin polarization survives when the photocarriers reach the FM electrodes, the spin alignment with the FM electrodes yields the different effective resistance. Fig. 3 A–D also shows that the photocurrents and the photocurrent difference $I_{\sigma +}-I_{\sigma -}$ are uncorrelated. It is because the scanning photocurrent directly reflects the strength of local electric fields, whereas the photocurrent difference $I_{\sigma +}-I_{\sigma -}$ also depends on the photocarriers’ spin polarization arriving at the FM electrodes and the efficiency of the electrode–TMD junction for spin filtering.

Fig. 3.

(A) Laser scanning reflection image of the photocurrent device. The areas outlined with red dashed line are FM electrodes. (Inset) Corresponding optical image. (B) Photocurrent map with a scanning excitation under bias $V_G=-80\hspace{0.5em}\text{V}$ and $V_{DS}=-5\hspace{0.5em}\text{V}$. (C and D) Differential photocurrents $\left(I_{\sigma +}-I_{\sigma -}\right)$ between the ${\sigma }^{+}$ and ${\sigma }^{-}$. circularly polarized excitations through the FM electrodes with opposite magnetization $\text{M}\uparrow$ and $\text{M}\downarrow$ under zero magnetic field. The difference changes sign at opposite magnetizations. The photocurrent difference ${\text{I}}_{\text{σ}+}-{\text{I}}_{\text{σ}-}$ keeps the same polarity at both source and drain electrodes under the same FM magnetization. (E and F) Degree of photocurrent polarization $P=(I_{\sigma +}-I_{\sigma -})/(I_{\sigma +}+I_{\sigma -})$ through the FM electrodes with opposite magnetization $\text{M}\uparrow$ and $\text{M}\downarrow$.

Fig. 4.

(A) Photocurrent and degree of photocurrent polarization P as a function of the excitation intensity. (B) Photocurrent difference between circularly polarized excitations with opposite helicities as a function of external magnetic field along the out-of-plane direction. The photocurrent difference shows an FM-like loop which is consistent with the magnetization of the FM electrodes. (C) Representative photocurrent polarization P as a function of the distance from the FM electrodes with opposite magnetization $\text{M}\uparrow$ and $\text{M}\downarrow$. The hatched area labels the FM electrodes. The fit curve (blue) assuming $P\sim P_0{e}^{-(x-x_0)/l_s}$ yields peak polarization $P_0=0.15\pm 0.02$ and spin-free path $l_s=1.7\pm 0.2\hspace{0.5em}\text{μm}$ for holes, and $P_0=0.07\pm 0.01$ and $l_s=1.3\pm 0.1\hspace{0.5em}\text{μm}$ for electrons, respectively.

To quantitatively evaluate the spin polarization of the photocurrent, we define the degree of the photocurrent polarization $P=(I_{\sigma +}-I_{\sigma -})/(I_{\sigma +}+I_{\sigma -})$, where $I_{\sigma +}$($I_{\sigma -}$) is the photocurrent under the excitation of ${\sigma }^{+}$(${\sigma }^{-}$). Given that the photocurrent $I_{\sigma +}$($I_{\sigma -}$) at minimum is around several nanoamperes, which is far beyond the dark current and the noise level of tens of picoamperes in the system, artifacts in calculating polarization P are safely excluded. The photocurrent polarization P peaks around 0.15 at electrode–TMD junctions and decays to a negligible level when the optical excitation scans away from the FM electrodes as shown in Figs. 3 E and F and 4C. The polarization P reverses the sign if the magnetization of FM electrodes switches, showing a signature of efficient spin–valve structure. As a result of valley-dependent optical selection rules and spin–valley locking in monolayer TMD, the photocurrent polarization P reflects the spin polarization of the electrons (holes) arriving at the electrode–TMD junction. At the experimental conditions the photocurrent is dominated by the diffusive drift current (SI Appendix), and the electrons/holes’ trajectory could be simplified as a collective movement with a drift velocity. Without considering many-body interactions, the spin polarization exponentially decays with a characteristic time, equivalently distributing with a characteristic spin-polarization-free path in space. Consequently the profile of the spin polarization in the scanning photocurrent measurements follows $P\sim P_0{e}^{-\left(x/l_s\right)}$, where $P_0$, x, and $l_s$ denote the peak polarization, the distance between the optical excitation and the electrode–TMD junction, and the spin-free path, respectively (SI Appendix). The representative contour demonstrated in Fig. 4C yields $P_0=0.15\pm 0.02$ and $l_s=1.7\pm 0.2\hspace{0.5em}\text{μm}$ for holes, and $P_0=0.07\pm 0.01$ and $l_s=1.3\pm 0.1\hspace{0.5em}\text{μm}$ for electrons, respectively. The peak polarization $P_0$ is attributed to the spin polarization of the photocarriers and the anisotropic magnetization resistance of the FM electrodes superimposed by the efficiency of the spin-injection junction. If we assume that the detected polarization is a simple product of the spin polarization of electrons at Fermi level of cobalt electrodes at 0.4, the (up-bound) efficiency of the spin injection η at 0.7 (35), and the photocurrent spin polarization, the spin polarization of the photocurrent is estimated to be 54% (low-bound), surpassing all demonstrated in conventional semiconductors.

The micrometer-size spin-free path of electrons also implies a sizable spin-splitting in the conductance band edge which was theoretically predicted to be around 30 meV (26, 36). The similar spin-free paths of electrons (1.3 $\text{µm}$) and holes (1.7 $\text{µm}$) could be interpreted as the result of the close effective masses of electrons and holes and the large spin-splitting gaps at the conduction and valence band edges with respect to the thermal energy (10 K ∼ 0.86 meV) and the Fermi energy (around zero at intrinsic state) at the experimental conditions. Meanwhile Fig. 3 E and F shows that the degree of spin polarization of holes is significantly higher than that of electrons, 15% vs. 7%. This is consistent with the calculations that the spin-splitting carries the same sign between conduction band and valence band monolayer WS₂ as shown in Fig. 1A (26, 27). As spin is conserved in the optical interband transition, electrons are pumped to the spin-split upper subband under near-resonant excitations. Unlike photogenerated holes which are around the band edge with a spin-splitting in valence band of around 0.45 eV, the electron relaxation could take place through two channels, intravalley scattering (to the spin-split lower subband in the same valley) where spin-flip is required, or intervalley scattering (to the spin-split lower subband in the opposite valley) where spin is conserved. This explains why the spin polarization of electrons (at the source side) is weaker than that of holes (at the drain side). Fig. 3 C–F shows that the photocurrent difference $I_{\text{σ}+}-I_{\text{σ}-}$ and the degree of spin polarization carry the same polarity with comparable strength (15% vs. 7%) at both drain and source electrodes under the same FM magnetization. It implies that the spin-conserved intervalley scattering predominates the electron relaxation process.

We also could estimate the magnitude of the spin lifetime from the spin-free path. Given that the effective bias added on the channel is on the order of $V_{ds}-\left(E_g+E_{exciton\hspace{0.17em}binding}\right)\sim 2.5\hspace{0.5em}\text{eV}$ where we assume the band bending at both contacts is roughly of the electronic band gap at most and the mobility of 0.1–1 ${\text{cm}}^2\cdot \text{v/s}$ of the devices (SI Appendix), the spin-free path indicates the estimated spin–valley lifetime around 10¹∼10² ns. This estimate is orders of magnitude larger than the valley lifetime estimated from polarization-resolved photoluminescence and pump–probe spectroscopy in which the exciton effect predominates the optical properties and consequently the valley lifetime of excitons instead of free carriers is probed (37, 38). Note that the electron–hole exchange interaction provides the major channel for excitons’ spin–valley depolarization (39), whereas the exchange interactions are greatly suppressed in oppositely drifting free carriers in a nearly intrinsic state, and consequently the free carriers presumably show significantly longer spin–valley lifetime. The capability of monitoring spin–valley lifetime of free carriers makes the present technique complementary to optical approaches.

Summary

In summary, we have demonstrated the highly spin-polarized photocurrents in monolayer WS₂ by controlling the polarization field of optical excitations. The spin polarization is well achieved as the result of valley-dependent optical selection rules and spin–valley locking in monolayer TMDs. The spin polarization of free carriers could be electrically detected with a lateral spin–valve structure. The demonstrated micrometer-size spin-free path and spin lifetime in the range of 10¹∼10² ns, and the unique spin–valley locking make monolayer TMDs a promising candidate for spintronics applications.