# Large spin-to-charge conversion at the two-dimensional interface of
transition metal dichalcogenides and permalloy

Himanshu Bangar  Department of Physics, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi-110016, India  Akash Kumar  Department of Physics, Indian
Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India  Department
of Physics, University of Gothenburg, Gothenburg-412 96 , Sweden  Niru
Chowdhury  Department of Physics, Indian Institute of Technology Delhi, Hauz
Khas, New Delhi-110016, India  Richa Mudgal  Department of Physics, Indian
Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India  Pankhuri
Gupta  Department of Physics, Indian Institute of Technology Delhi, Hauz Khas,
New Delhi-110016, India  Ram Singh Yadav  Department of Physics, Indian
Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India  Samaresh
Das  Center for Applied Research in Electronics, Indian Institute of
Technology Delhi, Hauz Khas, New Delhi-110016, India  P. K. Muduli1,
<EMAIL_ADDRESS>
###### Abstract

Spin-to-charge conversion is an essential requirement for the implementation
of spintronic devices. Recently, monolayers of semiconducting transition metal
dichalcogenides (TMDs) have attracted considerable interest for spin-to-charge
conversion due to their high spin-orbit coupling and lack of inversion
symmetry in their crystal structure. However, reports of direct measurement of
spin-to-charge conversion at TMD-based interfaces are very much limited. Here,
we report on the room temperature observation of a large spin-to-charge
conversion arising from the interface of Ni80Fe20 (Py) and four distinct large
area ($\sim 5\times 2$ mm2) monolayer (ML) TMDs namely, MoS2, MoSe2, WS2, and
WSe2. We show that both spin mixing conductance and the Rashba efficiency
parameter ($\lambda_{\textrm{IREE}}$) scales with the spin-orbit coupling
strength of the ML TMD layers. The $\lambda_{\textrm{IREE}}$ parameter is
found to range between $-0.54$ and $-0.76$ nm for the four monolayer TMDs,
demonstrating a large spin-to-charge conversion. Our findings reveal that
TMD/ferromagnet interface can be used for efficient generation and detection
of spin current, opening new opportunities for novel spintronic devices.

Inverse Rashba Edelstein effect, spin pumping, ferromagnetic resonance,
transition metal dichalcogenides, spin-to-charge conversion

##  I INTRODUCTION

Spintronics offers a route to fulfill the increasing demand for faster
processing hardware and mobile applications in the age of the internet of
things. 1, 2 One of the key requirements in spintronics is the efficient
generation and detection of spin currents, which was traditionally
accomplished by the use of ferromagnetic (FM) layers. Recent research has
focused on utilizing spin-orbit interaction of heavy metal (HM) and FM
heterostructures for spin-to-charge conversion. 3, 4, 5, 6 This has led to a
growing field of spin-orbitronics in which coupled interaction of spin and
orbital momentum of the electron is employed for interplay between charge and
spin currents 7, 5. When an electric current is passed through the HMs with
strong spin-orbit coupling (SOC), it produces a transverse spin current due to
the spin Hall effect (SHE) 8, 9, 7, 5. Conversely, when a spin current is
applied to a HM, charge current can be generated via inverse SHE (ISHE). Spin
currents have been used in a number of spintronic applications, such as domain
wall motion 10, spin-torque switching 4 and spin Hall nano-oscillators 11. For
optimum performance of these spin-orbitronics based devices, high spin-to-
charge conversion efficiency is essential 4, 6. Recent years have seen a surge
of interest in two-dimensional (2D) interfaces for spin-to-charge
interconversion via the Rashba-Edelstein effect (REE) 12, 13, 14, 15, 16, 17,
18, 19, 20. The REE mechanism has the potential to be more efficient than the
SHE mechanism in three-dimensional (3D) HMs.15, 21

Spin-charge interconversion via REE occurs at interfaces with broken spatial
inversion symmetry due to the spin-orbit interaction and built-in electric
potential in the direction normal to the film surface 3, 22, 5. Fig. 1A, 13
shows the Rashba-type spin splitting of the energy dispersion that arises at
the interface. It is characterized by (i) spin splitting of bands and (ii)
spin-momentum locking, which leads to two Fermi contours with opposite
helicity, as shown by the dashed lines in Fig. 1B. The Rashba Hamiltonian,
$H_{\rm\textrm{R}}$ is expressed as:
$H_{\rm\textrm{R}}=\alpha_{\textrm{R}}\left(\bm{k}\times\bm{\hat{z}}\right).\hat{\bm{\sigma}}$,
where, $\bm{k}$ denotes the momentum vector, $\hat{\bm{\sigma}}$ denotes the
Pauli spin matrix vector, $\bm{\hat{z}}$ denotes the unit vector normal to the
interface and $\alpha_{\textrm{R}}$ is the Rashba coefficient 12, 15. The
energy dispersion depicted in Fig. 1A is a solution of the Rashba Hamiltonian.
The relation for the in-plane momentum, $k_{x}$ of the Rashba interface is
given as 15:

Figure 1:  Schematic representation of the REE, IREE effects, and key features
of ML TMDs. (A) A typical energy dispersion curve for the Rashba interaction.
The inner and outer circles have an opposite spin texture at the Fermi level
15. (B) Illustration of the shift in Fermi contours under the influence of a
charge current along $-x-$direction leading to spin accumulation at the
interface (REE effect). (C) Schematic representing the shift in Fermi contours
due to injection of spin current with polarization along $+y-$direction
leading to a charge current at the interface (IREE effect). (D) Schematic
illustration of spin splitting in the valence band around the $K$-point of
MoX2 and WX2 ML TMDs. Here, X denotes S or Se. (E) Theoretical spin splitting
of the uppermost valence band at the $K$-point for different ML TMDs 23. (F)
The ML TMD/ferromagnet (FM) structure used in this work is depicted
schematically, illustrating how spin current is injected via spin pumping.

$\begin{split}E(k_{x})=\frac{\hbar^{2}k^{2}_{x}}{2m^{*}}\pm\alpha_{\textrm{R}}k_{x},\end{split}$
(1)

where, $m^{*}$ denotes the effective mass of the electron. Hence, the
magnitude of the spin splitting of bands caused by the Rashba interaction
depends on $\alpha_{\textrm{R}}$, which is dependent on the SOC at the
interface. The Fermi contour of Fig. 1B shows that for $k_{x}>0$, the number
of spin-up ($\uparrow$) carriers is larger than that of the spin-down
($\downarrow$) carriers. When an in-plane electric field is applied along the
$-x-$direction, two Fermi contours (solid lines), which have opposite spin
helicity, are shifted along the $+x-$direction, resulting in a net spin
accumulation with spin polarization along the $+y-$direction. This is referred
to as the REE 15. On the other hand, if the spin is injected into the Rashba
interface with spin current having a polarization along $+y-$direction, then
the two Fermi contours are shifted in opposite directions (Fig. 1C, solid
lines), leading to a net charge current at the interface along the
$-x-$direction. This phenomenon is referred to as the inverse REE (IREE),
which is the Onsager reciprocal of the REE 16.

Spin-to-charge conversion utilizing IREE has received considerable interest
after Rojas Sánchez et al. reported a high spin-to-charge conversion
efficiency at the silver (Ag)/bismuth (Bi) interface 17. Subsequently, several
works have reported spin-to-charge conversion at the interface between two
non-magnetic materials. 24, 25, 26, 27, 28 IREE has also been used for the
generation of THz radiation 29. The spin-to-charge conversion becomes very
complex in a 3D FM-HM system with large REE contributions due to entangled
surface and bulk contributions 5. Additionally, the error in estimating
interfacial thickness leads to important parameters being underestimated or
overestimated. It is thus desirable to have a system that is truly 2D, from
which the extracted parameters can be accurately attributed to the IREE.
However, the reported studies of spin-to-charge conversion in large area true
2D-based systems are very much limited. 30, 31.

Recently, monolayers (ML) of semiconducting 2D materials such as the
transition metal dichalcogenides (TMDs) has gained huge interest for spin-to-
charge conversion owing to their (i) large SOC derived from the $d$-orbitals
of the transition metal 32 and (ii) lack of inversion symmetry in their
crystal structure 33, 34. Both of these characteristics are necessary
components of a Rashba interface. Recently, strong REE induced spin-orbit
torques 35, unconventional charge-spin conversion and spin-orbit torques 36,
37 are reported in TMD/FM systems. It is also demonstrated that the TMDs
enhances the spin-to-charge conversion efficiency significantly when used as
an insertion layer between HM and FM layers. 38, 39, 40 Out of various studied
TMDs, Mo and W-based TMDs stand out due to the presence of heavy transition
metals. Moreover, the valence band of ML MoX2 and WX2 TMDs (X= S or Se)
exhibits a spin splitting around the $K$-point due to the presence of a large
SOC as schematically shown in Fig. 1D 23. The theoretical spin splitting
values of the valence band around the $K$-point for these ML TMDs are shown in
Fig. 1E 23, which allows the control of spin-to-charge conversion via SOC of
the ML TMD 18.

Here, we report a systematic study of spin-to-charge conversion at the
interface of Ni80Fe20 (Permalloy, abbreviated as Py hereafter) and large area
ML TMDs namely MoS2, MoSe2, WS2, and WSe2 (Fig. 1F). To date, spin-charge
interconversion studies on such systems are mostly performed in non-local
geometry as growing TMDs with large area coverage is challenging 41, 42. We
use large area chemical vapor deposited ML TMDs interfaced with sputtered Py
thin films. TMD layers having different SOC allows us to control
$\alpha_{\textrm{R}}$ and hence spin-to-charge conversion. We observe a large
spin-to-charge conversion in these systems having efficiencies that scale with
SOC of the ML TMD layer consistent with the IREE effect. The magnitude of
spin-to-charge conversion efficiency exceeds that of the 3D FM/HM systems with
the maximum efficiency in W-based TMDs as compared to Mo-based TMDs.

##  II RESULTS AND DISCUSSION

Figure 2:  Raman measurements. (A-D) Raman spectra for different ML TMDs
before (open triangles) and after the deposition of Py and Ta layers (open
circles) (A) MoS2, (B) MoSe2, (C) WS2, and (D) WSe2, respectively.

We studied Al2O3/ML TMD/Py(10 nm)/Ta(3 nm) samples for four distinct large
area ($\sim 5\times 2$ mm2) TMDs namely, MoS2, MoSe2, WS2, and WSe2. A
reference sample without the TMD layer was also prepared simultaneously for
comparison. Figure 2A-D shows the measured Raman spectra observed on pristine
ML TMDs (open triangles) and after deposition of Py/Ta bilayer (open circles),
respectively. Two peaks corresponding to E${}_{\rm 2g}^{1}$ and A1g Raman
modes were observed for MoS2 (Fig. 2A) and WS2 (Fig. 2C) samples. 43, 44 The
separation of the E${}_{\rm 2g}^{1}$ and A1g peaks is found to be 20.3 cm-1
for MoS2 and 62.2 cm-1 for WS2, confirming their ML thickness 45, 46. The
absence of B${}_{\rm 2g}^{1}$ mode around 353 cm-1 (Fig. 2B) and 309 cm-1
(Fig. 2D) is consistent with the previously reported Raman spectra for ML
MoSe2 and WSe2, respectively 47. A single strong A1g Raman mode at 240 cm-1
(Fig. 2B) and 251 cm-1 (Fig. 2D) are the fingerprints of ML MoSe2 and WSe2,
respectively. 48 In order to confirm that we have large area coverage of ML
TMDs, we performed Raman measurements at multiple locations and obtained very
consistent Raman spectra (Fig. S1 and S2), indicating that our TMD samples
have ML thickness over the entire area of the sample ($5\times 2$ mm2). The
peak positions of the Raman spectra obtained after the deposition of Py and Ta
layers in Fig. 2 coincides with their corresponding pristine ML TMDs for all
four cases. This demonstrates that the quality of the ML TMD is not affected
after the deposition of the Py and Ta layers. In addition, this reveals no
diffusion of Mo, W, S, or Se into the Py layer, which would have adversely
altered the Raman signal from the ML TMDs. We also did not observe any
degradation of the surface morphology of the Py/Ta stacks grown on top of the
TMD, as shown in Supplementary Fig. S3. This is because of the (1) low atomic
roughness ($<$0.15 nm) of all the TMD layers, and (2) the low working pressure
for the growth of the Py layer. The Py deposition was optimized following our
earlier work on the growth of Py on Graphene, where we obtained minimum
defects in Graphene for room temperature deposition and low working pressure.
49

Figure 3:  FMR and IREE measurements. Field dependence of FMR (top row) and
corresponding $I_{\rm C}$ derived from IREE measurements (middle and bottom
row) for (A) Py(10)/Ta(3), (B) ML MoS2/Py(10)/Ta(3), (C) ML
MoSe2/Py(10)/Ta(3), (D) ML WS2/Py(10)/Ta(3), (E) ML WSe2/Py(10)/Ta(3) samples.
Here, numbers in parenthesis reflect thickness in nanometers and ML is
abbreviation for monolayer. The middle row is for for $H>0$ while the bottom
row is for $H<0$. The solid lines in middle and bottom row are fits to
experimental data.

In order to measure the spin-to-charge conversion in our samples, we drive the
Py layer to the ferromagnetic resonance (FMR). The upper panel of Fig. 3 shows
the measured derivative of FMR absorption around the resonance field
($H_{\rm\textrm{r}}$) for various ML TMD/Py samples along with the reference
sample (without TMD layer). The FMR of the magnetization of the Py layer leads
to the pumping of the spin current to the ML TMD/Py interface, as shown
schematically in Fig. 1F. The pumped spin current is subsequently converted to
charge current and is measured as a voltage signal ($V_{\rm dc}$) using field
modulation technique 50. The field dependence of charge current ($I_{\rm C}$)
around $H_{\rm\textrm{r}}$ corresponding to the measured $V_{\rm dc}$ is
plotted in the middle panel ($H>0$) and lower panel ($H<0$) of Fig. 3.

The measured field dependence of $I_{\rm C}$ is dominated by a symmetrical
lineshape for all samples, including the reference sample. We fitted the
measured spectrum using a combination of the symmetric and antisymmetric
components of the Lorentzian function and found the antisymmetric component to
be negligible, indicating the lack of signal due to the galvanic effects such
as anomalous Hall effect (AHE) and/or anisotropic magnetoresistance (AMR) 51,
50, 52. In fact, our measurement geometry is optimized to minimize the
galvanic effects by using a thin mica sheet (100 $\mu$m) between the sample
and CPW, which minimizes RF electric field. Furthermore, we observe the
expected sign reversal of $I_{\rm C}$ when the field direction is reversed as
shown in the middle and bottom row of Fig. 3. These observations indicated
that the signal we observe is primarily due to spin-to-charge conversion.

The magnitude of $|I_{\rm C}|$ is found to drop with respect to the reference
sample as TMD layer is varied in the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2 (second
and third row of Fig. 3). Furthermore, the drop is stronger for W-based TMDs
compared to the Mo-based TMDs. Since our system comprises of Al2O3/ML
TMD/Py/Ta, $I_{\rm C}$ can arise due to spin-to-charge conversion from (i) the
ML TMD/Py interface, (ii) from the bulk of Py layer due to self-induced ISHE
53 and (iii) from the ISHE of Ta capping layer as well other interfacial
mechanisms from Py and Ta interface. We found all these contributions to be
present in our measurements. The signal from the reference sample is due to
the self-induced ISHE as explained in the supplementary material Sec. S5.
Hence, in order to extract the signal coming from ML TMD/Py interface, we
subtracted the signal coming from the reference layer: $I_{\rm
C}^{TMD/Py}=I_{\rm C}^{TMD/Py/Ta}-I_{\rm C}^{Py/Ta}$. The 2D or the surface
charge current density ($j_{\rm\textrm{C}}$) corresponding to $I_{\rm C}$ is
given as $j_{\rm\textrm{C}}=\frac{I_{\rm C}}{b}$ 25. Here, $b$ is the width of
the sample, which was the same for all the samples. Thus, we can determine the
2D charge current density of the ML TMD/Py interface
$j_{\rm\textrm{C}}^{TMD/Py}$, which is found to have a negative sign. The
magnitude of $|j_{\rm\textrm{C}}^{TMD/Py}|$ is found to increase monotonically
(Fig. 4C) in the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2,
suggesting a direct correlation of the measured $j_{\rm\textrm{C}}^{TMD/Py}$
and SOC strength of the ML TMD.

To further confirm that the signal originates at the ML TMD/Py interface, we
also measure $I_{\rm C}$ by inserting a Cu spacer layer between the ML TMD and
the Py layer. We no longer observe the decrease in $I_{\rm C}$ as shown in
Fig. S4 of supplementary material Sec. S3. Cu was chosen as the insertion
layer due to its extremely long spin diffusion length [$>$350 nm] 54, 55 and
hence spin current should travel through it without dissipating. Thus, the
decrease in $I_{\rm C}$ in the case of ML TMD/Py samples in comparison to
their reference sample in Fig. 3 can be attributed to the IREE at the ML
TMD/Py interface rather than ISHE in the Py layer or Ta capping layer. As
another confirmation of this behavior, and to understand the negative sign of
$I_{\rm C}^{TMD/Py}$, we also prepared a series of Py samples with various
capping layers of Ta, Pt, and SiO2 as discussed in supplementary material Sec.
S4. The analysis shows that the decrease of $I_{\rm C}$ in the case of ML
TMD/Py samples can be attributed to a negative sign of the spin-to-charge
conversion. As a further confirmation of negative sign, we replace Py with
Co60Fe20B20 (CFB) [supplementary material Sec. S4.] and show that negative
spin to charge conversion is driven by spin-orbit coupling of the TMD layer.

In order to understand the observed behavior of $j_{\rm\textrm{C}}^{TMD/Py}$
with respect to the type of TMD layer, we then calculated the 3D spin current
density ($j_{\rm s}$) from the FMR measurements by using the theory of spin
pumping 56:

$\begin{split}j_{\rm s}=\frac{\mathrm{g}_{\uparrow\downarrow}\gamma^{2}\hbar
h_{\rm RF}^{2}}{8\pi\alpha_{\rm eff}^{2}}\left[\frac{4\pi
M_{\rm\textrm{s}}\gamma+\sqrt{(4\pi
M_{\rm\textrm{s}}\gamma)^{2}+4\omega^{2}}}{(4\pi
M_{\rm\textrm{s}}\gamma)^{2}+4\omega^{2}}\right]\frac{2e}{\hbar},\end{split}$
(2)

$h_{\rm RF}$ is the RF field generated due to the RF current of frequency
$f=\omega/2\pi$ flowing through the co-planar waveguide (CPW), $\gamma$ is the
gyromagnetic ratio, $4\pi M_{\rm\textrm{s}}$ is the saturation magnetization,
$\alpha_{\rm eff}$ is the effective Gilbert damping constant, $\hbar$ is the
reduced Planck’s constant, and $e$ is the electronic charge.
$\mathrm{g}_{\uparrow\downarrow}$ is the effective spin mixing conductance of
the ML TMD-FM interface and denotes the efficiency of spin pumping. It can be
calculated from measured damping constant as 56:

Figure 4:  Determination of spin current density and magnetic properties (A)
The extracted data (symbols) for $\Delta H$ versus $f$ and its fit to Eq. 4
(solid line). (B) The plot of $\Delta H_{\rm 0}$ extracted from the fit in
Fig. 4A. (C) Plot of $|j_{\rm\textrm{C}}^{TMD/Py}|$ and $j_{s}$ for various ML
TMDs, which follows the trend of SOC strength shown in Fig. 1E. (D) $f$ vs.
$H_{\rm\textrm{r}}$ data (points) fitted with Kittel’s formula (solid lines)
to extract $M_{\rm eff}$. (E) Magnetization curves for various ML TMD/Py
samples measured using VSM. (F) Comparative plot of $M_{\rm eff}$ (green axis)
and $M_{\rm\textrm{s}}$ values (brown axis) showing that the magnetic
properties of Py is similar for all ML TMD/Py samples.

$\begin{split}\mathrm{g}_{\uparrow\downarrow}=\frac{\Delta\alpha_{\rm eff}4\pi
M_{\rm\textrm{s}}t_{Py}}{g\mu_{B}},\end{split}$ (3)

where $t_{Py}$, $g$, $\mu_{B}$ denote Py layer thickness, the Landé
$g$-factor, and the Bohr magneton, respectively. $\Delta\alpha_{\rm
eff}=\alpha_{\rm eff}^{TMD/Py/Ta}-\alpha_{\rm eff}^{Py/Ta}$ represents the
change in effective damping constant of the TMD/Py stacks with respect to the
reference sample without the TMD layer. $\alpha_{\rm eff}$ was determined from
the fitting of the linewidth ($\Delta H$) versus frequency ($f$) data using
the following equation:

$\Delta H=\frac{2\pi\alpha_{\rm eff}f}{\gamma}+\Delta H_{\rm 0},$ (4)

where, $\Delta H_{\rm 0}$ denotes the inhomogeneous line broadening. The slope
of the linear fits (as shown in Fig. 4A) of the above equation gives
$\alpha_{\rm eff}$, which is found to be higher for TMD/Py samples compared to
the reference sample. $\alpha_{\rm eff}$ and hence $\Delta\alpha_{\rm eff}$
increase in the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2 (Table
1). $\Delta H_{\rm 0}$ is a measure of magnetic inhomogeneity and sample
imperfections of the FM layer. The value of $\Delta H_{\rm 0}$ for all the ML
TMD/Py samples showed low values of $\Delta H_{\rm 0}$ ($<$ 6 Oe), as shown in
Fig. 4B, indicating that the Py quality is similar on the ML TMDs and
comparable to the reference sample. We also determine the magnetization of Py
to ascertain whether the magnetic characteristics of the Py layer formed on ML
TMD layers have changed. We determine $M_{\rm eff}$ from the $f$ versus
$H_{\rm\textrm{r}}$ plot (Fig. 4D) by fitting with Kittel’s equation 57. The
saturation magnetization $M_{\rm\textrm{s}}$ is measured using a vibrating-
sample magnetometer (VSM) (Fig. 4E). $M_{\rm eff}$ and $M_{\rm\textrm{s}}$ are
found to be similar for all the ML TMDs/Py samples as shown in Fig. 4F,
indicating that there is no significant difference in magnetic properties of
the Py layers grown on the ML TMDs. Thus the decrease of $I_{\rm C}$ with ML
TMD can not be explained on the basis of a possible change of the magnetic
properties of the Py layer. As illustrated in Fig. 4C, the $j_{\rm s}$
calculated using Eq. 2 is found to increase in the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2 which
is similar to $j_{\rm\textrm{C}}$. This indicates that the measured magnitude
of the 2D charge current is directly proportional to the observed magnitude of
the spin current.

Our findings reveal that both $j_{\rm s}$ and $j_{\rm\textrm{C}}$ increase in
the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2, the
same sequence for which theoretically predicted SOC also increases (Fig. 1E).
In the IREE mechanism, $j_{\rm s}$ is related to $j_{\rm\textrm{C}}$ as 16, 17

$\begin{split}j_{\rm\textrm{C}}=\lambda_{\textrm{IREE}}j_{\rm s},\end{split}$
(5)

where, $\lambda_{\textrm{IREE}}=\alpha_{\textrm{R}}\tau_{s}/\hbar$. Here
$\tau_{s}$ is the momentum relaxation time 16. The $\lambda_{\textrm{IREE}}$
denotes the efficiency of spin-to-charge conversion. It has the unit of length
as it is a ratio of 3D charge current density to the 2D spin current density
(Eq. 5). The values of efficiency parameter $\lambda_{\textrm{IREE}}$ are
summarized in Table 1. The value of $\lambda_{\textrm{IREE}}$ is found to
increase in the sequence
MoS${}_{2}\rightarrow$MoSe${}_{2}\rightarrow$WS${}_{2}\rightarrow$WSe2 and it
lies in the range of $-0.54$ to $-0.76$ nm. Moreover, the values of
$\lambda_{\textrm{IREE}}$ are significantly larger for W-based TMDs as
compared to that of Mo-based TMDs. This may be due to stronger interfacial
$d$-$d$ hybridization resulting from the higher spin-orbit coupling of W as
compared to Mo atoms 58.

The magnitude of $\lambda_{\textrm{IREE}}$ in our system is found to be
significantly larger compared to other Rashba interfaces such as Bi/Ag 17,
Ag/Sb 25, Cu/Bi 26, and NM/Bi2O3 (where NM denote non-magnetic metals Cu, Ag,
Au, Al) 59 (see Fig. S8 for direct comparison). In the case of YIG/MoS2 a
value of $\lambda_{\textrm{IREE}}=0.4$ nm was reported 33. Our value is
comparable to YIG/MoS2 system. A recent theoretical work on ML TMD predicts
the presence of a large orbital Hall effect (OHE) with a sign that is opposite
to that of the SHE 34. However, in our work, the FM layer is in direct contact
with the TMD layer. Theoretical calculation for such ML TMD/Py interface is
yet to be performed. The large and negative sign of spin-to-charge conversion
in our work may appear to agree with the negative OHE predicted in Ref 34.
However, OHE is independent of SOC of the TMD layer, while in our experiment,
we see an excellent correlation of $\lambda_{\textrm{IREE}}$ with SOC. Hence,
we believe that the mechanism of spin-to-charge conversion in the present ML
TMD/Py system is not due to the OHE, but rather it is governed by the SOC-
dependent IREE.

For comparison of the spin-to-charge conversion efficiency of these ML TMDs
with traditional 3D HMs, we also calculate the so-called pseudo spin Hall
angle ($\theta_{\textrm{PSH}}$) as 17

$\begin{split}\theta_{\textrm{PSH}}=2\lambda_{\textrm{IREE}}/t\end{split}$ (6)

where $t$ denote the thickness of ML TMDs. In the above equation, the
thickness of the TMD is assumed to be less than the spin diffusion length 60.
Considering the thickness of Mo and W-based ML TMDs to be 0.7 and 0.8 nm,
respectively 61, 62 we estimated $\theta_{\textrm{PSH}}$ for all the ML TMDs
as shown in Table 1. The value of $\theta_{\textrm{PSH}}$ is found to be
greater than 1 and at least one order higher than any of the reported values
for heavy metals 63, 64, 65, 6, 66. The enormous magnitude of pseudo spin Hall
angle ($>$ 1) is unphysical for a 3D system, supporting our assertion that the
spin-to-charge conversion process is driven by IREE rather than ISHE.

##  III CONCLUSIONS

In summary, we demonstrate spin-to-charge conversion in large area monolayer
TMDs, namely MoS2, MoSe2, WS2 and WSe2 with the efficiency that exceeds that
of the traditional heavy metals such as Pt by about at least one order. We
also demonstrate that the efficiency of spin-to-charge conversion is directly
proportional to the SOC strength of the ML TMDs, indicating that the
phenomenon is driven by the IREE effect arising from the two-dimensional
interface of ML TMD and Py. Our findings suggest that the IREE has a negative
sign of spin-to-charge conversion for the ML TMD/Py interface. The large spin-
to-charge conversion of these interfaces is extremely promising for emerging
spintronics applications such as for non-volatile memory and logic devices.

Table 1: Values of effective damping parameter subtracted from reference
sample
---
($\Delta\alpha_{\rm eff}$), spin mixing conductance
($\mathrm{g}_{\uparrow\downarrow}$), charge current density
($j_{\rm\textrm{C}}$), spin current
density ($j_{\rm s}$), Rashba efficiency parameter
($\lambda_{\textrm{IREE}}$), pseudo spin Hall angle ($\theta_{\textrm{PSH}}$)
TMD | $\Delta\alpha_{\rm eff}$ | $\mathrm{g}_{\uparrow\downarrow}$ | $j_{\rm\textrm{C}}$ | $j_{\rm s}$ | $\lambda_{\textrm{IREE}}$ | $\theta_{\textrm{PSH}}$
| $(\times 10^{-3})$ | $(\times 10^{19}\textrm{m}^{-2})$ | $(\mu\textrm{A/m})$ | $(\times 10^{4}\textrm{A}/\textrm{m}^{2})$ | $(\times 10^{-10}\textrm{m})$ |
MoS2 | 1.4 $\pm$ 0.1 | 0.72 $\pm$ 0.04 |  $-267\pm$ 3 | 50 $\pm$ 3 | -5.4 $\pm$ 0.4 | -1.5 $\pm$ 0.1
MoSe2 | 1.5 $\pm$ 0.1 | 0.78 $\pm$ 0.05 |  $-290\pm$ 5 | 52 $\pm$ 4 | -5.6 $\pm$ 0.4 | -1.6 $\pm$ 0.1
WS2 | 2.4 $\pm$ 0.1 | 1.26 $\pm$ 0.04 |  $-571\pm$ 2 | 86 $\pm$ 3 | -6.7 $\pm$ 0.3 | -1.7 $\pm$ 0.1
WSe2 | 3.6 $\pm$ 0.2 | 1.84 $\pm$ 0.11 |  $-635\pm$ 2 | 83 $\pm$ 6 | -7.6 $\pm$ 0.6 | -1.9 $\pm$ 0.2

##  IV METHODS

### Material growth

We prepared Al2O3/ML TMD/Py(10 nm)/Ta(3 nm) for four different ML TMDs, namely
MoS2, MoSe2, WS2 and WSe2 along with a reference sample Al2O3/Py(10 nm)/Ta(3
nm) simultaneously. Py thin film of 10 nm thickness was grown using AJA ATC
Orion 8 ultra-high vacuum magnetron sputtering system on commercially
purchased chemical vapor deposited monolayer TMD samples (from 2D
semiconductors Inc.) on the $c$-cut sapphire substrates (with the size of
$5\times 2$ mm2). The base pressure of the sputtering chamber was better than
8$\times 10^{-8}$ Torr and the working pressure was 2$\times 10^{-3}$ Torr. A
Tantalum (Ta) layer of 3 nm thickness was deposited as a capping layer to
prevent oxidation of Py thin film.

### Raman measurements

Raman spectroscopy was used to determine the thickness and quality of TMD
samples before and after Py layer deposition. The measurements were performed
using Renishaw inVia confocal microscope with 532 nm laser wavelength and 2400
lines per mm grating at 5 mW power.

### Magnetostatic characterization

The saturation magnetization of the reference sample Py(10 nm)/Ta(3 nm) and ML
TMD/Py(10 nm)/Ta(3 nm) samples were determined using the VSM module of
physical property measurement system (PPMS) manufactured by Quantum Design
(Model-PPMS EverCool-II ). All the VSM measurements were performed at room
temperature.

### Spin pumping and IREE characterization

Broadband FMR spectroscopy technique was used to characterize the
magnetization dynamics. The sample was placed upside down on the co-planar
waveguide (CPW), through which RF current is passed, generating an RF field to
excite the resonance in the Py layer. Field modulation technique with lock-in-
based detection is employed to enhance the sensitivity of FMR measurements.
For this purpose, the external DC field was modulated with a low frequency
(213 Hz) AC field generated in the Helmholtz coils using the lock-in
amplifier. The RF excitation frequency was varied from 2 to 9 GHz. The
spectrum obtained by field sweep is then fitted using the derivative of the
Lorentzian line-shape function to extract ($H_{\rm\textrm{r}}$) and ($\Delta
H$). $h_{\rm RF}$ is calculated to be 0.35 G using Ampère’s law, $h_{\rm
RF}=\frac{\mu_{\rm 0}}{2\pi w}\sqrt[]{\frac{P_{\rm
RF}}{Z}}\log(1+\frac{w}{D})$, where $Z$ is the impedance of CPW (50 $\Omega$),
$P_{\rm RF}$ is the applied RF power, $w$ is the width of the signal line
(0.25 mm), and $D$ is the separation between the signal line to the sample
(0.5 mm).

For the IREE measurements, electrical contacts were made using copper pads
beneath the inverted sample. We employed a field modulation technique, which
involves modulating the DC field with a small AC field created by a pair of
Helmholtz coils. 50 The coils are powered by a lock-in amplifier which also
measures the voltage generated by the IREE. For IREE measurements, RF
microwave power was set at 0.5 W and the RF frequency was set at 3 GHz.

##  V acknowledgement

The partial support from the Ministry of Human Resource Development under the
IMPRINT program (Grant no: 7519 and 7058), the Department of Electronics and
Information Technology (DeitY), Science & Engineering research board (SERB
File no. CRG/2018/001012), Joint Advanced Technology Centre at IIT Delhi,
Grand Challenge Project, IIT Delhi, and Department of Science and Technology
under the Nanomission program (grant no: $SR/NM/NT-1041/2016(G)$) are
gratefully acknowledged. H.B. gratefully acknowledges the financial support
from the Council of Scientific and Industrial Research (CSIR), Government of
India.

##  VI Supplementary information

###  VI.1 Raman measurements

Figure 5:  Raman measurements. (A) Raman spectra at 8 different points for (A)
MoS2 and (D) WS2. The peak position difference between A1g and E${}_{\rm
2g}^{1}$ peaks for (B) MoS2 and (E) WS2. Trend of intensity for (C) MoS2 and
(F) WS2 to confirm uniformity of the TMDs.

To validate that the commercial CVD grown-monolayer (ML) TMDs were completely
covered, we performed Raman measurements at several locations on the sample
using the same measurement conditions (Laser wavelength of 532 nm, 2400 lines
per mm grating at 5 mW power). The laser spot size was approximately 0.8
$\mu$m. The location was chosen at random to encompass the whole $5\times 2$
mm2 sample region. The Raman data for MoS2 are shown in Fig. 5 (A), while the
difference in peak position between the E${}_{\rm 2g}^{1}$ and A1g peaks and
the intensity of the peaks is shown in Fig. 5 (B) and (C) respectively, for
several locations on the sample. The variation in peak location and the
intensity is essentially identical for all locations, confirming the presence
of large-area ML MoS2 over the entire substrate. A similar result is obtained
for WS2 as shown in Fig. 5 (D), (E) and (F). The absence of the B${}_{\rm
2g}^{1}$ mode for MoSe2 and WSe2 is employed as a signature to determine the
ML thickness. The position of B${}_{\rm 2g}^{1}$ mode for MoSe2 and WSe2 are
353 cm-1 and 309 cm-1, respectively. 47 As demonstrated in Fig. 6 (A) and Fig.
S2 (C), these peaks are absent from all the measured locations in both MoSe2
and WSe2. The trend of the peak intensity for MoSe2 and WSe2 is shown in Fig.
6 (B) and Fig. 6 (D) respectively, which is nearly constant. As a result, we
conclude that all of our TMD samples cover the entire area of the sample. We
observed a weak defect peak near the main A1g peak in MoSe2 and WSe2 samples.
This peak appears due to Se vacancies, and it can be utilized to estimate the
concentration of Se vacancies in the sample. 48 Based on the A1g/(defect peak)
ratio [Fig. 6 (A) and (C)], we estimate the selenium (Se) vacancies in both
the MoSe2 and WSe2 to be $<2.5$% 48.

Figure 6:  Raman measurements. (A) Raman spectra at 8 different points for (A)
MoSe2 and (C) WSe2. Trend of intensity for (B) MoSe2 and (D) WSe2 to confirm
uniformity of the TMDs.

###  VI.2 Surface Morphology by Atomic Force Microscopy

Our 2D TMD ML have atomic roughness ($<0.15$ nm). Hence we expect good quality
of thin films grown on top the 2D TMD ML samples. We performed atomic force
microscopy (AFM) measurements to study the surface morphology and to determine
the surface roughness. The measurements were performed in tapping mode using
Bruker AFM system. Figure 7 shows the AFM images for the (A) reference, (B)
MoS2, (C) MoSe2, (D) WS2, (E) WSe2 samples. Surface morphology of all the
samples is similar as they were prepared simultaneously inside the sputtering
chamber. The root mean square (rms) surface roughness for reference, MoS2,
MoSe2, WS2, and WSe2 samples are 0.32, 0.30, 0.34, 0.29, and 0.30 nm
respectively. This indicates high quality of the films.

Figure 7:  Surface morphology. Atomic force microscopy (AFM) images of (A)
reference, (B) MoS2, (C) MoSe2, (D) WS2, (E) WSe2 samples respectively. All
the samples have similar morphology and roughness as they are prepared
simultaneously inside sputtering chamber. Figure 8:  Effect of Cu spacer.
Measured $I_{\rm C}$ for ML MoS2/Cu(5 nm)/Py(10 nm)/Ta(3 nm) (Red symbols) and
Cu(5 nm)/Py(10 nm)/Ta(3 nm) (black symbols).

###  VI.3 Effect of copper spacer

Figure 9:  Effect of capping layer on the magnitude of $I_{\rm C}$. Plot of
$I_{\rm C}$ for Py (10 nm) samples having different capping layers, namely,
Pt, Ta, and SiO2.

To confirm that the decrease of $I_{\rm C}$ in TMD/Py/Ta samples was driven by
IREE from TMD/Py interface, we grew samples with a Cu spacer layer: TMD/Cu(5
nm)/Py(10 nm)/Ta(3 nm). The Cu layer is used to break the interface between
the TMDs and Py layer. Figure 8 shows the IREE signal for the sample with and
without Cu insertion layer for MoS2. The reference sample without the TMD
layer was grown in the same chamber together with the TMD/Cu/Py sample so that
measurement artifacts due to the variation in growth conditions can be
removed. The reference sample (black circles in Fig. 8) and the TMD/Cu/Py have
the same magnitude of $I_{\rm C}$, as illustrated in the figure. The Cu layer
has a spin diffusion length, which is larger than the thickness of Cu (5 nm).
54, 67 Thus, the ISHE signals due to the Py layer itself and the Ta capping
layer (which are bulk effects) are unaffected by the presence of the Cu layer.
The IREE signal from the TMD/Py interface, on the other hand, will be
affected. We detect no decrease of $I_{\rm C}$ in the figure, in contrast to
the scenario when the TMD layer is in direct contact with the Py layer [Fig. 3
of the main text]. As a result, the decrease of $I_{\rm C}$ seen in the main
text is interfacial in nature and can be attributed to IREE.

###  VI.4 Determining the sign of IREE signal

In the main text, we observe a decrease of $I_{\rm C}$ when the TMD layer
directly contacts the Py layer. We attribute this behavior to a negative spin-
to-charge conversion. To further corroborate the sign of spin-to-charge
conversion, we prepared a series of sample stack of Al2O3/Py (10 nm) with Pt
and Ta capping layers, which are known to exhibit the opposite sign of spin-
to-charge conversion. Figure 9 shows measured $I_{\rm C}$ for the capping
layer of Ta, Pt, and SiO2. We observe a finite signal even in the case of
Py/SiO2, the origin of which is discussed in the following section. We observe
a decrease of $I_{\rm C}$ with Pt capping and an increase in $I_{\rm C}$ with
Ta capping-consistent with the opposite sign of spin-to-charge conversion for
Pt and Ta. The sign of spin-to-charge conversion also depends on the stacking
order of the FM and HM layers. In Fig. 3 of the main text, the TMDs layers are
beneath the Py layer, whereas in Fig. 9, the Pt or Ta layer is above the Py
layer. Hence, the decrease of $I_{\rm C}$ for TMD/Py samples relative to the
corresponding reference sample implies that the sign of spin to charge
conversion at the TMD/Py interface is similar to that of Ta, which has
negative spin-to-charge conversion relative to Pt. 50, 6, 68 Thus we conclude
that the drop in $I_{\rm C}$ with the TMD layer is owing to a negative sign of
spin-to-charge conversion at the interface of TMD and Py layer. This is
further supported by scaling of $I_{\rm C}^{TMD/Py}$ ($I_{\rm C}$ from the
interface of TMD and Py) with the SOC of the TMD layer.

To further confirm the negative sign of $I_{\rm C}^{TMD/Py}$, we also replace
Py with Co60Fe20B20 (CFB) for which the self-induced ISHE is known to be
negligible. 53 We simultaneously prepared two samples: CFB (10 nm)/Al (3 nm)
and MoS2 (ML)/CFB (10 nm)/Al (3 nm). As shown in Fig. 10, we did not observe
any signal from the CFB (10 nm)/Al (3 nm) sample showing the absence of self-
induced ISHE signal in CFB sample. In contrast, the MoS2 (ML)/CFB (10 nm)/Al
(3 nm) sample produce a clear negative signal (for same measurement conditions
as in Fig. 3) establishing a negative spin to charge conversion driven by
spin-orbit coupling in MoS2 rather than the FM layer. Please note that in Fig.
3 all measurements are shown for positive magnetic field. Furthermore, in Fig.
3 the heavy metal Pt and Ta are capping layers. Hence the stacking order need
to be taken in to the account while comparing sign of the signal between Fig.
3 and Fig. 10.

Figure 10:  Measured $I_{\rm C}$ for CFB (10 nm)/Al (3 nm) (black) and MoS2
(ML)/CFB (10 nm)/Al (3 nm) (red). The measurement conditions were kept
identical with Fig. 3. Figure 11:  Self-induced ISHE in Py/SiO2. Measured
$I_{\rm C}$ in Py/SiO2 for two different thicknesses of the Py layer. Figure
12:  Comparative plot of $\lambda_{\textrm{IREE}}$ for different Rashba
interfaces.

###  VI.5 Origin of $I_{\rm C}$ in Py/SiO2

We observe a finite $I_{\rm C}$ in Py/SiO2, which contains no HM layer.
Additionally, the line shape is almost symmetrical with SiO2 capping, which
indicates that the signal is not due to galvanic effects. 51 We believe that
the signal arises from self-induced inverse spin Hall effect (ISHE), which has
been reported recently for Py layer via the spin-pumping-induced spin current
ISHE measurement. 69, 53 Because the ISHE is a bulk effect, the self-induced
ISHE signal should increase with the increase in thickness of the Py layer. In
Fig. 11, we show measured $I_{\rm C}$ in Py/SiO2 for two examples with
different thicknesses of the Py layer. We see a clear increase of signal with
the thickness of Py, which is a signature of self-induced ISHE. 53 Relatively
larger self-induced ISHE signal observed in our work is due to larger
thickness of Py used in our work, which was chosen to obtain better signal
strength in ISHE measurements.

###  VI.6 Comparison of $\lambda_{\textrm{IREE}}$ with other Rashba interfaces

In Fig. S8, we compare the magnitude of $\lambda_{\textrm{IREE}}$ in our study
with selected Rashba interfaces reported in literature. We found our
$\lambda_{\textrm{IREE}}$ to be significantly larger compared to other Rashba
interfaces such as Cu/Bi 26, Ag/Sb 25, NM/Bi2O3 (where NM denote non-magnetic
metals Cu, Ag, Au, Al) 59, Bi/Ag 17, and YIG/MoS2 33 with exception of
$\alpha$-Sn/Ag 19, for which a larger value is reported.

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