Transition metal dichalcogenides (TMDs) are of great interest due to their unique

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1 Imaging Spin Dynamics in Monolayer WS 2 by Time-Resolved Kerr Rotation Microscopy Elizabeth J. Bushong, 1 Yunqiu (Kelly) Luo, 1 Kathleen M. McCreary, 2 Michael J. Newburger, 1 Simranjeet Singh, 1 Berend T. Jonker, 2 Roland K. Kawakami 1 * 1 Department of Physics, The Ohio State University, Columbus OH 4321, USA 2 Naval Research Laboratory, Washington DC 2375, USA * kawakami.15@osu.edu Transition metal dichalcogenides (TMDs) are of great interest due to their unique band structure with large valley-dependent spin-orbit splittings, Berry curvature, and spin/valley-selective optical selection rules. 1-1 While these properties make TMDs extremely attractive for spintronics, utilization of these properties in nanoscale devices demands a fundamental understanding as obtained, for example, through imaging of spin dynamics with high spatial resolution. Here, we report the first spatially-resolved images of spin dynamics in monolayer WS 2 using time resolved Kerr rotation 11 (TRKR) microscopy with ~1 micron resolution. We discover a complex spatial dependence of spin density varying on the micron length scale, with spin lifetimes exceeding 5 ns. Comparing micro-photoluminescence and TRKR microscopy reveals an unexpected anticorrelation between strong A exciton luminescence and high spin density, which provides new insights on the transfer of spin angular momentum from short-lived excitons to long-lived spin states of resident conduction electrons We also find that the spin lifetime in WS 2 is robust against external magnetic fields, in contrast to MoS 2, 12 which confirms predictions that larger spin-orbit coupling will stabilize spins against relaxation, contrary to conventional materials. 4,7,12,15-17 These results demonstrate high resolution imaging of spin dynamics as a powerful technique for investigating spindependent physics in 2D materials. The band structure of monolayer WS 2 is characterized by a direct gap and large spin splittings with opposite polarities in the +K and K valleys (Figure 1a). 6,7,18-2 This produces spin- 1

2 valley coupling that is predicted to suppress spin-flip scattering and spin dephasing, resulting in long spin and valley lifetimes. 4,7,12,15-17 Because the helicity of light couples to the spin and valley polarization via optical selection rules, 4,5 optical probes have been utilized to investigate the spin and valley dynamics in TMDs. Early studies utilizing polarization-resolved photoluminescence spectroscopy found high retention of circular polarization in MoS 2 monolayers (up to 99%), suggesting valley lifetimes exceeding 1 ns. 6-9 While initial timeresolved optical techniques observed short lifetimes for valley polarization of excitons (tens of ps or less), more recent TRKR measurements observed nanosecond spin lifetimes of resident conduction electrons in n-type monolayer MoS 2 and WS 2, and resident holes in p-type monolayer WSe To investigate the origin and character of the long lived spins, we utilize TRKR microscopy to directly image the spin dynamics in a monolayer TMD with unprecedented spatial resolution (~1 micron) and ~15 fs temporal resolution (see Methods). Experiments are performed on high quality monolayer WS 2 grown by chemical vapor deposition (CVD) on SiO 2 /Si substrates. 28 As shown in Figure 1b, a given WS 2 sample has small isolated triangles, typically 1-4 microns in size, which are believed to be single-crystalline. We verify the quality and monolayer nature of the WS 2 using photoluminescence (PL) spectroscopy. The PL spectrum measured at 6 K (Figure 1c) shows a strong peak at 63 nm corresponding to the A exciton, while the absence of indirect gap PL emission at longer wavelengths, which is present in bilayer and bulk samples, confirms the films are monolayer. 2,3 Transport measurements indicate that the as-grown material is n-type. Spin dynamics in monolayer WS 2 are investigated using TRKR microscopy, depicted in Figure 1d. The sample is held at 6 K in a low vibration, closed-cycle optical cryostat. Ultrafast pulses from an optical parametric oscillator (~15 fs, 625 nm, 76 MHz) are split into pump and probe pulses, each of which is focused onto the sample with ~1 μm spot size. The circularlypolarized pump pulse creates valley-polarized excitons, each consisting of a spin polarized electron and hole, as shown in the band diagram (Figure 1a). The time-delayed, linearly- 2

3 polarized probe pulse measures the combined spin and valley polarization through the Kerr rotation of its linear polarization axis. Figure 1e shows the Kerr rotation as a function of time delay between the pump and probe pulses. As shown in the inset of Figure 1e, there is an initial rapid exponential decay of 3 ps (curve fit in green), which is due to the loss of valley polarization of excitons, consistent with previous TRKR studies. 22,25,26 However, a substantial Kerr rotation remains beyond the initial decay and persists beyond several nanoseconds. Excitons could not produce this signal because they recombine within the first few hundred picoseconds, 21,24,29 so the long lifetime must therefore originate from the spin and/or valley polarization of resident conduction electrons of the n-type material. For the conduction electrons, the Kerr rotation is due to spin and valley polarization and is given, to lowest order, by ~ +, where =,, +,, is the spin imbalance and =, +,,, is the valley imbalance of the electron density. We find that the Kerr rotation is well described by a biexponential decay with time constants of τ short = 32 ps and τ long = 5.4 ns (the curve fit is the solid red line in Figure 1e). Such bi-exponential behavior agrees, for example, with a spin relaxation model based on fast intervalley scattering in monolayer TMDs. 12 In this model, which we discuss again later, fast intervalley scattering between the K and K valleys produces Dyakonov-Perel-like spin relaxation (i.e. spin dephasing by a fluctuating spin-orbit field). By scanning the overlapped pump and probe spots relative to the sample at a fixed time delay, a spatial image of the spin density is obtained. By repeating this mapping for different time delays, the microscopic evolution of spin dynamics can be directly revealed. Figure 2 shows a series of Kerr rotation images taken on a triangular island of monolayer WS 2 at different time delays. The sequence of images illustrates a previously undiscovered complex spatial dependence of the spin density on the WS 2 island. Areas with a large spin density (colored in yellow/orange/red) are separated by only a few microns from regions with almost no spin density (colored blue/black). The spatial distribution is striking, with a central core of low spin density surrounded by regions of higher spin density. It is worthwhile to note that even at 3

4 11 ns, there is still a measurable spin density. Interestingly, the images at longer time delays appear to show the spin density evolving to a more symmetric distribution within the triangle. To gain further insight into the spatial dependence of the Kerr rotation, we investigate its relationship with the photoluminescence (PL) spectra. Figures 3b and 3c show a series of TRKR delay scans and PL spectra taken along a linecut within the triangular island, as indicated in Figure 3a. The most notable trend is that in the region with strongest PL, the TRKR has a fast decay (<1 ps) and shows very little amplitude in the long lived spin state. On the other hand, regions with high spin density in the long lived state have much weaker PL. This anticorrelation between high spin density and high PL intensity is initially counterintuitive as both properties should benefit from high material quality. However, the connection becomes apparent if we consider that the valley-polarized excitons excited by the pump pulse must transfer spin angular momentum to the resident conduction electrons in order to populate the long lived spin states. This spin transfer could occur, for example, through a spin flip-flop process mediated by an exchange interaction = / where is the spin of an electron bound in the exciton and is the spin of a resident electron. This would dynamically polarize the resident electrons while converting the exciton to a spin triplet state, which would favor nonradiative recombination. As the transfer of spin angular momentum becomes more efficient, higher spin densities are generated while radiative recombination is further suppressed. Thus, the origin of the complex spatial dependence of spin density observed in Figure 2 is related to factors that promote the transfer of spin angular momentum from excitons to resident electrons. Future studies will investigate the role of various factors on this spin transfer (e.g. point defects, grain boundaries, substrate interactions, etc.). It is worth noting that other proposed mechanisms for generating spin density of free carriers do not account for the anticorrelation observed here. 14 We turn our attention to the important role that strong spin-orbit coupling has on the spin relaxation and dynamics in WS 2. Specifically, there are predictions that larger spin-orbit fields 4

5 will enhance the spin lifetime, 4,7,12,15-17 contrary to what is seen in conventional materials such as GaAs in which larger spin-orbit fields reduce the spin lifetime. Monolayer WS 2, with a calculated spin-splitting of ~3 mev in the conduction band, 19 may have large enough spin-splitting to bring about spin stabilization due to a large spin-orbit field. This would result in spins that are more robust to external factors such as a magnetic field and thermal fluctuations. It is therefore important to experimentally investigate the spin dynamics as a function of external magnetic field and temperature. The experimental signature of spin stabilization by spin-orbit coupling is illustrated by considering a particular model of spin dynamics in monolayer TMDs. We calculate the dynamics of spin polarization (S) in the presence of a transverse magnetic field (B ext ), as depicted in Figure 4a, using the model of spin dynamics based on fast intervalley scattering. 12,17 The calculated spin lifetime vs. spin-orbit field (at fixed B ext ), as shown in Figure 4b, exhibits two distinct regimes: a conventional regime for small spin-orbit field (blue curve), and the spin-orbit stabilized regime when there is large spin-orbit field (orange curve). In the conventional regime, spins precess about the external field (blue curve in Figure 4c) and increasing the spin-orbit field will produce shorter spin lifetimes due to increased dephasing (blue curve in Figure 4b). However, when the spin-orbit field becomes very large, it will dominate over the external field, and the spins will be stabilized against dephasing. In this spin-orbit-stabilized regime, increasing the spin orbit coupling will produce longer spin lifetimes (orange curve in Figure 4b), which is opposite of the conventional behavior. Furthermore, application of the external field will not produce spin precession (orange curve in Figure 4c). The experimental results for TRKR on WS 2 as a function of B ext (Figure 4d) indicate that the dynamics are governed by spin stabilization resulting from strong spin orbit coupling. The data presented was measured on a spot with high spin density on the spatial map, and the observed behavior was consistent across multiple flakes and samples. The spin lifetimes, obtained by fitting the data in Figure 4d, exhibit very little dependence on B ext (Figure 4e). The similarity of 5

6 the TRKR scans to the orange spin-orbit stabilized curve (Figure 4c), the lack of large oscillations such as those depicted in the blue conventional curve (Figure 4c), and the robustness of the spin lifetime to external fields are all characteristics of the spin-orbit stabilized regime. However, detailed TRKR delay scans with smaller time steps and more signal averaging (Figure 5a) reveal the presence of a small oscillatory signal (<3% of the total Kerr signal), which is not predicted by the spin dynamics model used for Figure 4b. The simultaneous presence of oscillating and non-oscillating components of TRKR delay scans has two possible explanations. First is that there are two separate populations of spins that contribute to the overall signal. The second possibility is a single spin population in a tilted total magnetic field, which produces spin precession about a cone with oscillating transverse component and non-oscillating longitudinal component. 3 For example, in monolayer TMD, a spin residing in a fixed K valley will have a constant out-of-plane spin orbit field B SO and in-plane B ext to produce a tilted total field. In this case, the precession frequency is given by = h +, which is a non-linear function of B ext. However, fitting the oscillatory part of the Kerr rotation with a damped sinusoidal function yields a linear relation between and B ext (Figure 5b), which is inconsistent with precession about a tilted total field. Instead, this indicates a separate spin population with g-factor of 1.9 ±.4 (by fitting vs. B ext ) and a dephasing rate 1/T 2 * that grows linearly with B ext (Figure 5c). These dynamical properties are consistent with a spin population where dephasing is governed by inhomogeneous broadening of the g-factor. Such oscillatory Kerr signals with similar dynamical properties have been observed in monolayer MoS 2 and have been attributed to the presence of spins in localized states. 13 Thus, we conclude that there are two separate spin populations. Most of the Kerr signal comes from non-precessing conduction band spins in the spin-orbit stabilized regime, and a small contribution to the Kerr signal comes from precessing spins in localized states. 6

7 It is worthwhile to contrast our results on WS 2 with previous TRKR studies of monolayer MoS 2 (Yang et. al. 12 ) and WSe 2 (Hsu et. al. 14 ). The main difference with the MoS 2 data is the robustness of the spin lifetime to B ext, which shows little variation for WS 2 up to 7 mt in our data (Figure 4e), whereas the spin lifetime for MoS 2 was shown to collapse in fields as low as 1 mt. This is likely due to the increased spin-orbit splitting in the conduction band of WS 2 (calculated to be approximately +3 mev) compared to MoS 2 (calculated to be approximately -3 mev), yielding substantially larger spin-orbit field for WS This comparison provides further support that the robustness of spin lifetime to external fields is due to the stabilization of spins by strong spin-orbit coupling. The temperature dependence of the spin lifetime in WS 2 (n-type), MoS 2 (n-type), and WSe 2 (p-type) supplies additional evidence for spin stabilization. As shown in Figure 4f, the spin lifetime in WS 2 persists to 13 K, beyond which it drops to <2 ps. The inset shows representative TRKR delay scans at different temperatures. In comparison, the spin lifetime of electrons in MoS 2 is much less robust, falling to <2 ps at only 4 K. 12 In WSe 2, there are shorter spin lifetimes (~1 ns) but the spins persist up to room temperature. 14 While spin relaxation in WSe 2 was only discussed in terms of phonon scattering, 14 the current results suggest that spin-orbit stabilization due to strong spin-orbit fields is also relevant for the WSe 2 data. Moreover, the trend these materials exhibit, with spins persisting to higher temperatures for increased spin-orbit splitting, is the expected behavior for spin-orbit stabilized spins. We finally note that stabilizing spins by strong spin-orbit coupling is more general than the particular example of spin relaxation by fast intervalley scattering, and further studies are needed to understand the mechanism for spin relaxation in monolayer TMDs. 4,7,12,15-17 In conclusion, we utilize TRKR microscopy to image the dynamics of spin density in monolayer WS 2. We discover a complex spatial dependence of spin density in triangular islands that evolves into more symmetric patterns at longer time delays. Comparing microphotoluminescence and TRKR microscopy reveals an unexpected anticorrelation between strong A exciton luminescence and high spin density in the long lived state, which is due to the 7

8 transfer of spin angular momentum from excitons to resident conduction electrons. Application of in-plane magnetic fields indicates the presence of two spin populations that contribute to the Kerr rotation signal. A small contribution to the Kerr signal likely comes from precessing spins in localized states, however most of the Kerr signal comes from non-precessing conduction band spins that are stabilized by large spin-orbit coupling against spin relaxation. The temperature dependence provides further evidence for spin stabilization by spin-orbit coupling. The successful demonstration of high resolution TRKR microscopy on monolayer TMD enables numerous studies of spin and valley dynamics in TMD films and heterostructures that are crucial for developing spintronic applications. Acknowledgements The work at Ohio State was primarily supported by NSF (DMR ) and received partial support from NSF MRSEC (DMR ) and C-SPIN STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA. The work at NRL was supported by core programs at NRL and the NRL Nanoscience Institute and received partial support from AFOSR (F4GGA24233G1). Author Contributions E.J.B., Y.K.L., and M.J.N. performed the optical measurements. K.M.M. performed the CVD synthesis of samples. S.S. prepared samples for measurement. E.J.B., Y.K.L., K.M.M., M.J.N., S.S., B.T.J., and R.K.K. discussed the results and contributed to the manuscript. Competing financial interests: The authors declare no competing financial interests. Methods Time-resolved Kerr rotation microscopy Time-resolved Kerr rotation microscopy measurements are performed using ~15 fs laser pulses from an optical parameteric oscillator (Coherent OPO) pumped by a Ti:sapphire laser (Coherent Mira) with repetition rate of 76 MHz. The pump beam is helicity-modulated at 5 khz using a photoelastic modulator (Hinds) and the probe beam is chopped at 493 Hz and linearly polarized with a 5x1 5 extinction ratio. A Soleil-Babinet compensator is placed in the pump line after the photoelastic modulator to ensure that the polarization is circular at the sample. The time delay between the pump and probe pulses is adjusted using a mechanical delay line. The overlapped beams are tightly focused into ~1 μm spots on the sample using a 1x Mitutoyo objective with 13 mm working distance. Typical pump and probe powers are 1 µw and 1 µw, respectively. We verified that measurements with a 1:1 pump/probe ratio exhibit the same characteristics, however the stronger probe power was employed for better signal-to-noise. The 8

9 sample is mounted on an XYZ piezo stage in high vacuum at 6 K in a closed cycle Montana Instruments Cryostation with an external electromagnet which can apply up to 72 mt. The rotation of linear polarization of the reflected probe pulse is detected using a photodiode bridge, and the signal is amplified using a voltage pre-amp (Stanford Research 56). Heterodyne detection using two lock-in amplifiers (Signal Recovery 727) is used for noise reduction and cancellation of the pump beam. For the temperature dependent measurement, the wavelength is tuned to maximize the Kerr rotation at each temperature. Photoluminescence spectroscopy The photoluminescence measurements are performed using a 532 nm diode laser excitation source, which is focused down on the sample to ~1 μm using a 1x Mitutoyo objective with 13 mm working distance. In the detection path, the excitation source is blocked using a notch filter and the photoluminescence spectrum is detected using a.55 m spectrometer (Horiba ihr55) and thermoelectrically-cooled, back-thinned CCD camera (Horiba Synapse). Calculation of spin lifetimes and spin dynamics We utilize the model of spin dynamics based on fast intervalley scattering presented in reference 12. The parameters used in the calculations are as follows: spin-relaxation rate within a single valley γ s =.2 GHz, intervalley scattering rate γ v = 1 THz, transverse field B ext = 15 mt. We utilize ħω = for spin-orbit field and ħω = for external field, and assume a g-factor of 2 for the conversion. References 1. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nature Phys. 1, (214). 2. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically Thin MoS 2 : A New Direct- Gap Semiconductor. Phys. Rev. Lett. 15, (21). 3. Splendiani, A., Sun, L., Zhang, Y., Li, T., Kim, J., Chim, C.-Y., Galli, G. & Wang, F. Emerging Photoluminescence in Monolayer MoS 2. Nano Letters 1, 1271 (21). 4. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS 2 and Other Group-VI Dichalcogenides. Phys. Rev. Lett. 18, (212). 5. Cao, T., Wang, G., Han, W., Ye, H., Zhu, C., Shi, J., Niu, Q., Tan, P., Wang, E., Liu, B. & Feng, J. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nature Comms. 3, 887 (212). 6. Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS 2 monolayers by optical pumping. Nature Nano. 7, (212). 7. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS 2 by optical helicity. Nature Nano. 7, (212). 9

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12 (a) K -K -K K (b) 5 μm -K Γ K σ- σ+ K -K (c) Intensity (a.u.) 1 5 (e) Wavelength (nm) Kerr Rotation θ K (a.u.) K 6 K θ K (a.u.) (d) Linear Probe Δt (ps) Circular Pump θ K 1x Objective Time Delay Δt (ns) Figure 1. Time resolved Kerr rota4on on high quality CVD WS 2 monolayers. a, (le$) The atomic structure of WS 2 ; tungsten is the central blue atom, and the sulfur atoms are yellow. (right) The schema?c band structure of monolayer WS 2 at the K and -K points. The spin-valley coupling allows one to selec?vely excite spins in either the K or -K valley. b, Op?cal micrograph of one of the triangular islands used in this study. c, Photoluminescence spectroscopy of monolayer WS 2 measured at 6 K. d, Diagram of the TRKR microscopy set-up. e, Representa?ve Kerr rota?on as a func?on of pump-probe?me delay for monolayer WS 2 at 6 K and zero magne?c field. The red curve is a bi-exponen?al fit yielding?me constants of 32 ps and 5.4 ns. Inset: Kerr rota?on at short?me delays. An exponen?al fit to the fast decay (green curve) yields a?me constant of 3. ps.

13 5 µm Kerr Rotation (a.u.) 1.5 Δt = 8 ps Δt = 25 ps Δt = 6 ps Δt = 2 ps Δt = 4 ps Δt = 11 ps Figure 2. Spa4ally-resolved images of 4me resolved Kerr rota4on. Scanning a WS 2 island beneath the overlapped pump and probe beams at a fixed?me delay produces a high-resolu?on spa?al map of spin density. The series of images are snapshots of the spin density at?me delays of 8, 25, 6, 2, 4, and 11 ps. The images reveal a complex spa?al dependence and?me evolu?on of the spins, with regions of high and low spin density in close proximity.

14 (a) 5 µm y position (µm) Δt = 8 ps Kerr Rotation (a.u.) (b) y = 15 µm y = 11 µm y = 7 µm y = 3 µm (c) y = 15 µm y = 11 µm y = 7 µm y = 3 µm Photoluminescence Intensity (a.u.) Time Delay (ns) (d) Wavelength (nm) (e) 2 y position (µm) y position (µm) 1 1 Kerr rotation (a.u.) PL intensity (a.u.) Figure 3. An4correla4on of photoluminescence and 4me resolved Kerr rota4on. a, The dashed line indicates the line-cut where TRKR and PL are compared. b-c, TRKR delay scans and PL spectra measured at 6 K at representa?ve points along the line-cut. The posi?on with the brightest photoluminescence has lowest spin density. d-e, Detailed spa?al dependence of TRKR and PL along the line-cut.

15 (c) (a) (b) Calculated S Z (a.u.) Calculated Lifetime (ns) B SO (T) Conventional Spin-Orbit Stabilized B SO = 2 T B SO = 25 T Time Delay (ns) Time Delay (ns) Kerr Rotation (a.u.) (d) 7 mt 5 mt 3 mt 1 mt mt Time Delay (ns) Spin Lifetime (ns) Spin Lifetime (ns) (e) Magnetic Field (mt) (f) Kerr Rotation (a.u.) 3 K 6 K 11 K 18 K 2 4 Time Delay (ns) Temperature (K) Figure 4. Spin-orbit stabilized spins in WS 2. a, A diagram of the ini?al spin direc?on S (red arrow) and transverse magne?c field B ext (blue arrow) applied in the plane of the WS 2 island. b, Spin life?me as a func?on of spin-orbit field, calculated for fixed B ext using the model in reference 12. c, At low spin-orbit coupling, the spins exhibit conven?onal behavior and precess about B ext (blue curve). At much larger spin-orbit coupling, B ext does not induce spin precession (orange curve) and the spin life?me is robust against external fields. d, Kerr rota?on as a func?on of?me delay for different B ext. The non-precessing decay curves are characteris?c of the spin-orbit-stabilized regime (orange curve in c). e, Spin life?me as a func?on of B ext, obtained by fixng the TRKR data in (d). The spin life?me is robust to an external magne?c field up to 7 mt, indica?ng that WS 2 is in the spin-orbit stabilized regime. f, Spin life?me as a func?on of temperature. The inset shows representa?ve delay scans at different temperatures. The magne?c field and temperature dependences were measured on different samples.

16 (a) Kerr Rotation (a.u.) 7 mt 5 mt 3 mt 1 mt ν L (GHz) 2 1 (b) 1 2 Time Delay (ns) 1/T 2 * (GHz) (c) Magnetic Field (mt) Magnetic Field (mt) Figure 5. Oscillatory component of TRKR in transverse magne4c fields. a, Detailed?me delay scans of Kerr rota?on for different B ext. Curves are zoomed in and offset to show a small oscillatory component of the overall TRKR signal (<3%). b-c, Larmor precession frequency and dephasing rate, respec?vely, of the oscillatory component. Both exhibit a linear dependence on B ext, which indicate spin dynamics in the conven?onal regime.