Ultrafast THz probing of nonlocal orbital current in transverse multilayer metallic heterostructures

THz generation from femtosecond photoexcited spintronic heterostructures has become a versatile tool for investigating ultrafast spin-transport and transient charge-current in a non-contact and non-invasive manner. The equivalent effect from the orbital degree of freedom is still in the primitive stage. Here, we experimentally demonstrate orbital-to-charge current conversion in metallic heterostructures, consisting of a ferromagnetic layer adjacent to either a light or a heavy metal layer, through detection of the emitted THz pulses. Our temperature-dependent experiments help to disentangle the orbital and spin components that are manifested in the respective Hall-conductivities, contributing to THz emission. NiFe/Nb shows the strongest inverse orbital Hall effect with an experimentally extracted value of effective intrinsic Hall-conductivity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${({\sigma }_{{SOH}}^{{{{{\mathrm{int}}}}}})}^{{eff}} \sim 195{\varOmega }^{-1}{{cm}}^{-1}$$\end{document}(σSOHint)eff~195Ω−1cm−1, while CoFeB/Pt shows maximum contribution from the inverse spin Hall effect. In addition, we observe a nearly ten-fold enhancement in the THz emission due to pronounced orbital-transport in W-insertion heavy metal layer in CoFeB/W/Ta heterostructure as compared to CoFeB/Ta bilayer counterpart.


INTRODUCTION
Efficient generation and detection of spin currents is required in spintronic devices for their different potential applications. 1,2hese include, the spin-orbit torque (SOT), spin-pumping, magnetic memories, excitation of magnons, manipulating the magnetic damping, etc. Mainly, the spin Hall effect 3,4 (SHE) and Rashba-Edelstein effect 5,6 (REE), governed by the spin angular momentum (S) transfer, have been invoked commonly in the generation of a spin current from a charge current.It has become clear from a few recent studies that in certain solids, [7][8][9] the transport of electron's orbital angular momentum (L) and hence the associated magnetic moment, is also responsible for different interesting phenomena in the emerging field of orbitronics.Orbital Hall effect (OHE), which was conceived 10,11 just after the SHE, 3 has often been neglected due to orbital quenching in the periodic solids. 12,13Bearing many similarities with the SHE, in the OHE, a transverse flow of orbital angular momentum occurs in response to a longitudinally applied electric field.][16] Therefore, it helps in resolving some of the conflicts in the reported values of the spin Hall conductivities for certain materials. 14 few theoretical and experimental studies in the recent literature 13,14,17 have indicated a gigantic OHE in the light as well as several heavy metals and therefore, it has necessitated more careful investigations of SHE-based phenomena and devising new schemes to disentangle the OHE.
As indicated above, OHE is a fundamental phenomenon, which can be observed in a variety of materials, including transition metals [13][14][15][17][18][19][20] , semiconductors 11 , two-dimensional materials [21][22][23] , etc. 24 Unlike the SHE, whose strength greatly depends on the spin-orbit coupling (SOC) in the material, OHE, on the other hand, can be found even in the light materials, having very weak SOC 13,20 . Aftera few theoretical reports 13,14,17 on the large orbital Hall conductivity (  ) in both the strong and weak SOC-type materials, detailed experimental demonstrations are required to obtain further insights for harnessing the same in practical applications.For instance, a high value of the Hall conductivity is always advantageous as it helps in the enhancement of spinorbit torque (SOT), which is technologically relevant to memory applications. Coventionally, in SHE induced torque (SHT), the spin angular momentum transfer exerts a torque directly on the local magnetization of the material. Howevr, due to the lack of direct exchange coupling 7 of orbital angular momentum with the local magnetization, a similar direct realization of the OHE induced torque or the orbital Hall torque (OHT) was lacking. Ths pertinent issue has found a regenerated interest among researchers 7,8,17,19 to make OHT based applications viable 9,25 by devising novel orbital-spin (L-S) conversion schemes and suitable material combinations.19,26 It follows from the magnetization manipulation through the exerted net torque, dominated by either SHT or OHT, and acts as a key in distinguishing the orbital character indirectly from the pure spin transport.Y.G. Choi t al., 16 have used magneto-optical Kerr effect (MOKE) in addition to the orbital torque measurement technique for direct detection of orbital magnetic moment accumulation created by the charge current flow in a light metal, Ti.A non-contact method is always promising to non-invasively measure the spin and orbital transport in materials.
Like the toque method to detect the charge to spin or orbital conversion, the inverse of the SHE (ISHE) and REE (IREE) are routinely used for the detection of spin transport through the spin-charge conversion, where the spin source can be one from either spin pumping or spin Seebeck current or optical excitation, etc.The Onsager reciprocity 27 allows an interconversion between the orbital and charge currents, where, similar to the ISHE and IREE for the spin counterpart, here, inverse orbital Hall effect (IOHE) and inverse orbital Rashba-Edelstein effect 25 (IOREE) are both in play.In several studies [28][29][30][31][32][33][34][35][36][37] in the last decade or so, ISHE and IREE have been utilized in the THz electromagnetic pulse generation from ultrafast photoexcited magnetic/nonmagnetic (NM) multilayer systems.Consequently, the scheme, in conjunction with the multilayers, is not only recognized as a source of effective THz radiation, 38 but also a highly sensitive contactless optical probing tool [39][40][41][42][43][44][45][46] for the detection and control of the ultrafast processes at femtosecond time scale, spin-charge conversion mechanisms, demagnetization dynamics and transport, interfacial properties, etc.For the case of the ISHE based spintronic THz emitters, spin current from the ferromagnetic (FM) or antiferromagnetic layer is injected into the NM layer, where it gets converted to charge current.Therefore, heavy metal layer with large SOC is desirous for efficient THz generation from a bilayer 47 .Similar effects are envisaged to exist for the orbital counterpart too. 48For the THz emission utilizing the orbital transport properties, i.e., orbital-charge conversion through IOHE, a material capable of generating an orbital current (JL) is required.
In the current work, existence of nonlocal orbital transport is experimentally detected through IOHE mediated efficient THz emission from femtosecond NIR (near-infrared) pulse excited bi-and tri-layer metallic heterostructures using temperaturedependent time-domain spectroscopy that has not been reported hitherto.Since the orbital degree of angular momentum is strongly correlated with the crystal field potential, therefore, the temperature-dependency of the phonon scattering would severely affect the OHE and the related phenomena, microscopically.The specially chosen heterostructures, in this work, consist of FM and NM material combinations, where the choice of the FM is from either CoFeB or NiFe, whereas the NM is from both the light metal (Nb) as well as the heavy metals (Pt, Ta, and W).While the THz emission from CoFeB/Pt and Fe/Ta bilayers is shown to originate from the ISHE, the same from NiFe/Nb is attributed primarily to the IOHE.The temperature-dependence of the THz amplitude vis-a-vis the Hall conductivities are used to distinguish spin-to-charge and orbital-to-charge signatures.For the observation of IOHE mediated THz emission from structures consisting of heavy metal layer, we fabricated a tri-layer system of CoFeB/W/Ta and measured the temperature-dependent THz amplitude and the Hall conductivities.The THz emission from such a tri-layer, having the W-insertion layer, interfaced with another heavy metal layer of same sign of the spin Hall angle and placed side-by-side, is nearly one-order stronger than the CoFeB/Ta bilayer counterpart.We have confirmed through experimental findings that the origin of this enhancement is due to efficient orbital transport in the W-insertion layer.The next section provides our results and detailed discussion on them.First, the case of a NiFe/Nb bilayer is taken up, followed by the study on CoFeB/NM (Pt,Ta) bilayers and, finally, the trilayer of CoFeB/W/Ta.All these heterostructures are grown on quartz substrates by using UHV RF sputtering.A nearly optimized thickness and phase of the individual layers in the heterostructures has been used.The W and Ta layers are in their -phase.For all the THz results reported here, femtosecond pulses having time-duration of ~50fs, central wavelength of 800nm, pulse energy (fluence) of ~35J (0.5mJ/cm 2 ) were used.However, results with the varying pump fluence on different samples are shown in the Supplementary Section S11.Complete details about the experimental arrangements in the THz setup, material synthesis and characterization, are provided in the Supplementary Information.Briefly, they are mentioned in the Methods section also.

NiFe/Nb: Probing inverse orbital Hall effect in light metal through generation of THz pulses
Figure 1(a) schematically illustrates the emission of THz pulses from the NiFe/Nb bilayer following optical excitation by linearly polarized femtosecond NIR pulses whereas, the same for bare NiFe sample is presented in the Supplementary Section S12.The thicknesses of the layers were kept at 5 nm for NiFe and 10 nm for Nb layer.The full THz bandwidth of the signals from NiFe/Nb sample as obtained by fast Fourier transform is shown in the Supplementary Section S6.A constant external magnetic field (B), having a value just above the saturation (~200 Oe), is applied along the y-direction.A few consistency checks were recorded, to initially validate the origin for the generation of THz pulses, for four geometries of the direction of the optical excitation and the magnetic field, as presented in Figs.1(b) and 1(c), respectively.NiFe is a popular FM material for spintronic applications.Dominant presence (≥90%) of Ni (light element) in NiFe makes it possess a large and positive value of spin-orbit correlation factor, 8 η = 〈.〉 > 0. As shown in Fig. 1(d), in positive spin-orbit correlation materials, transverse orbital and spin Hall effects are induced in response to the flow of a longitudinal charge current,   such that the polarization direction of the accumulated orbital and spin magnetic moments is the same. 8An optimal material composition and growth of NiFe enriched with Ni can provide a better value of η as compared to that in Ni. 49 Moreover, a transient change in the spin-orbit coupling in Ni, triggered by an ultrafast excitation, has been seen to enhance the η value significantly. 50ollowing the optical pulse excitation of NiFe/Nb (Fig. 1a), ultrafast demagnetization 51 in the NiFe layer stimulates flow of a spin current with density   .Due to a large positive value of η in the NiFe, a fraction of the ultrafast spin current is converted into an ultrafast orbital current (JL) of same polarity through the L-S conversion, given 8,48 as,   = η − .  .Therefore, an ultrafast optically induced orbital current sets in, 48,52 which possess similar symmetry properties to the spin current but can exhibit relatively different transport dynamics. 9,53Furthermore, as the ultrafast excitation of spin and orbital magnetization has been reported 50,[54][55][56] to exhibit a similar evolution, the emergence of orbital current can be comprehended through the analogy with the already established spin current formation. 52Consequently, as indicated in Fig. 1(a), both the spin and orbital currents are now launched into the adjacent Nb layer.A very weak negative SOC strength and about an order difference in the values of orbital Hall conductivity and spin Hall conductivity (  ) in Nb make it a suitable candidate 57,58 for realizing orbital transport phenomena.In case of heavy metals, although the value of   is typically much larger than the   , 14 however, OHE is greatly suppressed by the inherently present SOC owing to the identical macroscopic geometries between OHE and SHE in response to the applied electrical current. 20Therefore, to overcome the effect of spin transport in the realization of OHE, selection of an appropriate light element material is regarded as one of the solutions.The spin and orbital currents injected into the Nb layer convert to respective in-plane transient charge currents.Charge current,   is produced via ISHE and   is produced via IOHE.The magnitude and polarity of the emitted THz radiation is finally dependent on the net transient charge current in the Nb layer.Typically, the orbital diffusion length in Nb is comparable to that of spin diffusion length (see Supplementary Section S13).Due to the negligible SOC and subsequently smaller spin Hall angle in Nb, the ISHE signal is nearly quenched as against the IOHE.The net charge current in the Nb layer is the vectorial sum of the two charge currents, i.e.,   =  − +  − , and it can be further expressed as Here,   and   are the spin and orbital Hall angles of Nb, which are negative and positive, respectively. 15,18Since the spinorbit correlation factor,  −  is positive for the NiFe, therefore, the charge current contribution from the individual components would have opposite signs, as represented in Fig. 1(a).The net charge current is, therefore, the difference of the two, and the dominant one among them would control the amplitude and polarity of the emitted THz radiation.If the THz signal from the NiFe/Nb bilayer structure is a result of the inverse spin Hall effect (ISHE), its polarity would be expected to be the same as that of the Fe/Ta bilayer but opposite to that of the CoFeB/Pt bilayer structures.This distinction arises because Nb and Ta both have the negative sign of    , while Pt has a positive sign of    .However, the observed polarity of the THz signals in the NiFe/Nb bilayer structure opposite to that of Fe/Ta bilayer structure but coincides with the CoFeB/Pt bilayer structure, as schematically depicted in Figs.1(a), 3(a), and 3(b), respectively.In fact, the polarity of the THz signals emitted from NiFe/Nb bilayer structure aligns with the sign of    . −  implying that the THz emission from NiFe/Nb takes place via IOHE, mainly.A few consistency checks are carried out in Figs.1(b) and 1(c) to reveal the magnetic origin of the THz signal.The THz signal polarity is inverted by reversing either the direction of the optical excitation while keeping the magnetic field unchanged or the direction of the external magnetic field while keeping the direction of optical excitation unchanged.In the first case, the THz sign reversal is due to the change in the direction of the spin current and consequently the flow of orbital current, whereas, in the second case, it is due to the change in the spin current polarization and subsequently the polarization of orbital current as both are constrained by positive  −  .Temperature-dependent studies [59][60][61] have been proven to be important in identifying various scattering mechanisms in the materials and subsequent determination of respective Hall conductivities.To validate the IOHE origin of the THz emission from NiFe/Nb bilayer, we have performed temperature-dependent experiments by monitoring the changes in the peak-to-peak amplitude of the THz signal as a function of the sample temperature (T) from 10 K to 300 K.The temperature sensitivity of the phonon scattering would have a significant impact on the OHE and associated phenomena because the orbital degree of angular momentum is tightly coupled with the crystal field potential. 13,20.The result is presented in Fig. 2(a), where the error bars represent the largest absolute deviation from the mean of three THz signal outputs at each temperature.As indicated in the inset of the figure, the sample is optically excited from the substrate side and the same orientation for sample excitation is followed in all the results presented below in the paper.The substrate side optical excitation geometry does not create any temperature dependent contributions (see Supplementary Section S15).Since, the sign and magnitude of the emitted THz pulse is directly related with the   , hence, by looking at the THz signal's amplitude and phase, a qualitative information about the   can be obtained. 32For exactly determining the dominating role of either the   or   , detailed analysis is presented below.
By employing the four-point van der Pauw method, electrical longitudinal resistivity () was also determined for the Nb and NiFe/Nb films in the entire experimental temperature range (see inset of Fig. 2(a)).The resistivity information, together with the THz amplitude data in Fig. 2(a), are used to obtain the results presented in Fig. 2 Here,   .,   ,  0, ,   are intrinsic spin Hall conductivity, side-jump spin Hall conductivity, residual resistivity, and skew scattering angle of the NM layer, respectively.The second and the third terms on the right-hand side of Eq. ( 2) represent the extrinsic contributions to scattering.Because of the correspondence between the SHE and OHE, a similar equation for the orbital Hall resistivity (  ) can be constructed by accounting for the intrinsic and extrinsic orbital scattering processes. 8,15,20Hence, temperature-dependence of   can be expressed as, On the right side of the above equation, the first term, consisting of the intrinsic orbital Hall conductivity,    , represents the intrinsic scattering, while the extrinsic contributions are represented by the second term, .The extrinsic contribution to the spin or the orbital Hall resistivity in the above equations, is usually neglected for pure materials 61,63 while, it can be significantly high for materials with high impurity concentration.For capturing the temperature-dependence of the effective Hall resistivity, Eqs. ( 2) and (3) can be combined and    is expressed as following, For simplicity, we have ignored the temperature variation of the extrinsic terms in both the spin and the orbital Hall resistivities.Also, we have used (   )  = (   +  − .   ) to represent the effective intrinsic spin(orbital) Hall conductivity.As shown in Section S10 of the Supplementary Information, the effective Hall resistivity is related to the amplitude of the THz signal, 59,62 and it is given by the relation, The extracted data for    vs   2 at each temperature, has been presented in Fig. 2 Nb film, i.e.,    ( −1  −1 ) ≅ −100 14,18 ,  − ≅ 0.045 8 , and    ( −1  −1 ) ≅ 6000 18 , we obtain, (   ) .= (   +  − .   )~+ 170  −1  −1 .Although the experimental value of (   )   is slightly higher than the calculated value, they can still be considered to be in good agreement, signifying that the orbital current in the NiFe layer governs the THz emission from NiFe/Nb via IOHE provided its efficient conversion to the transient charge current in Nb takes place.In fact, theoretical predictions of a gigantic +ve value of   over a small -ve value of   in Nb 64 , are well supported by our experimental observations.

FM(CoFeB,Fe)/NM(Pt,Ta): ISHE mediated THz emission from heavy metal layers based FM/NM heterostructures
Experimental results are now presented and discussed on Fe/Ta and CoFeB/Pt, in conjunction with those on CoFeB/Ta, presented elsewhere, 59 and re-examined again as presented in the Supplementary Section S8.These bilayer heterostructures contain a heavy metal layer, either Pt or Ta, and are chosen selectively for their opposite sign of the spin Hall angle. 32,34Moreover, CoFeB and Fe are selected because of their negligible 8,48 spin-orbit correlation factor, i.e.,  −  and  −  ~0 as compared to Ni or NiFe.By these choices, we initially ensure that there is no fractional conversion of the spin current into orbital current within the FM layer.Consequently, from the femtosecond pulse excited FM/NM bilayers, THz generation takes place via ISHE only.
For the CoFeB/Pt with the Pt layer having positive spin Hall angle (   > 0), the experimental configuration is depicted in Fig. 3(a), where the directions of the external magnetic field, spin current, charge currents and the THz signal polarities are indicated.Owing to the opposite sign of the spin Hall angle in Ta (   < 0), emission of opposite polarity THz signal from Fe/Ta, under the same experimental configuration, is depicted in Fig. 3(b).In both cases, the THz signal polarity dependence on the experimental configuration, including the direction of the external magnetic field and the optical excitation, are found to be as expected from the ISHE mediated THz emission. 29,32Moreover, ultrafast demagnetization mechanism is mainly responsible for the THz emission from the bare FM layer (see Supplementary Section S12).Variations of the peak-to-peak THz signal amplitude as a function of the sample temperature for the CoFeB/Pt and Fe/Ta bilayers, are presented in Figs.3(c) and 3(d), respectively.The temperature-dependent longitudinal resistivities for both the samples is provided in the Supplementary Section S7.From the experimentally measured THz amplitude and resistivities, we have derived the effective Hall resistivity,    at each temperature using the procedure discussed in Section S10 of Supplementary Information, and the results for the same as a function of squared longitudinal resistivity,   2 ( = , ) are presented in Figs.3(e) and 3(f) for CoFeB/Pt and Fe/Ta, respectively.In the next paragraph, we establish sole ISHE origin of the THz signal generation through the dominance of the extracted respective spin Hall conductivities in CoFeB/Pt and Fe/Ta bilayers.
We fit the results in Figs.3(e) and 3(f) using Eq. ( 4) to obtain (   )  from the slope of the linear fit.Firstly, in the case of Fe/Ta, a negative slope value, i.e., (   )  = (   +  − .   ) < 0, is obtained.As it is well known in the literature that for Ta,    is negative, while,    is positive. 14,18Also, the spin-orbit correlation factor for Fe, ( − ), is known to be insignificantly positive. 8Therefore, a negative value of (   )  directly implies that    >  − .   .Moreover, positive   value of Ta demands the slope to be positive in Fe/Ta sample, which is not the case here.Hence, it can be concluded that the THz emission from Fe/Ta is entirely due to the spin-to-charge conversion via ISHE in Ta.On the other hand, a positive slope of the fit, i.e., (   )  > 0 is obtained in the case of CoFeB/Pt.Since,    ,    and  − , all are positive for Pt, 14,18 the positive valued effective conductivity, (  .)  = (   +  − .   ) is as per the expectation.Thanks to the negligible value of  −  , the contribution,  − .   becomes far smaller than    , and this would results into the condition    >  − .   , same as in the case of Ta.The dominating    dictates flow of majorly a spin current from CoFeB and its conversion to charge current takes place in Pt via ISHE.Therefore, it can be concluded here that an ISHE mediated THz pulse emission takes place in the CoFeB/Pt bilayer.

CoFeB/W/Ta: A heavy metal insertion layer enhances orbital transport and hence the THz generation efficiency
In the above two sections, we have established role of solely IOHE in NiFe/Nb and ISHE in CoFeB/Pt and Fe/Ta, as the reason for the generation of THz pulses from them.Due to the large   , the existence of high IOHE is expected in some heavy metals.But to harness the effect for its direct observation, one needs to choose their appropriate combinations with the FM layers.To launch an orbital current into the heavy metal layer, use 53 of Ni or NiFe, or similar other FM layers, would be the proper choice; otherwise, despite of large   in heavy metals, especially, nearly an order high   than   in Ta, it is very difficult to observe orbital transport in either Fe/Ta or CoFeB/Pt.Here, we show that by adding/interfacing a heavy metal W-insertion layer in technologically relevant CoFeB/Ta heterostructure, the orbital transport gets pronounced.For this study, CoFeB(2)/W(2)/Ta(2) and CoFeB(2)/W(1)/Ta(2), where, the integers inside small parentheses represent layer thickness in nm, were fabricated.The thickness and good interface quality of the W-insertion layer is confirmed by analyzing the elemental stack using secondary ion mass spectroscopy (SIMS) technique, as shown in Supplementary Section S2.The thickness constraint on the W-insertion layer is motivated by the previous studies. 65,66We may emphasize that by adding the W-insertion layer, the magnetic properties of the trilayers are nearly unchanged from the bilayer counterparts, as confirmed from both the MH and MT-measurements (see Sections S3 and S4 of the Supplementary Information).Figure 4(a) schematically shows the ultrafast optically excited spin current injection into the W layer, where it induces the large additional orbital current through the efficient L-S conversion within the W layer along with the spin to charge current via ISHE in W. The W layer here, has a distinctive quality of generating spin current induced orbital current. 53Due to the negative  −  of W, as explained in Fig. 4(b), the orbital and spin magnetic moments are oppositely polarized in the propagation of spin and orbital current.Both spin and orbital current are further encountered to the adjacent Ta heavy metal layer.Ta has been shown 8,14 to possess more than an order higher and positive value of   then its   (see Table 1); therefore, maximal conversion of orbital current to charge current is expected.On the other hand, the conversion from spin to charge current in -phase Ta is weaker due to its small value of   and hence the spin Hall angle.Thus, the total current generated from the heterostructure is the sum of the charge current converted either from ISHE or IOHE.Similar to Eq. 1, it can be expressed as   =  − +  − = (   .  +    .  ) +    . −  .  (6)   Here, the sign of    ,    ,  −  is negative, while it is positive for    , therefore, the total sum of transient charge current adds up constructively to give the efficient generation of THz radiation.
Figure 4(c) presents THz time-domain traces emitted from CoFeB(2 nm)/W(t)/Ta(2 nm) trilayer samples of varying thickness of the W-insertion layer from t = 0 to 2 nm.While the THz amplitude for t = 2 nm is ~10 times stronger than that from t = 0 nm, the same is nearly 4 times higher than from the CoFeB(2)/W(2) bilayer (see Supplementary Section S14).It is clear from the results of Fig. 4(c) that the THz signal amplitude increases with the thickness, t of the W-insertion layer.This observation is in contradiction with a previous study 39 where, irrespective of the type of insertion layer material, a monotonic decrease in the THz emission efficiency with the increasing insertion layer thickness is reported.There, the results were interpreted in the context of increased spin memory loss in the insertion layer.At the same time, in few other reports in the recent literature, [65][66][67][68] significant enhancement in the spin current flow due to an insertion layer was attributed to the atomically thin nature of the insertion layer.We argue that such inconsistency in the literature is arising because of the fact that conventionally, the experimental outcomes have been interpreted solely in terms of the spin current, neglecting the effect of orbital contribution altogether, though the latter can be gigantic even in the light metals with weak SOC. 13,14The orbital current diffusion length can be several times larger than the spin counterpart. 7,25,48,52,57The induced orbital current within the W-insertion layer is given by 48   ∝ ∫    0  −  ., according to which, higher thickness and strength of , are favourable.These reasons clearly justify our observation of W-insertion layer thickness dependent enhancement in the THz emission via IOHE in CoFeB/W/Ta.More importantly, the nearly one order increase in the THz generation efficiency of CoFeB/W/Ta relative to CoFeB/Ta, as shown in Fig. 4(c), is attributed to IOHE due to the emergence of long-range orbital current within the W-insertion layer.To strengthen our point that, indeed the orbital current within the W-insertion layer contributes to enhance the THz pulse emission from CoFeB/W/Ta as compared to CoFeB/Ta bilayer counterpart, we now present temperature-dependent results on them.The governing role of IOHE for THz emission from CoFeB/W/Ta, due to the orbital current within the W-insertion layer that increases in proportion with its thickness, is brought out clearly.In Fig. 4(d), we have plotted the variation in the THz signal amplitude as a function of CoFeB/W(2)/Ta sample temperature.The corresponding longitudinal resistivities are also recorded at each sample temperature and presented in Supplementary Section S7.The resistivity information, together with the THz amplitude data in Fig. 4(d), are used to obtain the results presented in Fig. 4(e), where we have plotted the behavior of extracted effective Hall resistivity (   ) with respect to the squared longitudinal electrical resistivity ( /

2
) following the same procedure discussed earlier in the paper.Additional results obtained on CoFeB/W(1)/Ta sample with different thicknesses of the Winsertion layer, are included in the Supplementary Section S9.We fit the experimental data in Fig. 4(e) using Eq. ( 4) to obtain (   )  from the slope of the linear fit.Clearly, the data fits for a negative slope, i.e., (   )  = (   +  − .   ) < 0 and provides a value of (   )  ~− 3256 (ℏ/)  −1  −1 , which is much larger than the theoretical values of the intrinsic spin Hall conductivities 15 of both -phase W 69 and Ta 70 , i.e., ~− 700 (ℏ/)  −1  −1 , and ~− 103 (ℏ/)  −1  −1 , respectively.Therefore, it simply suggests the dominance of  − .   term in the overall effective intrinsic Hall conductivity which is negatively large due to much larger orbital Hall conductivity than the spin Hall conductivity,    ≫    , in Ta making the orbital to charge conversion more pronounced.A value of (   )  ~− 1250 (ℏ/)  −1  −1 is obtained by us for the CoFeB/W(1)/Ta, where the magnitude of the THz signal reduces in proportion with the thickness of the W-insertion layer.Therefore, the large negative value of (   )  for CoFeB/W/Ta strengthens our argument that the enhanced THz signal from CoFeB/W/Ta is due to the orbital current generation within the W-insertion layer, thus providing an additional charge current by orbital to charge current conversion via IOHE in the Ta-layer of the heterostructure.
Figure 4(f) summarizes our results on the effective intrinsic spin(orbital) Hall conductivity of different heterolayer systems that are experimentally determined in a non-contact and non-invasive manner by time-domain THz emission spectroscopy.To have a ready comparison of the values for different materials and heterostructures, available from different resources, either experimental or theoretical, Table 1 lists them together with the values of the spin-orbit correlation factor, wherever applicable.

CONCLUSION
In summary, we have experimentally demonstrated the ultrafast optically induced orbital current and its conversion to transient charge current via IOHE by temperature-dependent THz emission measurements.To show the role of the spin and orbital currents exclusively, we have chosen the material combinations in the layered heterostructures such that they comprise either a heavy or a light metal layer.THz pulses emitted from them have been measured, where temperature-dependence of the THz amplitude helps to disentangle the contributions from the spin and the orbital transports.Purely orbital-charge conversion via IOHE in NiFe/Nb and spin-charge conversion via ISHE in CoFeB/Pt and Fe/Ta, are manifested from the extracted values of effective intrinsic Hall conductivities.We also find that an insertion layer of W heavy metal in CoFeB/W/Ta, provides a pathway to constitute an ultrafast orbital current within it and subsequently its conversion to transient charge current in the Ta layer via IOHE that significantly enhances the THz generation efficiency as compared to the CoFeB/Ta counterpart.These findings will be proven to be highly useful in efforts towards realizing ultrafast orbitronic devices as well as adding new knowledge of the underlying physics.

METHODS
Heterostructures comprising of ferromagnetic Co20Fe60B20 (CoFeB) and Ni90Fe10 (NiFe) layers, and nonmagnetic Pt (platinum), Ta (tantalum), W (tungsten), Nb (niobium) material layers were created by using ultra high vacuum radio frequency magnetron sputtering technique.Bilayer systems, Sub./CoFeB(2)/Pt(3), Sub./CoFeB(2)/Ta(2), Sub./Fe(2)/Ta(3) and Sub./NiFe(5)/Nb (10), and trilayer systems, Sub./CoFeB(2)/W(2)/Ta(2) and Sub./CoFeB(2)/W(1)/Ta(2), were deposited layer by layer on 1 mm thick quartz substrates (Sub.).The information related to the film thickness, roughness and phase is obtained by using various structural and topographical measurements techniques, such as X-ray diffraction (XRD), X-ray reflectivity (XRR), and atomic force microscopy (AFM), and can be found in the Supplementary Section S1.SIMS depth profile experiments reconfirmed the elemental stack and the quality of interfaces in the heterostructures (see Supplementary Section S2).The magnetic measurements shown in Supplementary Sections S3 and S4, were performed in a magnetic properties measurements system (MPMS3, Quantum Design).We have employed a closed-cycle helium optical cryostat system (SHI-4-2-XG, Janis) operating in the temperature range of 10-450 K for all the temperature-dependent electrical transport and time-domain THz experiments.Complete details of the temperature-dependent THz setup 59 are provided in the Supplementary Section S5.A regenerative femtosecond amplifier (Astrella, Coherent Inc.) providing laser pulses of ~50 fs pulse duration at 1 kHz repetition rate and centred at 800 nm wavelength, were used for the THz generation and detection.The collimated optical excitation (pump) beam diameter on the sample was kept at ~3 mm.All the samples were excited from the substrate side, unless specified.The emitted THz pulses were collected from behind the sample by a set of two 90 0 off-axis gold-coated parabolic mirrors of focal length of 15 cm.THz pulses were detected by electro-optic sampling scheme in a (110)-oriented ZnTe crystal of thickness 500 micron by using a combination of a quarter wave plate, a Wollaston prism, a balanced photodiode and a lock-in amplifier. 59The THz setup was under the normal conditions of the room temperature and humidity.

Fig. 1 .
Fig. 1.Orbital-to-charge current conversion mediated THz emission from NiFe/Nb bilayer.(a) Schematic illustration of ultrafast optically induced spin current   and orbital current   in the NiFe and their injection into the Nb layer producing ultrafast charge current and hence emission of THz pulses.The positive value of η  represents the spin-to-orbital current conversion efficiency in NiFe.  and   represent charge currents converted from   and   through the ISHE and IOHE, respectively. represents the external applied magnetic field.(b) Temporal profiles of THz signal obtained from NiFe/Nb under four experimental geometries with the direction of the optical excitation and the magnetic field: (b) 1. substrate side excitation; 2. Nb film side excitation, while keeping B fixed along  ̂direction, (c) 1. (+ ̂); 2. (− ̂), while keeping the optical excitation from the substrate side.(d) Schematic of OHE and SHE in a prototype material.A charge current,   in the − ̂-direction induces accumulation of spin (S) and orbital (L) angular momenta in the transverse -direction.For positive spin-orbit correlation, η > 0, both the spin and orbital polarizations are parallel along either + ̂direction or − ̂-direction.

2 +
(b), where we have plotted the behavior of extracted effective spin(orbital) Hall resistivity (   ) with respect to the squared longitudinal resistivity (  2 ) of NM = Nb.See Supplementary Section S10 for details to obtain    .This data is analyzed in the light of a temperature scaling relation[59][60][61][62] for the spin Hall resistivity (  ) as,   () =    .  2 () +   . 0,   . 0, (b), where, the continuous curve represents a linear fit with slope, (   )   as per Eq.(4).With the information at hand that, for Nb,    is negative and  − is positive, a positive value of (   )   from Fig. 2(b) clearly reveals that  − .   for Nb is a large positive value.The experimental value of (   )   as obtained from Fig. 2(b) is ~+ 281  −1  −1 .From the theoretically provided values of different parameters of

Fig. 2 .
Fig. 2. Temperature-dependent THz emission from NiFe/Nb (Nb = light metal).(a) Peak-to-peak value of THz amplitude as a function of varying sample temperature.The error bars at each temperature correspond to the largest absolute deviation of the peak-to-peak THz amplitude from the mean of three measurements.Inset: The optical excitation from the substrate side; and temperature-dependent resistivity (ρ) variations of NiFe/Nb and Nb samples measured by the four-point van der Pauw method.(b) Effective spin(orbital) Hall resistivity as a function of the squared longitudinal resistivity for the Nb film.Solid line is fit to the data using Eq.(4).

Fig. 3 .
Fig. 3. Temperature-dependence of THz signal and effective Hall resistivity for CoFeB/Pt and Fe/Ta bilayers (Pt, Ta = heavy metal).Schematic illustration of the ultrafast optical excitation, spin magnetic moment transport and its conversion to transient charge current through ISHE to emit a THz pulse from (a) CoFeB/Pt and (b) Fe/Ta.The spin Hall angle (SH) and the direction of the external magnetic field are indicated.Temperature-dependent variation of the THz signal peak-to-peak amplitude for (c) CoFeB/Pt, and (d) Fe/Ta.Effective Hall resistivity,   .as a function of the squared longitudinal resistivity,   2 for (e) Pt and (f) Ta.The continuous curves in (e) and (f) are linear fits to the data using Eq.(4).

Fig. 4 . 2 .
Fig. 4. Enhanced spin-to-orbital current conversion by W-insertion layer in CoFeB/W/Ta.(a) Schematic to illustrate spin current conversion into orbital current by large negative spin-orbit correlation factor, η −  (< 0) of the W-insertion layer in the CoFeB/W/Ta heterostructure, ultrafast optically excited from the substrate side.The transient charge currents due to spin-charge conversion in W and Ta layers are labelled as  − and  − , respectively.The charge current in Ta layer due to orbital-to-charge conversion is represented by   .(b) Schematic illustration of spin and orbital magnetic moments in a material of negative spin-orbit correlation (η − < 0), i.e., W and Ta.(c) THz time-domain traces with varying thickness, t = 0, 1, 2 nm of the W-insertion layer in CoFeB/W(t)/Ta heterostructure.(d) Peak-to-peak THz signal amplitude variation with respect to the temperature of CoFeB/W(2)/Ta.(e) Effective Hall resistivity,   .as a function of the squared longitudinal resistivity,  W/Ta 2 .(f) Extracted values of effective intrinsic Hall conductivity, (   )  for different bi-and trilayer heterostructures used in the current study.

TABLE . 1
. Comparison of the spin (  ), orbital (  ), and effective Hall conductivity, (  .)  in different materials and heterostructures.Values, where available, of the spin-orbit correlation factor,  − are also listed.