D, hysteresis loops exhibit larger coercive
fields (B⊥↑andB⊥↓) for bothn= +1 and +2 (Fig.
3, B and C). Transport measurements near
the CNP show that the width of the disorder
regime remains the same over a wide range
ofDfield (fig. S10B), which suggests that
changes in the coercive field are not caused by
the influence of disorder across two graphene
layers. Because the value of the coercive field
reflects the robustness of magnetic order, the
DdependenceshowninFig.3Cprovidesan-
other indication that the orbital ferromag-
netism is stabilized by proximity-induced SOC.
The effect of varyingDatn= +2 is dras-
tically different in the presence of an in-plane
magnetic fieldB||: ChangingDinduces a mag-
netization reversal, as evidenced by hysteresis
loops with opposite signs inRxy(Fig. 3D and
fig. S12A) ( 16 ). TheD-induced reversal is also
manifested in the sign change of coercive
fieldsB
∥
↑andB
∥
↓atD~–100 mV/nm (Fig. 3E).
A possible explanation for this uniqueDde-
pendence is obtained by examining the aver-
age in-plane spin moment for valleyK,hS∥Ki.
Calculations using the four-band model show
thathS∥Kichanges sign with varyingDatn=2
(Fig. 3F), indicating that an in-planeBfield
favors opposite valley polarizations at differ-
ent values ofD. By comparison, Fig. 3F shows
that no sign change inhS∥Kiis expected atn= 1,
whichisconsistentwithourexperimentalob-
servation (Fig. 3E). Because carrier density
remains the same when changingD, the
D-controlled magnetization reversal repre-
sents electric field control of the magnetic
order, which is made possible by proximity-
induced SOC.
Next, we consider the effect of SOC on iso-
spin polarization and superconductivity. In the
absence of SOC, the ground state atn=–1 was
shown to be isospin-unpolarized atB=0
( 38 , 39 ). The application of a large in-plane
magnetic field lifts the isospin degeneracy,
stabilizing an isospin ferromagnetic state (IF 3 )
nearn=–1, which is separated from the un-
polarized state (IU) by a resistance peak inRxx
and a step in the Hall density ( 38 , 39 ). Figure 4,
AandB,showsthatthisphaseboundarybe-
tween IF 3 and IU extends toB||= 0 in the pres-
ence of proximity-induced SOC. These studies
show that the influence of SOC on the iso-spin
degeneracy is comparable to that of a large
in-plane magnetic field (fig. S7) ( 16 ).
Our findings show that the superconducting
phase is unstable against proximity-induced
SOC in our sample. As shown in Fig. 4C, no
zero-resistance state is observed over the full
density range of the moiré band. In addition,
Rxx-Ttraces exhibit no clear downturn with
decreasingTat moiré fillingn=– 2 – d, where a
robust superconducting phase usually emerges
in magic-angle tBLG (Fig. 4D). Because strong
Ising and Rashba SOC breakC 2 Tsymmetry,
the absence of superconductivity, combined
with the emergence of AHE, is potentially
consistent with a recent theoretical proposal
thatC 2 Tsymmetry is essential for stabilizing
the superconducting phase in tBLG ( 40 ). Our
results are distinct from another experimental
report showing robust superconductivity sta-
bilized by SOC in tBLG away from the magic
angle ( 28 ). Apart from the difference in twist
angle range, these distinct observations could
result from other factors discussed below. The
Ddependence shown in Fig. 3 suggests that a
dual-gated geometry, which allows indepen-
dent control onDandntBLG, is key to inves-
tigating the influence of proximity-induced
SOC in WSe 2 /tBLG samples. When carrier
density is controlled with only the bottom-
gate electrode ( 28 ), doping tBLG with electrons
also gives rise to aDfield that pulls electrons
away from the WSe 2 crystal (fig. S1) ( 16 ). This
results in weaker SOC strength, which could
contribute to the observation of superconduc-
tivity in singly gated tBLG/WSe 2 samples ( 28 ).
In addition, it has been proposed that the
strength of proximity-induced SOC is sen-
sitive to the rotational alignment between
graphene and WSe 2 : Strong SOC is expected
when graphene is rotationally misaligned with
WSe 2 by 10° to 20°, whereas perfect alignment
produces weak proximity-induced SOC ( 41 ).
If confirmed, this rotational degree of freedom
could provide an additional experimental knob
to engineer moiré band structure ( 42 ). Our
sample features a twist angle of ~16° (fig. S1F)
between tBLG and WSe 2 , falling in the range
that is predicted to induce the strongest SOC
strength. We investigated the effect of rota-
tional misalignment between tBLG and WSe 2
in two additional samples near the magic angle:
AHE and hysteresis loops were observed at
n= +2 in sample A1, where tBLG and WSe 2
were misaligned at ~10° (fig. S14). On the other
hand, tBLG and WSe 2 were perfectly aligned
in sample A2, where AHE was absent (fig. S15)
( 16 ). The superconducting phase was absent or
suppressed in all samples. These observations
provide experimental support for the notion
that the rotational misalignment between
tBLG and WSe 2 , and thus the SOC strength,
plays a key role in determining the stability of
the ferromagnetic and superconducting states.
Although transport measurement alone can-
not definitively confirm the influence of SOC
on the superconducting phase near the magic
angle, our results could motivate future ef-
forts, both theoretical and experimental, to
investigate the influence of SOC on moiré struc-
tures as a function of graphene twist angle and
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ACKNOWLEDGMENTS
We thank A. F. Young, M. Yankowtiz, and A. Vishwanath for helpful
discussions and A. Mounce and M. Lilly for experimental assistance.
Funding:This work was primarily supported by Brown University.
Device fabrication was performed in the Institute for Molecular and
Nanoscale Innovation at Brown University. This work was performed,
in part, at the Center for Integrated Nanotechnologies, an Office of
Science User Facility operated for the US Department of Energy
(DOE) Office of Science. J.-X.L., E.M., and J.I.A.L. acknowledge the use
of equipment funded by MRI award DMR-1827453. Synthesis of WSe 2
(S.L., D.R., J.H.) at Columbia was supported by the NSF MRSEC
program through the Center for Precision-Assembled Quantum
Materials (DMR-2011738). K.W. and T.T. acknowledge support from
the EMEXT Element Strategy Initiative to Form Core Research Center,
grant JPMXP0112101001, and CREST (JPMJCR15F3), JST.Author
contributions:J.-X.L., E.M., and Z.W. fabricated the devices and
performed the measurements. J.-X.L., E.M., Z.W., and J.I.A.L. analyzed
the data. Y.-H.Z. constructed the theoretical model. K.W. and T.T.
provided the hBN crystals. S.L., D.R., and J.H. provided the WSe 2
crystals. The manuscript was written with input from all authors.
Competing interests:The authors declare no competing financial
interests.Data and materials availability:Experimental data files
are available at the Open Science Framework ( 43 ).SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abh2889
Materials and Methods
Supplementary Text
Figs. S1 to S19
References ( 44 – 46 )
26 February 2021; accepted 15 December 2021
Published online 6 January 2022
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