This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright © American Chemical Society after peer review. To access the final edited and published work see: https://dx.doi.org/10.1021/acs.nanolett.9b01485. Spin States Protected from Intrinsic Electron-Phonon-Coupling Reaching 100 ns Lifetime at Room Temperature in MoSe2 Manfred Ersfeld,1 Frank Volmer,1 Pedro Miguel M. C. de Melo,2, 3 Robin de Winter,1 Maximilian Heithoff,1 Zeila Zanolli,3, 4, 5 Christoph Stampfer,1, 6 Matthieu J. Verstraete,2, 3 and Bernd Beschoten1 1 2nd Institute of Physics and JARA-FIT, RWTH Aachen University, D-52074 Aachen, Germany 2 nanomat/Q-mat/CESAM, Université de Liège, B-4000 Sart Tilman, Liège, Belgium 3 European Theoretical Spectroscopy Facilities (ETSF) 4 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain 5 Institute for Theoretical Solid State Physics, RWTH Aachen University, D-52056 Aachen, Germany 6 Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, D-52425 Jülich, Germany We present time-resolved Kerr rotation measurements, showing spin lifetimes of over 100 ns at room temperature in monolayer MoSe2 . These long lifetimes are accompanied by an intriguing temperature dependence of the Kerr amplitude, which increases with temperature up to 50 K and then abruptly switches sign. Using ab initio simulations we explain the latter behavior in terms of the intrinsic electron-phonon coupling and the activation of transitions to secondary valleys. The phonon-assisted scattering of the photo-excited electron-hole pairs prepares a valley spin polarization within the first few ps after laser excitation. The sign of the total valley magnetization, and thus the Kerr amplitude, switches as a function of temperature, as conduction and valence band states exhibit different phonon-mediated inter-valley scattering rates. However, the electron-phonon scattering on the ps time scale does not provide an explanation for the long spin lifetimes. Hence, we deduce that the initial spin polarization must be transferred into spin states which are protected from the intrinsic electron-phonon coupling, and are most likely resident charge carriers which are not part of the itinerant valence or conduction band states. Monolayers of transition metal dichalcogenides induced spin relaxation. We show that phonon-induced (TMDs) like molybdenum diselenide (MoSe2 ) are scattering rates of valence and conduction band states are two-dimensional (2D) semiconductors with a direct the key to understand the formation of an initial valley band gap and a strong spin orbit splitting of the magnetization, which is directly probed by the Kerr ro- valence band of several 100 meV.1 Optical selection tation. An intriguing increase of the Kerr rotation ampli- rules allow a valley selective excitation of spin states tude, followed by a sign reversal at higher temperatures, with circular polarized light, which makes this class of can be explained by a temperature-activated change of material interesting for spintronic applications.2–4 The the conduction and valance band scattering rates with performance of TMDs for spintronics is backed by the phonons. We argue that the initial laser-prepared magne- measurement of extraordinarily long spin lifetimes in the tization is transferred within ps to long-lived spin states, µs range both in TMD monolayers and heterostructures which are then probed on the ns time scale by Kerr ro- at cryogenic temperatures.5–7 Nevertheless, realizing tation measurements. the technological potential of monolayer TMDs will The MoSe2 flakes were mechanically exfoliated from require technologically relevant spin properties at room bulk crystals from different suppliers with a poly- temperature (RT). In this respect, already the archetype dimethylsiloxane (PDMS) membrane and transferred 2D-material, graphene, has demonstrated that it is onto Si/SiO2 substrates.11,12 For the TRKR experiments possible to outperform conventional spintronic materials we use two mode-locked Ti:sapphire lasers to indepen- such as GaAs and Si.8 In the case of graphene, spin dently tune the energies of both pump and probe pulses. lifetimes up to 12.6 ns were measured in all-electrical An electronic delay between both pulses covers the full spin precession measurements at RT.9 In TMDs, optical laser repetition interval of 12.5 ns. The pulse widths are Kerr rotation measurements revealed that a spin signal on the order of 3 ps, the laser spot sizes have a FWHM with a lifetime of hundreds of ps can survive up to RT.10 value of approximately 6 − 8 µm and the laser power was Here, we present time-resolved Kerr rotation (TRKR) kept to 600 µW for both pump and probe beams. The measurements on exfoliated monolayer MoSe2 flakes, probe energy was set near the trion peak position, deter- showing room temperature spin lifetimes up to 100 ns. mined for each sample and temperature by photolumi- By the combination of energy-dependent, two-color nescence measurements, whereas the pump energy was pump-probe Kerr measurements, and photoluminescence set to a slightly higher energy if not noted otherwise. A spectroscopy on samples with different doping and defect detailed scheme of the experimental setup can be found levels, we show that these long lifetimes are likely linked in Ref. 13. to resident carriers which are not itinerant states. ab ini- Fig. 1(a) depicts the TRKR traces for the sample show- tio calculations of electron-phonon coupling show that ing the unprecedented long spin lifetimes at higher tem- itinerant carriers are expected to undergo fast phonon- peratures (sample M1). A spin polarization is created 2 (a) (b) (c) 5 1.5 sample M1 measurement #1, τs ≈ 100 ns 40 sample M1 4 T = 10 K T = 20 K 1.0 T = 40 K #4, τs ≈ 100 ns 30 θK, norm (arb. units) 3 T = 60 K |θK| (µrad) A2 (µrad) T = 100 K #2, τs ≈ 100 ns 20 2 τs = 8 ns T = 300 K 0.5 #5, τs = 55±3 ns 1 10 τs = 1 ns #3, τs = 24±3 ns 0 0 sample M1 τs ≈ 100 ns T = 300 K -1 -10 0 2 4 6 8 10 12 0 2 4 6 8 10 12 10 30 60 100 300 ∆t (ns) ∆t (ns) T (K) Figure 1. (a) TRKR data of one MoSe2 monolayer (sample M1) at different temperatures, with bi-exponential fits (red curves), showing spin lifetimes of 100 ns at room temperature (purple curve). While these long-lived spin states appear above 60 K with a Kerr angle of ΘK < 0, there are different spin states with ΘK > 0 at lower temperatures with strongly temperature dependent spin lifetimes. We note that all traces have normalized amplitudes to visualize the overall change in lifetime more clearly. (b) TRKR curves measured at RT on different days yield varying lifetimes from 24 ns to 100 ns. Due to the logarithmic representation of the data, we plot |ΘK |. (c) The amplitude A2 of the long-lived spin signal from the bi-exponential fit shows an intriguing initial increase with temperature, before it abruptly switches sign at 60 K. by the circularly polarized pump pulse while the lin- extremely long spin lifetimes. Most interestingly, this early polarized probe pulse measures its temporal decay. trend holds over the whole temperature range up to RT, The corresponding Kerr rotation ΘK (t) is fitted by a bi- where we observe spin lifetimes of up to 100 ns, 2 or- exponential fit function of the form: ders of magnitude larger than previously reported values at this temperature. We note, however, that the mea- surements at RT underwent temporal changes on labo- 2 ratory time scales, which result in a spread of lifetimes   X t ΘK (t) = Ai · exp − , (1) ranging from 24 ns up to 100 ns for subsequent measure- i=1 τs,i ments taken over several days (see Fig. 1(b), where we plot |ΘK | on a semi-logarithmic scale for easier compar- where Ai are the amplitudes and τs,i are the respective ison). We emphasize that the spin lifetimes did not de- spin lifetimes. This accounts for a rapid initial depolar- crease continuously with each successive measurement, ization which occurs on a time scale of tens to hundreds but fluctuated without a discernible pattern (measure- of ps followed by a slower decay which strongly varies ments in Fig. 1(b) are labeled in chronological order). with temperature. If not noted otherwise, all amplitudes Such temporal changes in the spin properties of TMD and lifetimes in this paper refer to the latter decay. flakes were already reported previously13,19 and will be The overall temporal evolution of ΘK and its temper- discussed further below in more detail. ature dependence up to 40 K are qualitatively similar to many other studies on TMDs, i.e. there are ns-scale spin We note that the amplitudes of the TRKR traces in lifetimes at low temperatures which strongly decrease to- Fig. 1(a) are normalized in such a way that the discussed wards higher temperatures.7,10,14–18 It is important to overall change in spin lifetimes is most clearly seen. The note that even the reported µs spin lifetimes in TMDs can actual amplitudes are depicted in Fig. 1(c), where we only be measured at cryogenic temperatures and undergo plot the fitted Kerr amplitude A2 of the longest spin the same strong decay, yielding very short lifetimes at signal seen in the bi-exponential fit at each tempera- elevated temperatures.5–7 In contrast, we observe strik- ture. Hence, for temperatures below 60 K the black data ingly different spin dynamics at higher temperatures: at points represent the spin states with a lifetime which de- 40 K (green curve in Fig. 1(a)) ΘK approaches zero for creases strongly with temperature, whereas for tempera- delay times ∆t > 4 ns, which results from the strong de- tures of 60 K and above, the red data points correspond crease of the spin lifetime. But at higher temperatures to the long-lived spin states with negative Kerr ampli- an additional spin signal with negative sign emerges. It tudes. The trend of the Kerr amplitude shows a second first appears as a small signal with negative sign for time intriguing feature besides the extraordinary long RT life- delays larger than 1 ns at 60 K (orange curve), and be- times: an increase of the Kerr rotation amplitude from comes fully developed at 100 K at all ∆t. Remarkably, 10 K to 50 K, followed by a sign reversal at the temper- there is a very weak temporal decay of ΘK , indicating ature at which the long-lived RT spin states emerge. 3 (a) low temperatures (b) (e) 1.0 3 E K Λ K‘ laser occupation (arb. units) T = 20 K 2 pulse Mz (arb. units) vb, K II I vb, K‘ 1 III 0.5 cb, K cb, K‘ 0 5K 60 K 20 K 100 K -1 40 K 300 K 0 0 1 2 3 0 2 4 6 8 10 k t (ps) t (ps) (c) elevated temperatures (d) (f ) 1.0 2.0 T = 100 K vb, K E K Λ K‘ occupation (arb. units) vb, K‘ 1.5 M z (∆ t = 8 ps) cb, K cb, K‘ II 0.5 1.0 I III 0.5 0 0 0 1 2 3 10 100 300 k t (ps) T (K) Figure 2. (a) and (c) - Representation of the bands’ spin-texture (blue for spin-down, red for spin-up, and black for mixed states) near K and K’ at low (a) and elevated (c) temperatures, illustrating the phonon-mediated allowed transitions. White dots mark the electron-hole pair’s position in the band structure. At higher temperatures, electrons can transit to an intermediate valley at Λ. (b) and (d) - time-dependent evolution of the integrated occupations of both valence band (vb) and conduction band (cb) in the K and K’ valleys at 20 K (b) and 100 K (d) for a prepared ideal exciton. (e) Time evolution of the magnetization at different temperatures when a real pulsed laser field and the e-ph interaction are both turned on. (f) Magnetization at a time delay of ∆t = 8 ps as a function of temperature, showing the initial increase in amplitude and the crossover to a magnetization with reversed sign at around 60 K, matching the experimental data in Fig. 1(c). Before we explore the spin dynamics of other samples, band at different temperatures (see SI for an extensive we first focus on the theoretical understanding of the analysis). The underlying physical processes are illus- intriguing temperature dependence of the Kerr rotation trated in Fig. 2 (a). The direct transition between the amplitude in MoSe2 . The dependence can be understood states at the K and K’ points is forbidden by selection essentially by changing electron-phonon scattering rates rules. However, only the states at band extrema are in the conduction and valence bands. We consider in- purely spin-up or spin-down. Those at neighboring trinsic MoSe2 , and take into account electron-hole pair wave-vectors contain a mixture of both spins. As a (exciton) formation by the absorption of a pulsed laser result, inter-valley scattering of a pure spin state requires field. We compute the temporal evolution of both con- a two-step electron-phonon process: first, by absorbing duction and valence band polarizations, solely driven by an acoustic phonon, carriers are sent away from the electron-phonon (e-ph) interactions, by performing real- band extrema to nearby states (transition from I to II time calculations with the Yambo code20 (see SI for de- in Fig. 2 (a)); then, temperature permitting, a phonon tails). These are based on approximations to the full with a large wave-number can be absorbed or emitted, Baym-Kadanoff equations.21–24 In the simulations we use and the carrier can be transferred to the other valley a laser pulse field with parameters (energy, temporal (transition from II to III in Fig. 2 (a)). width, and intensity) which track those used in the ex- To separate the effects arising from e-ph interaction periment. from those created by the laser field, we first discuss We find a striking resemblance between the the case of a simple initial state, where we prepare an temperature-dependence of the total MoSe2 mono- electron-hole pair exactly at the band extrema in the K layer magnetization after the pulse and the measured valley (further details in the SI). Both carriers are inde- Kerr amplitude. At 60 K (see Fig. 2(e) and 2(f)) there pendently allowed to interact with the phonon bath, and is a complete inversion of the magnetization signal, we track the time evolution of carrier populations in each consistent with the inversion of the Kerr signal shown band. These are shown in Fig. 2 (b) and (d) where we de- in Fig. 1(a). This behaviour can be explained by the pict the temporal changes of both conduction (electrons, differences in the dynamics of carriers in the conduction shown as the dashed lines) and valence band occupations 4 (holes, solid lines). At low temperatures (Fig. 2 (b)) for samples M2a and H1a in Figs. 3(a) and 3(b), respec- holes predominantly scatter into the other valley, leading tively. At first glance, there is a continuous decrease of to faster depolarization of the valence bands. The over- the Kerr rotation amplitude with increasing temperature. all magnetization predominantly comes from the electron In this context, however, it is important to note that, in population imbalance, which barely reduces over the 3 ps contrast to sample M1 (Fig. 1(a)), the other samples have time scale. spin lifetimes of more than 100 ns at 10 K (Fig. 3(c)), The situation changes qualitatively at higher temper- which is much longer than the laser repetition interval of atures (Fig. 2(d)), where the e-ph scattering rates of the 12.5 ns. Therefore, the Kerr rotation signal from previ- conduction band states have drastically increased. This ous pump pulses is not fully decayed prior to the arrival is largely due to an additional scattering channel through of the pump pulse at ∆t = 0 ns (see non-vanishing ΘK a valley at Λ (also see supplementary Fig. S4) which be- for time delays ∆t < 0 ns in Figs. 3(a) and 3(b)). As a comes accessible by thermal excitation (transition from result, the constructive superposition of the valley polar- I to II in Fig. 2(c)). This new scattering channel turns ization from successive pulses increases the overall Kerr out to be faster than those available to the hole popula- amplitude. As the spin lifetime decreases with tempera- tion. Electrons will thus depolarize more quickly, leaving ture (see Fig. 3(c)), the residual valley polarization from behind an imbalanced distribution of holes, which mag- previous pump pulses also drops significantly, which ex- netizes the system, but now with a reversed sign. We plains the overall decrease in the Kerr amplitude with point out that the valley populations shown in Figs. 2(b) temperature as seen in Figs. 3(a) and 3(b). and (d) are obtained by summing all state occupations We now focus on the additional valley polarization cre- for a given band near either the K or K’ points. As tem- ated by the pump pulses at ∆t = 0 ns, which is high- perature increases, electrons and holes can spread more lighted by arrows in Figs. 3(a) and 3(b). The gain of the widely throughout the Brillouin zone, so the total num- Kerr rotation amplitude first increases with temperature, ber of electrons and holes inside the region of integration then it strongly decreases at around 60 K (see light blue need not to add up to 1. curves) for all samples. This temperature corresponds The final step is the full simulation with both e-ph very well to the crossover predicted by our simulation interaction for different temperatures and the optical ex- in Fig. 2(f) and to the data of sample M1 in Fig. 1(c), citation by the laser pulse. The resulting time-evolving demonstrating that the temperature-dependent increase magnetization is shown in Fig. 2(e).The magnetization is of the valley polarization probed by the Kerr effect is a evaluated by summing up over all occupied states in the hallmark for the spin dynamics in MoSe2 . We note, how- whole Brillouin zone, taking into account the different ever, that we do not observe the sign reversal of the Kerr spins of electrons and holes. This should not be confused signal at higher temperatures, or the long lived RT spin with the valley occupations shown in Figs. 2 (b) and (d). signal, in any other sample. In contrast, the spin lifetime Initially the system has no magnetization, as the laser in those samples dramatically decreases at high temper- field creates an equal population of electrons and holes. atures, reaching values on the order of 100 ps at 100 K Only after carriers start to spread through the Brillouin (Fig. 3(c)). zone, due to e-ph interaction, do we observe an magneti- To unravel why only sample M1 shows the intriguing zation due to the phonon-induced spin flip processes. At high temperature spin dynamics, we conduct photolumi- low temperatures (T = 5 K), since holes scatter faster nescence (PL) measurements on all samples, as summa- than electrons, the density of electrons is spin polarized rized in Fig. 4. For PL excitation we use a continuous (Mz > 0 at 10 ps). Increasing the temperature strongly wave (cw)-laser with an energy of 2.33 eV, at a similar increases Mz up to 20 K, before it drops and reverses its laser power and spot size as used for TRKR measure- sign at 60 K (Mz < 0 at 10 ps). This behavior nicely ments. The spectra in Figs. 4(a) to 4(c) show typical matches the Kerr rotation amplitudes in Fig. 1 (c) (see emission from neutral (X0 ) and from charged excitons also Fig. 2(f)) and results from the difference in thermal (X+/− ) which were fitted by Voigt functions (dotted lines activation of the e-ph scattering rates between electrons in Fig. 4(a)) to extract both their width (Figs. 4(d)) and and holes, demonstrating that the e-ph interaction is the energy position (Figs. 4(e)). key to understand the initial formation of the valley po- Details in the sample fabrication process have a strong larization in the TRKR measurements. impact on the excitonic properties of the samples, as seen To support these findings, we next discuss the temper- for samples H1a and M2a in Figs. 4(b) and 4(c). These ature dependent spin dynamics on five other MoSe2 sam- two samples were fabricated from two different crystals ples. The capital letter of the sample’s name indicates the from different suppliers, but the samples were fabricated supplier (“M” for Manchester Nanomaterials and “H” for simultaneously under identical conditions, i.e. using the HQ Graphene), followed by the sample number indicat- same exfoliation method, the same chemicals for the same ing the crystal used for fabrication. A final small letter duration of time, and were stored and measured identi- - if present - represents measurements done at different cally. Both samples show low-temperature spin lifetimes stages of the fabrication process (see below). For all sam- of over 100 ns, which are, to our knowledge, the longest ples we observe the temperature activated increase in val- lifetimes reported so far for MoSe2 at these temperatures ley polarization, which can be seen in the TRKR curves (see Fig. 3(c)). Interestingly, the absolute values of the 5 (a) 5 (b) 1.0 (c) sample M2a 20 K 45 K sample H1a 20 K 45 K 25 K 65 K 30 K 60 K M1 4 35 K 95 K 0.8 35 K 80 K 100 H1a spin lifetime (ns) H1b θK (arb. units) θK (arb. units) 3 0.6 H2 10 M2a 2 0.4 M2b 1 1 0.2 0 0.0 0.1 0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 20 40 60 80 100 ∆t (ns) ∆t (ns) T (K) Figure 3. (a) and (b): Temperature dependent TRKR traces for MoSe2 samples M2a and H1a, respectively. The overall Kerr amplitude decreases as there is less remaining valley polarization from previous pump pulses (see ΘK signal for time delays ∆t < 0 ns) at elevated temperatures due to the decrease in spin lifetime. In contrast, the Kerr amplitude induced by the pump pulse at ∆t = 0 ns (see arrows) first increases with increasing temperature before it drops significantly at higher temperatures. (c) Spin lifetime of the long-lived spin signal from the bi-exponential fit (τs,2 ) of all MoSe2 samples vs. temperature. For sample M1 we only show low temperature spin lifetimes, which interestingly are the shortest of all samples. spin lifetimes and their temperature dependence are al- (Fig. 4(d)). These large peak widths are an indication most identical (Fig. 3(c), blue and red triangles) although of a significant variability in the potential landscape of their PL spectra differ qualitatively: the intensity ratio the flake, induced either by disorder in the crystal lattice between neutral and charged exciton emission inverts, or by impurities.26–29 However, there is also a striking and a low energy tail in the spectra of sample H1a is difference in sample M1, which becomes obvious when observed. comparing Figs. 4(d) and 4(e). For the other samples a The impact of further post processing steps on the narrower peak width is accompanied by a larger blue shift samples’ properties is also seen in Figs. 4(b) and 4(c). of the exciton peak position (see dashed lines, which are For sample H1a, we used a hot pick up process, which guides to the eyes). Despite the significant peak width is known for its surface cleaning effect,25 to deposit a of sample M1, its exciton peak position is the most blue- thin hBN flake on top of the MoSe2 monolayer. As a shifted among all samples, by 1.665 eV which is higher result, sample H1b shows a significant reduction in the than the vast majority of values reported in literature.30 PL line widths and the vanishing of the low-energy tail It was shown in several studies that either doping,31–33 (Fig. 4(b)). Independent of temperature, this encapsu- strain,34–36 or the change of the dielectric environment by lation yields an overall increase of the spin lifetimes by encapsulation with hBN27,30,37 can be associated with a a factor of three (Fig. 3(c), dark blue and light blue tri- red-shift of the exciton peak. As no sample except for angles). In contrast, sample M2b, which was made from H1b is in contact with hBN, and all samples are put on sample M2a by annealing under ambient conditions at Si/SiO2 substrates, we exclude the dielectric environment 180◦ C, shows additional defects as seen by the appear- as a reason for the large blue-shift: the high exciton en- ance of a low-energy tail (Fig. 4(c)). Simultaneously, we ergy of sample M1 is therefore indicative of low overall observe a decrease in measured spin lifetime after anneal- doping and strain. ing (compare red and orange triangles in Fig. 3(c)). Over- The large PL line widths of sample M1 indicate the all, these results show that, as could be expected, sam- presence of defects, but these do not carrier-dope the ples with less disorder (e.g. defects or adsorbates) show sample, which is apparent in the blue-shifted exciton longer spin lifetimes in TRKR measurements at low tem- peak and also the fact that the neutral exciton is much peratures. We have seen that both the spin lifetimes and more pronounced than the trion in Fig. 4(a). The impact the excitonic features strongly depend on details in the of defects on the electronic structure of sample M1 can fabrication process, indicating that the electronic proper- also be seen in an unconventional temperature dependent ties are dominated by extrinsic effects. This is a probable quantum yield, shown in Fig. 4(f) where we normalized explanation for the significant device-to-device variations the total counts of the exciton peak by the integration found in literature. time of the spectrometer and the power of the excita- Sample M1 also follows the trend between disorder seen tion laser. For comparison, sample H2 shows the ex- in PL and measured spin lifetime in TRKR: On the one pected temperature-dependent decrease in quantum yield hand, the low temperature spin lifetime is the lowest mea- for MoSe2 , which is attributed to the thermal activation sured for all our samples (Fig. 3(c)), on the other hand, of dark excitons.29,38 On the other hand, the quantum this sample shows by far the largest PL peak widths yield of sample M1 is orders of magnitude lower at cryo- 6 (a) (b) (c) normalized PL intensity 1.0 1.0 1.0 normalized PL intensity normalized PL intensity sample M1, T = 10 K T = 10 K sample H1 sample M2 T = 10 K 0.8 PL X0 0.8 w/o hBN (H1a) 0.8 exfoliated (M2a) fit with hBN (H1b) annealed (M2b) 0.6 0.6 0.6 X+/- low-energy 0.4 0.4 0.4 tail 0.2 0.2 0.2 0.0 0.0 0.0 1.56 1.60 1.64 1.68 1.72 1.56 1.60 1.64 1.68 1.72 1.56 1.60 1.64 1.68 1.72 energy (eV) energy (eV) energy (eV) (d) (e) (f ) 1.67 10 3 30 X0 width PL (counts · s-1· mW -1) peak position (eV) peak width (meV) X+/- width 1.66 10 2 20 1.65 X0 position sample M1 X+/- position sample H2 1.64 10 1 10 1.63 0 1.62 10 0 10 30 100 300 2b 2b 2a 2a b b a a 1 1 H2 H3 H2 H3 H1 H1 H1 H1 M M M M M M sample sample T (K) Figure 4. (a)-(c): Photoluminescence spectra of different samples measured at 10 K. The spectra were fitted with Voigt- functions (dashed lines in (a)) to determine the peak positions and widths of both the neutral exciton (X0 ) and the charged trion (X+/− ). The corresponding fit results for all of our samples at 10 K are shown in (d) and (e), respectively. Here, it can be seen that the sample with the long-lived room temperature spin signal (sample M1) has by far the largest peak width, but at the same time exhibits the most blue-shifted peak positions (dashed lines are guides to the eyes). Sample M1 also distinguishes itself from other samples by showing a pronounced suppression of quantum yield over the whole temperature range, as seen in (f) where the normalized PL intensity of the neutral exciton peak is depicted for samples M1 and H2. PL (lines), |A2| (symbols) (arb. units) genic temperatures and shows only a negligible temper- sample M1 ature dependence. This behavior can be explained by T = 150 K defects which provide non-radiative recombination chan- nels for the photo-excited charge carriers.29 T = 100 K To explore the origin of the extraordinary high- temperature spin dynamics in sample M1, we conducted T = 50 K energy-dependent Kerr rotation measurements, where the pump energy was scanned across the exciton energy T = 30 K range at different temperatures (see Fig. 5). The Kerr amplitude of the nanosecond spin signal (symbols) fol- lows the PL spectra (solid lines) only at low tempera- T = 10 K tures. This resonant behavior weakens with increasing 1.56 1.64 1.72 1.80 temperatures, and finally vanishes for T > 50 K. At energy (eV) this point, the Kerr rotation amplitudes correspond to the high temperature long-lived spin signal with inverted Figure 5. Comparison between PL spectra and amplitude sign (red data points in Fig. 1(c)). At temperatures be- |A2 | of the long-lived Kerr rotation signal at varying pump low 50 K the spin dynamics in sample M1 seems to be energies for different temperatures. Whereas the pump scans directly connected to the excitons. The fact that the follow the PL spectra for low temperatures, the excitonic en- pump scans at higher temperatures are almost energy ergy resonance in the Kerr measurements vanishes for higher independent indicates that the spin states are no longer temperatures. Each horizontal line is the zero baseline for hosted by the excitons. Rather, this indicates that there both the pump scan and the PL spectrum right above it. has been a transfer of spin polarization from excitons into other long-lived states. By combining all our findings, a complete picture of indicates an overall small combination of strain and dop- the spin dynamics observed in sample M1 can be ob- ing. This justifies our simulations of the temperature- tained. The high-energy exciton peak position (Fig. 4(e)) dependent spin dynamics, where we assumed an intrinsic, 7 undoped monolayer of MoSe2 (Fig. 2). On the one hand, samples which show a suppressed quantum yield similar our simulations can explain the intriguing temperature- to our sample M1 in Fig. 4(f).29 The large peak widths dependent Kerr amplitude of sample M1 seen in Fig. 1(c), of the PL spectra in sample M1 are also an indication which is due to the change of the ratio between phonon- of large spatial fluctuations of the electrostatic potential, induced conduction and valance band scattering rates. which could create puddles of hole or electron doping. But on the other hand, our simulations predict that the Because of the overall small doping of sample M1, these magnetization drops to zero within a few ps at 300 K puddles may be well separated. We imagine these pud- (Fig. 2(e)). At lower temperatures we expect that the dles to be similar to those in graphene,54 and in fact first strong e-ph coupling in TMDs39–43 will lead to a complete signatures of localized charge puddles have been seen in depolarization of the magnetization of itinerant states, µPL measurements of TMD materials.55 Defect states in both in the conduction and valence band, somewhere in these charge puddles would result in strong localization, the ps range. This was also the order of magnitude found which may protect the spin from phonon-induced scat- in WSe2 .39 All these time scales are much shorter than tering. Such a picture can also explain the strong varia- the measured ns spin lifetimes, whether at high or low T. tions in the repeated room temperature measurements in The solution to this apparent discrepancy is that the Fig. 1(b), as the constant desorption and absorption of strong electron-phonon scattering mechanism depicted in volatile gas species at RT constantly changes the charge Fig. 2 only serves to prepare an initial spin state on the ps puddles. time scale. Accordingly, part of the initial magnetization In conclusion, we have demonstrated that electron- must scatter into spin states which are protected over a phonon interaction is the key for the ultrafast forma- ns time scale from the strong electron-phonon interaction tion of a valley polarization in MoSe2 after optical ex- of itinerant band states. In this respect it is important citation by circularly polarized light. Different phonon- that excitons can be localized by trapping.44,45 The cap- induced scattering rates of both valence and conduction ture time by defects is measured to be around 1 ps,46 band states were shown to result in a temperature de- which is well within the lifetime of our simulated mag- pendent reversal of the valley polarization in good agree- netization process. Furthermore, defect-bound excitons ment to measurements from time-resolved Kerr rota- in monolayer TMDs are found to exhibit photolumines- tion. While electron-phonon scattering involving itiner- cence lifetimes in the hundreds of ns range.45,47 However, ant band states is expected to result in a rapid depolar- this picture only holds for low temperatures: for temper- ization, the measured spin lifetimes of up to 100 ns both atures approaching 100 K the thermal energy exceeds the at low temperatures and at room temperature indicate typical localization energy of excitons in such traps.44,48 that the spin polarization scatters into spin states which This explains the strong decrease of spin lifetimes with are protected from intrinsic electron-phonon interaction. temperature up to 100 K. Another possible explanation for the ns lifetimes at low temperatures might be connected to polarons, ACKNOWLEDGMENTS which recently have drawn quite some attention in TMDs.32,40,49–52 We think that it is reasonable to as- sume that (dark) excitons53 can be protected against the This project has received funding from the Euro- strong electron-phonon interaction through a polaronic pean Union’s Horizon 2020 research and innovation pro- reconstruction of the combined electron and phonon sys- gramme under grant agreement No 785219. Supported tem, which goes beyond the theory implemented in our by the Helmholtz Nanoelectronic Facility (HNF)56 at real time simulations. Both explanations (trapped exci- the Forschungszentrum Jülich. PMMCM and MJV ac- tons and polaron-exciton complexes) depend on excitons knowledge funding by the Belgian FNRS (PDR G.A. and therefore would explain why the Kerr amplitude at T.1077.15-1/7), and the Communauté Française de Bel- low temperatures follows the excitonic features in the PL gique (ARC AIMED G.A. 15/19-09). ZZ acknowledges spectra of Fig. 5. financial support by the Ramon y Cajal program (RYC- The long-lived spin states at higher temperatures, how- 2016-19344), the CERCA programme of the Generalitat ever, do not scale with the number of excitons created, de Catalunya (grant 2017SGR1506), and by the Severo as seen in Fig. 5, and therefore must have another origin. Ochoa programme (MINECO, SEV-2017-0706), and the We first note that due to different inter-valley scatter- EC H2020-INFRAEDI-2018-2020 MaX ”Materials De- ing rates of electrons and holes, their polarization can be sign at the Exascale” CoE (grant No. 824143). Com- transferred to resident charge carriers as soon as the exci- putational resources have been provided by the Consor- tons recombine.10 As explained above, we do not expect tium des Equipements de Calcul Intensif (CECI), funded that these resident charge carriers exhibiting ns spin life- by FRS-FNRS G.A. 2.5020.11; the Zenobe Tier-1 su- times are itinerant states of either the conduction or the percomputer funded by the Walloon Region under G.A. valence band. Instead, a recent combined scanning tun- 1117545; and by a PRACE-3IP DECI grant 2DSpin on neling spectroscopy and photoluminescence study iden- Beskow (G.A. 653838 of H2020). tified defect states in the band gap of monolayer MoSe2 The authors declare no competing financial interest. 8 1 24 Z. Y. Zhu, Y. C. Cheng, and U. Schwingenschlögl, Phys. E. Perfetto, D. Sangalli, A. Marini, and G. Stefanucci, Rev. B 84, 153402 (2011). Phys. Rev. B 92, 205304 (2015). 2 25 D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys. D. G. 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