# Out-of-plane spin-to-charge conversion at low temperatures in graphene/MoTe2
heterostructures

Nerea Ontoso  CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country,
Spain  C.K. Safeer  CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque
Country, Spain  Present address: Department of Physics, Clarendon Laboratory,
University of Oxford, Oxford, United Kingdom  Josep Ingla-Aynés  CIC nanoGUNE
BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain  Present address:
Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft,
The Netherlands  Franz Herling  CIC nanoGUNE BRTA, 20018 Donostia-San
Sebastian, Basque Country, Spain  Present address: Catalan Institute of
Nanoscience and Nanotechnology (ICN2), 08193 Barcelona, Spain  Luis E. Hueso
CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain
IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Basque Country, Spain
M. Reyes Calvo∗ Departamento de Física Aplicada, Universidad de Alicante,
03690 Alicante, Spain  Instituto Universitario de Materiales de Alicante
(IUMA), Universidad de Alicante, 03690 Alicante, Spain  Fèlix Casanova∗
Authors to whom correspondence should be addressed<EMAIL_ADDRESS><EMAIL_ADDRESS>CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque
Country, Spain  IKERBASQUE, Basque Foundation for Science, 48009 Bilbao,
Basque Country, Spain

###### Abstract

Multi-directional spin-to-charge conversion - in which spin polarizations with
different orientations can be converted into a charge current in the same
direction - has been demonstrated in low-symmetry materials and interfaces.
This is possible because, in these systems, spin to charge conversion can
occur in unconventional configurations in which charge current, spin current
and polarization do not need to be mutually orthogonal. Here, we explore, in
the low temperature regime, the spin-to-charge conversion in heterostructures
of graphene with the low-symmetry 1T’ phase of MoTe2. First, we observe the
emergence of charge conversion for out-of-plane spins at temperatures below
100 K. This unconventional component is allowed by the symmetries of both
MoTe2 and graphene and likely arises from spin Hall effect in the spin-orbit
proximitized graphene. Moreover, we examine the low-temperature evolution of
non-local voltage signals arising from the charge conversion of the two in-
plane spin polarizations, which have been previously observed at higher
temperature. As a result, we report omni-directional spin-to-charge conversion
- for all spin polarization orientations - in graphene/MoTe2 heterostructures
at low temperatures.

††preprint: AIP/123-QED

Spin-based logic devices offer a promising alternative to the limitations
imposed by Joule heating in traditional electronics Žutić, Fabian, and Sarma
(2004); Manipatruni  _et al._ (2019). These spintronic devices rely on the
efficient generation, precise control and detection of spin currents, for
which materials hosting spin-to-charge conversion (SCC) phenomena provide a
platform. SCC occurs in a variety of systems with high spin-orbit
interactions; mediated by the spin Hall effect (SHE) in bulk materials Sinova
_et al._ (2015); Valenzuela and Tinkham (2006); Kimura  _et al._ (2007) or the
Rashba-Edelstein (REE) effects D’Yakonov and Perel’ (1971a, b); Edelstein
(1990)in Rashba interfaces Sánchez  _et al._ (2013) or at the surface states
of topological insulators Mellnik  _et al._ (2014); Rojas-Sánchez  _et al._
(2016).

Spin-orbit-mediated SCC effects were initially investigated in zinc-blende
semiconductors and pure metals, such as GaAs Kato  _et al._ (2004), Ta Liu
_et al._ (2012) or Pt Sagasta  _et al._ (2016), all systems with a high degree
of crystal symmetry. As a consequence, SCC phenomena have been traditionally
expected to appear in configurations where charge current, spin current and
spin polarization directions are mutually orthogonal. Nonetheless, these
restrictions only hold for materials with high crystal symmetry and are lifted
for crystalline phases where certain mirror symmetries are broken Culcer and
Winkler (2007); Seemann  _et al._ (2015); Zhang  _et al._ (2021); Roy,
Guimarães, and Sławińska (2022).

Recent advancements in the preparation of atomically thin layers of van der
Waals materials have raised the interest in their spintronic properties. In
particular, transition metal dichalcogenides (TMDs) exhibit strong spin-orbit
interactions and are good candidates for hosting SCC phenomena. Besides
mutually orthogonal conventional SCC, non-orthogonal unconventional SCC
configurations have been recently reported for TMDs with strong spin-orbit
coupling and low-symmetry crystal phases Stiehl  _et al._ (2019); Safeer  _et
al._ (2019a); Ontoso  _et al._ (2023); MacNeill  _et al._ (2017); Zhao  _et
al._ (2020a); Kao  _et al._ (2022). Furthermore, TMDs have been integrated in
van der Waals heterostructures with graphene, which acts as spin channel due
to its long spin diffusion length Tombros  _et al._ (2007); Ingla-Aynés  _et
al._ (2015). The combination of SHE and REE effects, enabled by the strong
spin-orbit proximity from TMDs to graphene, has led to highly efficient
conventional SCC in these heterostructures Safeer  _et al._ (2019b); Herling
_et al._ (2020); Ghiasi  _et al._ (2019); Benitez  _et al._ (2020); Li  _et
al._ (2020); Hoque  _et al._ (2020, 2021); Zhao  _et al._ (2020b); Garcia  _et
al._ (2018); Offidani  _et al._ (2017). Additionally, unconventional SCC has
been observed in graphene/TMD heterostructures Safeer  _et al._ (2019a);
Camosi  _et al._ (2022); Ingla-Aynés  _et al._ (2022); Zhao  _et al._ (2020a).
Symmetry breaking at the van der Waals interface has been proposed to
facilitate unusual non-orthogonal SCC in graphene/TMD heterostructures - even
for highly symmetric TMD phases Li and Koshino (2019); David  _et al._ (2019);
Naimer  _et al._ (2021); Péterfalvi  _et al._ (2022); Veneri  _et al._ (2022);
Lee  _et al._ (2022). As a result, multi- and omni-directional SCC has been
already reported for heterostructures of graphene with MoTe2 Safeer  _et al._
(2019a), WTe2 Camosi  _et al._ (2022) and NbSe2 Ingla-Aynés  _et al._ (2022),
enhancing the efficiency of spin generation and detection and increasing the
versatility of graphene/TMD spintronic devices.

Both conventional and unconventional SCC have been observed in the low-
crystal-symmetry 1T’ phase of MoTe2 and for graphene/MoTe2 Stiehl  _et al._
(2019); Song  _et al._ (2020); Hoque  _et al._ (2021); Safeer  _et al._
(2019a); Ontoso  _et al._ (2023). In Ref. Safeer  _et al._ (2019a), we
reported SCC in a graphene/MoTe2 heterostructure for the two in-plane spin
orientations - one orthogonal and another parallel to the charge current -
from 75 K up to room temperature. New SCC processes may emerge at lower
temperatures, since conversion in proximitized graphene is enhanced in this
regime Ghiasi  _et al._ (2019); Safeer  _et al._ (2019b). In this work, we
explore SCC in graphene/MoTe2 lateral spin valve (LSV) devices below 100 K.
First, we track the low temperature dependence of both conventional and
unconventional SCC for in-plane spin polarization. We find a change of sign of
the signal associated to the conventional SCC - allowed by symmetry arguments
- that we relate to a change of the relative intensity of two competing
effects, namely SHE in MoTe2 and REE in graphene. More interestingly, we
detect the SCC of out-of-plane spin polarization, which increases with
lowering temperature and likely arises from SHE in the proximitized graphene.
Finally, we summarize all the SCC components observed for graphene/MoTe2 in
our experimental geometry and discuss on their possible origin. Regardless of
the conversion mechanisms, we achieve omnidirectional - for all three spin
orientations - SCC at low temperature.

Figure 1:  a) Optical microscope image (scale bar represents 1 $\mu$m) and b)
sketch of a graphene/MoTe2 lateral spin valve device. c) Crystal structure of
1T’-MoTe2. Mirror symmetry plane and Mo-chain directions are marked. d) Two-
terminal resistance of the MoTe2 flake as a function of temperature measured
using leads $3$ and $4$ in a.

LSV devices (Fig. 1a,b) were prepared as described in Refs. Safeer  _et al._
(2019a); Ontoso  _et al._ (2023). A flake of MoTe2, with thickness 11 nm, is
stacked perpendicularly on top of a graphene channel where magnetic TiOx/Co
electrodes (labeled as A and B in Fig. 1a) act as spin injectors (FM in Fig.
1b). Needle-like MoTe2 flakes are typically elongated along the Mo-chain
direction (Fig. 1b,c) Safeer  _et al._ (2019a). Non-magnetic electrodes
(Ti/Au) are also deposited both at the ends of the graphene channel and the
MoTe2 flake (labeled as 1-4 in Fig. 1a). Two-terminal resistance measurements
as a function of temperature (Fig. 1d) confirm the semimetallic behavior of
the MoTe2 flake, as expected for its thickness Song  _et al._ (2018). The lack
of signatures of structural phase transitions suggests that the MoTe2 flakes
remain in the 1T’ phase down to 10 K Stiehl  _et al._ (2019); Zhang  _et al._
(2016).

To explore SCC phenomena in graphene/MoTe2 heterostructures, non-local
resistance measurements were performed as sketched in Fig. 1b. A current
I${}_{\textrm{C}}=$ 10 $\mu$A is applied between the ferromagnetic electrode
(FM) and graphene (Fig. 1a,b). The spin accumulation generated at the FM-
graphene interface diffuses along the graphene channel, which lies along the
$x$-direction and can be absorbed at the graphene/MoTe2 region. The spin
current js diffuses along the z-direction from graphene to MoTe2 and along the
x-direction to the proximitized graphene. There, if SCC occurs, a non-local
voltage V${}_{\textrm{NL}}$ is recorded along the MoTe2 flake (Fig. 1a,b). It
is important to note that, in our experimental geometry (Fig. 1b), only the
charge current along the $y$-axis direction is detected.
$R_{\textrm{NL}}=V_{\textrm{NL}}/I_{\textrm{C}}$ is, thus, proportional to the
SCC resulting into charge current jc along the $y$-direction. The orientation
of the spin polarization s reaching the MoTe2/graphene region can be
controlled along the x\- and y\- directions by switching or pulling the
magnetization orientation of the FM injector by an external magnetic field.
Additionally, if the field is perpendicular to the spin polarization, spins
will precess while diffusing along the graphene channel. Thus, by changing the
value of the applied magnetic field along $x$-, $y$\- or $z$-directions we can
study SCC for the three different spin polarization orientations
($s^{x}$,$s^{y}$ and $s^{z}$) at the graphene/MoTe2 heterostructure.

If the magnetic field is applied along the FM in-plane easy axis
($y$-direction), a spin current with $s^{y}$ will diffuse on the graphene
channel without precessing. As $B_{y}$ increases, the magnetization of the FM
is reversed and a square hystheresis loop appears in Fig. 2a, as the sign of
R${}_{\textrm{NL}}$ switches at the coercive field of the FM. This
unconventional signal -corresponding to the SCC of $s^{y}$ spins - has been
already reported at room temperature in Ref. Safeer  _et al._ (2019a).
Conversion of spin polarization into a parallel charge current is forbidden by
crystal symmetries both in MoTe2 (see Supplementary Material) and in graphene.
In Ref.Safeer  _et al._ (2019a), this effect was attributed to symmetry
breaking due to strain induced either in the fabrication process or at the van
der Waals interface. This signal remains visible down to 10 K, but decreases
in amplitude with temperature (Fig. 2a).

Figure 2:  Non-local resistance $R_{\textrm{NL}}$ measured with the
configuration shown in Fig. 1b, while sweeping the magnetic field in (a) the
in-plane FM easy axis $y$-direction, and (b) in the in-plane FM hard axis
$x$-direction. In (b), curves are presented for initial magnetization of the
Co electrode saturated along positive (black) and negative (red)
$y$-direction. Measurements were performed at the temperature indicated in
each panel. Figure 3:  (a-c) Sketches of the R${}_{\textrm{NL}}$ signal shapes
associated to SCC from $s^{y}$ (a), $s^{z}$ (b) and $s^{x}$ (c). (d-g)
Analysis of the R${}_{\textrm{NL}}$ versus $B_{x}$ curves in Fig. 2b at
different temperatures: (d) Average non-local resistance, defined as
R${}_{NL}^{average}=$ (R${}_{NL}^{\uparrow}+$ R${}_{NL}^{\downarrow}$)/2. (e)
Spin-to-charge conversion resistance defined as R${}_{SCC}=$
(R${}_{NL}^{\uparrow}-$ R${}_{NL}^{\downarrow}$)/2. (f) Symmetric component of
the RSCC signal obtained from data in panel e. (g) Anti-symmetric component of
the RSCC signal obtained from data in panel e. All signals are measured at the
indicated temperatures.

Further SCC components can be detected by sweeping the magnetic field in the
in-plane hard axis of the FM injector, that is, along the $x$-direction
($B_{x}$). In Fig. 2b, R${}_{\textrm{NL}}$ is measured as a function of Bx for
two different initial states of the FM magnetization. Prior to sweeping Bx,
the FM magnetization is first set along the $+$y-direction
[R${}_{\textrm{NL}}^{\uparrow}$, black curve in Fig. 2b] and then along the
$-$y-direction [R${}_{\textrm{NL}}^{\downarrow}$, red curve in Fig. 2b]. This
process is repeated for temperatures from 100 to 10 K. In Ref. Safeer  _et
al._ (2019a), such R${}_{\textrm{NL}}$ measurements were performed from 300 to
100 K (the data at 100 K is the same than in this publication) and the curves
were interpreted as the sum of two contributions, one symmetric and another
antisymmetric, corresponding, respectively, to the SCC of $s^{x}$ and $s^{y}$.
This analysis was sufficient to provide an interpretation for the high
temperature data. However, Fig. 2b shows how, at very low temperature, the
R${}_{\textrm{NL}}$ signal not only changes in size, but it also undergoes
significant changes in shape. This suggests the emergence of extra SCC
contributions to R${}_{\textrm{NL}}$ that require of a more detailed analysis.
To separate the SCC contributions from each spin orientation, it is crucial to
consider how they depend on the initial state of the FM magnetization and
their parity with respect to the applied magnetic field. Initially, at zero
magnetic field, only spins polarized along the FM easy axis (sy) will reach
the graphene/MoTe2 region and contribute to R${}_{\textrm{NL}}$ , with a sign
that depends on the initial state of the FM magnetization, either along the
$+$y or the $-$y direction (Fig. 3a). As Bx increases, the amplitude of the
spin sy component decays due to spin precession in the y$-$z-plane (Fig. 3b)
and magnetization pulling of the injector along the x-direction (Fig. 3c). As
a consequence, the contribution to the R${}_{\textrm{NL}}$ signal coming from
SCC of sy is symmetric with respect to Bx and maximum at zero field (Fig. 3a).
Also, due to precession in the y$-$z-plane field, SCC of sz at graphene/MoTe2
can also be detected in the $B_{x}$ sweeps, with its contribution to
R${}_{\textrm{NL}}$ being described by an antisymmetric Hanle curve (Fig. 3b).
This signal reverses for the two opposite initial states of the injector
magnetization (Fig. 3b). Finally, for large values of Bx, the FM magnetization
is aligned along the hard $x$-axis and sx spins are injected, which do not
precess when diffusing along the graphene channel (Fig. 3c).
R${}_{\textrm{NL}}$ due to SCC of sx is linear at low fields, reaches
saturation values at large magnetic field with opposite signs at $+$Bx and
$-$Bx (S-shaped curve), and does not depend on the initial state of the
injector magnetization (Fig. 3c).

Because SCC from sx is the only contribution to R${}_{\textrm{NL}}$ that does
not depend on the initial state of the FM magnetization, it can be extracted
by taking the average R${}_{NL}^{average}=$ (R${}_{NL}^{\uparrow}+$
R${}_{NL}^{\downarrow}$)/2 (Fig. 3d). The saturation values of
R${}_{\textrm{NL}}^{average}$ as a function of $B_{x}$ change sign below 50 K.
On the other hand, both SCC contributions from $s^{y}$ and $s^{z}$ are
expected to change sign for opposite initial states of the FM magnetization.
Therefore, these contributions are included in R${}_{\textrm{SCC}}=$
(R${}_{\textrm{NL}}^{\uparrow}-$ R${}_{\textrm{NL}}^{\downarrow}$)/2 (Fig.
3e). While the sy contribution is symmetric with respect to Bx, the
contribution of sz is antisymmetric. This difference allows us to establish an
univocal relation between the SCC signal arising from sy,
R${}_{\textrm{SCC}}^{symm}$ (Fig. 3f) and the SCC signal from sz,
R${}_{\textrm{SCC}}^{anti}$ (Fig. 3g). R${}_{\textrm{SCC}}^{\textrm{symm}}$
shows a maximum at zero field and dissappears at the saturation value of Bx
field [Fig. 3f]. This SCC signal is the same one detected in the $B_{y}$
sweeps in Fig. 2a and is associated to SCC of sy spins in Ref. Safeer  _et
al._ (2019a). More interestingly, at 10 K,
R${}_{\textrm{SCC}}^{\textrm{anti}}$ displays a sharp antisymmetric Hanle
curve. This signal progressively disappears at higher temperatures, being
still visible at 75 K [Fig. 3g] and becoming nearly negligible at 100 K and
above (see Supplementary Material and Ref. Safeer  _et al._ (2019a)). These
signals evidence the SCC of sz spins, which was not observed at higher
temperature Safeer  _et al._ (2019a).

It is important to note that the signals in Fig. 3 are measured as a function
of Bx and, therefore, only R${}_{\textrm{SCC}}^{\textrm{anti}}$ (the sz
contribution) arises purely from spin precession, confirming its spin origin.
In contrast, R${}_{SCC}^{symm}$ and R${}_{NL}^{average}$ are determined not
only by precession, but partially or entirely by the pulling of the FM
magnetization. Spin precession measurements with applyed out-of-plane field
(Bz) were successfully performed at higher temperatures in Ref. Safeer  _et
al._ (2019a), confirming the spin origin of the SCC signals from sx and sy,
and discarding spurious effects Safeer  _et al._ (2022). However, at low
temperatures, large backgrounds coming from the magnetoresistance of MoTe2 and
the Hall effect in graphene prevented us from identifying clear Hanle signals.
Nevertheless, since the low temperature evolution of the amplitudes of the SCC
signals for sx and sy matches the trend at higher temperatures extracted from
Ref.Safeer  _et al._ (2019a)) (see Supplementary Material), the spin origin of
the R${}_{\textrm{NL}}^{average}$ and R${}_{\textrm{SCC}}^{symm}$ signals can
be inferred.

Figure 4:  a) Low-temperature dependence of the amplitude of
R${}_{\textrm{NL}}^{average}$ (SCC of sx), R${}_{SCC}^{anti}$ (SCC of sz), and
R${}_{\textrm{SCC}}^{symm}$ (from SCC of sy) extracted from Fig 3. Error bars
are calculated from the standard deviation of the signal noise.(b-d) Summary
of SCC processes in a graphene/MoTe2 van der Waals heterostructure that can be
detected in our experimental geometry (charge current along the
$y$-direction). SCC can take place either at the bulk of the MoTe2 or at the
proximitized graphene region, which is represented by a pink halo. (b) SCC of
$s^{x}$ can occur via the conventional SHE in MoTe2 if a spin current is
injected in the $z$-direction ($\sigma^{x}_{zy}$)or owing to a conventional
REE in the proximitized graphene. (c) SCC of $s^{z}$ can be attributed to an
unconventional, non-orthogonal SHE in MoTe2 ($\sigma^{z}_{zy}$) allowed by
crystal symmetry but can be also mediated by a conventional SHE in
proximitized graphene(d) SCC of $s^{y}$ (parallel to charge current), is
allowed only if the mirror symmetry of 1T’-MoTe2 or the ones of graphene/MoTe2
interface are broken (represented by a zigzag line), via unconventional,
symmetry forbidden, SHE in MoTe2 ($\sigma^{y}_{zy}$) or via an unconventional
EE in proximitized graphene.

Shunting due to the presence of the MoTe2 flake prevents us from determining
the transport parameters for the proximitized graphene when fitting the data
to a Hanle spin precession model. Still, we can extract the amplitude for each
SCC component as a function of temperature in the range from 10 K to 100 K,
which are presented in Fig. 4a (see Supplementary Material for a comparison
with the data at higher temperature from Ref. Safeer  _et al._ (2019a)). The
amplitude of R${}_{\textrm{NL}}^{average}$ (coming from SCC of $s^{x}$)
changes sign at low temperature; being negative above 50 K and positive at 25
K and 10 K. At higher temperatures, in Ref. Safeer  _et al._ (2019a), this
contribution was considered to arise from conventional SHE in the bulk of
MoTe2, with $s^{x}$ spins been injected in the $z$-direction and resulting in
a charge current along $y$. In other words, R${}_{\textrm{NL}}^{average}$ may
correspond to a conventional configuration of the SHE where where the electric
field $E$, spin current $j_{s}$, and spin polarization $s^{\alpha}$ are
mutually orthogonal ($j_{i}^{\alpha}=\sigma_{ij}^{\alpha}E_{j}$, with
$\sigma_{zy}^{x}$, see Supplementary Material). However, the conventional REE
at the proximitized graphene may also convey SCC in the $y$-direction from sx
(Fig. 4b). Indeed, at low temperatures, the efficiency of proximity-induced
REE in graphene, which is expected to be large Ghiasi  _et al._ (2019), could
overcome the bulk SHE in MoTe2 and result in a change of sign of the overall
detected signal. Therefore, the sign change of the $s^{x}$ signal with
lowering T suggests a competition of effects, namely conventional SHE in MoTe2
and conventional REE in proximitized graphene, with opposite sign in their
efficiencies. Nevertheless, since we could not prove the spin origin of the
low temperature component, we cannot discard that it might arise from
artifacts similar to those observed in Ref. Safeer  _et al._ (2022).

Likewise, $\Delta$R${}_{\textrm{NL}}^{symm}$ (from SCC of $s^{y}$) decreases
with lowering the temperature (Fig.4a). This can be also seen in Fig. 2a where
the amplitude of the R${}_{\textrm{NL}}$ hysteresis loop with By decreases
with temperature and becomes barely visible at 10 K. Conversion of $s^{y}$
spins into a current in the parallel $y$-direction requires the reduction of
the system symmetries. This signal can be attributed to an unconventional SHE
in MoTe2 with $\sigma_{zy}^{y}$, only if all mirror symmetries of MoTe2 are
broken, or to an unconventional REE in the proximitized graphene (Fig. 4d).
The hypothesis of a REE origin has recently gained force since the shear
strain needed to break the MoTe2 crystal symmetries is expected to be sample-
dependent Couto  _et al._ (2014), and this signal has been already observed in
several different graphene/MoTe2 heterostructures Ontoso  _et al._ (2023);
Safeer  _et al._ (2019a). Moreover, the misalignment between the mirror planes
of graphene and MoTe2 creates a non-symmetric interface, which enables the
unconventional REE mechanism in proximitized graphene David  _et al._ (2019);
Li and Koshino (2019); Naimer  _et al._ (2021); Péterfalvi  _et al._ (2022);
Veneri  _et al._ (2022); Lee  _et al._ (2022).

Interestingly, $\Delta$R${}_{\textrm{NL}}^{anti}$, observed only at low
temperatures and coming from SCC of sz, presents its largest value at 10 K and
decreases with increasing temperature. Two possible origins can lie behind the
conversion of out-of-plane spins: unconventional SHE in MoTe2, with
j${}_{s}||$ s $\perp$ jc and $\sigma_{zy}^{z}$ (see Supplementary Material),
and conventional SHE in proximitized graphene (with j${}_{s}\perp$ s $\perp$
jc) (Fig. 4c). The non-orthogonal SHE in 1T’-MoTe2 with spin polarization
parallel to the spin current $\sigma_{zy}^{z}$, is allowed by the reduced
crystal symmetry and has been reported in Ref. Stiehl  _et al._ (2019) with an
efficiency $\sim$ 8 times smaller than the conventional SCC of $s^{x}$
($\sigma^{x}_{zy}$, $\Delta$R${}_{\textrm{NL}}^{average}$ in this work). In
contrast, SHE in proximitized graphene has been demonstrated to increase
significantly with decreasing $T$ Safeer  _et al._ (2019b); Benitez  _et al._
(2020). Therefore, even if a non-orthogonal SHE in MoTe2 cannot be fully
discarded, the rising of $\Delta$R${}_{\textrm{NL}}^{anti}$ at low
temperatures with amplitude larger than $\Delta$R${}_{\textrm{NL}}^{average}$
points to a conventional SHE in proximitized graphene as the most likely
origin for the SCC of sz spins. Both the temperature at which the SCC signal
from $s^{z}$ becomes visible and the temperature at which the SCC signal from
$s^{x}$ changes sign seem to slightly vary from sample to sample (see
Supplementary Material). These facts are compatible with their possible origin
from conversion occurring in the proximitized graphene.

In conclusion, we observe omnidirectional SCC in graphene/MoTe2 van der Waals
heterostructures at low temperatures. Firstly, SCC from out-of-plane sz spins
emerges at low temperatures, likely owing to proximity-induced SHE in
graphene. This unconventional component, which is absent at room temperature,
is allowed by the symmetries of the system. The SCC signal from sx, which
reverses sign with T, is compatible with a competition between mutually
orthogonal SHE in MoTe2 and REE in proximitized graphene, having opposite
signs and varying differently in efficiency with temperature. The
unconventional SCC from sy spins requires mirror symmetries to be broken
either at the MoTe2, if mediated by unconventional SHE at the bulk of this
material, or at the interface between graphene and MoTe2, if the origin is
unconventional REE in the proximitized graphene. Overall, the results
presented in this work, together with those in Refs. Safeer  _et al._ (2019a);
Ontoso  _et al._ (2023), make graphene/MoTe2 a fascinating heterostructure
where a plethora of SCC processes arises from different mechanisms. In
particular, the crystal structure of MoTe2 makes this a unique system to
further investigate the unconventional components enabled by both the low
crystal symmetry of the TMD and those appearing in the proximitized graphene
interface.

## Supplementary Material

Supplementary material contains Spin Hall conductivity tensor for 1T’-MoTe2, a
comparative of the amplitudes of SCC signals at higher temperature, Atomic
Force Microscopy characterization of devices and SCC data from a second
device.

###### Acknowledgements.

This work is supported by the Spanish MICINN under Projects No.
PID2021-122511OB-I00, No. MAT2017-88377-C2-2-R, and the Maria de Maeztu Units
of Excellence Programme (Grants No. MDM-2016-0618 and No. CEX2020-001038-M);
the “Valleytronics” Intel Science Technology Center; the Gipuzkoa Regional
Council under Projects No. 2021-CIEN-000037-01; and the European Union H2020
under the Marie Sklodowska-Curie Actions (Grants No. 0766025-QuESTech and No.
794982-2DSTOP). N.O.thanks the Spanish MICINN for support from a
Ph.D.fellowship (Grant No. BES-2017-07963). J.I.-A. acknowledges support from
the “Juan de la Cierva-Formación” program by the Spanish MICINN (Grant No.
FJC2018-038688-I) for a postdoctoral fellowship. R.C. acknowledges funding
from Generalitat Valenciana through Grants No. CIDEGENT/2018/004,
IDIFEDER/2020/005 and IDIFEDER/2021/016.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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