Evidence of competing ground states between fractional Chern insulator and antiferromagnetism in moiré MoTe_2

Domain: biology
Published: 2026-04-04
Editorial outcome: major_revision

Abstract
Moiré materials—formed by stacking atomically thin crystals with a small twist—create
tunable electronic lattices where strong interactions and band topology can generate unusual
magnetic and topological phases. In twisted bilayer MoTe , ferromagnetism has been closely
2
linked to integer and fractional Chern insulators, while the true zero‑field ground state can
be sensitive to twist angle and vertical electric field. Here we show that devices with
intermediate twist angle (~3°) may host antiferromagnetic ordered ground states at fixed
hole fillings of 1 and 2/3, evidenced by suppressed zero‑field magneto‑optical and Hall
responses and field‑driven transitions into quantized Chern states. By tuning only the
vertical electric field, we reversibly switch the system from antiferromagnetism to
ferromagnetism accompanied by integer or fractional Chern insulating behavior near the
layer‑polarization threshold, and then to a paramagnetic regime at larger fields. These
results reveal competing correlated ground states in a single moiré platform and establish
electric‑field control of magnetism and topology.

Introduction
The interplay between strong correlations and topology can lead to the emergence of intriguing
quantum states of matter. Moiré materials based on transition metal dichalcogenides (TMDs) have
emerged as a promising platform for exploring novel quantum phenomena that arise from band
topology and many-body interactions1–12. Recently, there has been a surge in research focused on
rhombohedral-stacked (R-stacked) tMoTe , in which transport experiments have provided
2
unambiguous evidence of both QAH and FQAH effects on devices with relatively large twist
angles 𝜃 ∼ 3.7°−3.9° 13,14. Based on the obtained Chern numbers, photoluminescence and
compressibility measurements suggest the FQAH is the ground state of 𝑣 = 2/3 (𝜈 = 1 is
h h
defined as one hole per moiré unit cell, corresponding to a half-filled moiré valence band) over a
relatively large range of twist angle, specifically 𝜃~2.6°−3.9°, while QAH at 𝑣 = 1 extends
h
even down to 2.1°14–19. The Chern numbers were obtained by comparing the Streda formula with
the fitted dispersion slope of the filling factor versus the magnetic field (𝐵 ) of Tesla order.
However, the energy difference between the competing phases is usually subtle, and the applied
relatively large 𝐵 could hide the true ground state at zero 𝐵. Transport measurement can provide
unambiguous evidence of the true ground state as demonstrated in devices with relatively large
twist angles (𝜃 ∼ 3.7°−3.9°), while transport study of 𝑣 ≤ 1 states in tMoTe moiré device with
h 2
small 𝜃 is challenging due to the increasing difficulty of making transparent electrical contact. On
the other hand, in the moiré system, the ground states are usually expected to be sensitive to the
twist angle22, suggesting more unexpected correlated effects to explore in tMoTe moiré system
2
with smaller 𝜃19–24.

In this work, we performed a systematic twist angle dependence study on the R-stacked tMoTe
2
moiré system by combining optical and transport measurements. We observed competing magnetic
ground states depending on both twist angle and 𝐸. Specifically, we observed unexpected AFM
ground states with vanishing Hall resistance at both 𝑣 = 1 and 2/3, at intermediate twist angles
h
𝜃~3° , in between the FMCCI ground states of both larger and smaller 𝜃 . Moreover, applying
vertical electric field (𝐸) induces an AFM to FM (ICICFCI) transition and an emergent FM state
was observed near critical electric field (𝐸 ) of layer polarization.
c

Results
Twist-angle dependent magnetic ground states
Fig. 1a shows the schematic of our dual-gated device with a contact gate design for both optical
and transport measurements, fabricated following the similar procedure reported earlier14 (see the
Methods). We have fabricated tMoTe bilayer devices with twist angle 𝜃~2.4°−4.1°, denoted as
2
D(𝜃). Figure 1b illustrates the honeycomb moiré lattice with two sublattices centered at the MX
and XM (M=Mo; X=Te) stacking sites. The application of 𝐸 (here is the pure electric field, which
can be tuned independently to the 𝜈 due to our dual-gated device structure, see Methods) can
h
break energy degeneracy between the moiré orbitals localized in the MX (A ) and XM (B )
sublattices and induce layer polarization. 𝐸 dependence of reflectance contrast (RC) measurement
demonstrates a continuous tuning of hole distribution (Fig. 1c), from which 𝐸 of honeycomb-
c
triangular layer polarization transition can be determined (Fig. S2).

To investigate twist angle dependence of magnetic interactions, we performed reflective magnetic
circular dichroism (MCD) measurements under small 𝐵 on devices with representative twist
angles (see the Methods for details of MCD measurements). Fig. 1d shows the MCD intensity plot
as a function of 𝑣 and 𝐸 of D(4.1° ). The magnetic response maximizes at 𝐸 = 0 for 𝑣 ≤ 1 .
h h
Increasing 𝐸 suppresses the MCD signal until it finally vanishes at large 𝐸 . The MCD signal
versus 𝐵 at 𝑣 = 1 , 2/3, and 𝐸 = 0 are also measured (Fig. 1g). Sharp spin-flip transition and
h
pronounced hysteresis loop, a hallmark of ferromagnetism, are observed. These results are
consistent with the earlier report on devices with large twist angles (𝜃~3.4°−3.9°)15,25. Fig. 1f
shows the MCD map of a small 𝜃 device D(2.4°). Although the magnetic region shows a different
pattern, the 𝐸 dependence of magnetic response shows a qualitatively similar trend as in D(4.1°),
i.e., maximum at 𝐸 = 0 and decreases with increasing 𝐸. The MCSD signal versus 𝐵 at 𝑣 = 1 and
h
𝐸 = 0 are also measured (Fig. 1i). Appreciable hysteresis loop is observed, confirming its FM
order.

Interestingly, the magnetic response shows substantially different behaviors in devices with
intermediate 𝜃~3° . Firstly, two hollow features around 𝐸 = 0 at 𝑣 = 1 and 2/3 can be
h
identified in the MCD map of D(3.15° ) (Fig. 1e). The strongest MCD response
𝜕𝑀𝐶𝐷
appears not at zero but finite 𝐸, signifying non-monotonic 𝐸 dependence of 𝜒 = (see the
MCD
𝜕𝐵
Methods for definition and detailed of MECD analysis). Secondly, continues spin-switching without
appreciable hysteresis loop, i.e., no remnant magnetization at 𝐵 = 0, is observed in the MCD-𝐵
curves at 𝑣 = 1, 2/3, at 𝐸 = 0 (Fig. 1h). Thirdly, clear suppression of MCD response and a zero-
h
MCD plateau is observed at small 𝐵 is observed at 𝑣 = 1 and 𝐸 = 0 (Fig. 1h). The above
h
observations are in sharp contrast with large and small 𝜃 devices, suggesting the different magnetic
ground states in tMoTe 2 devices with intermediate 𝜃~3° (see supplementary Fig. S3 for additional
data from D(3.0°) and D(3.1°)).

Antiferromagnetism at 𝒗 = 𝟏 and 𝟐/𝟑
𝐡
To reveal the magnetic ground states of 𝑣 = 1 and 2/3 in devices with intermediate 𝜃 , we
h
performed systematic temperature (𝑇) dependent MCD measurements. Fig. 2a shows the MCD
map at various temperatures of D(3.15°). Remarkably, at 𝑣 = 1 and 2/3, while MCD minimums
h
are observed at 𝐸 = 0 at 1.6 K, their amplitudes gradually increase and evolve into maximums at
elevated temperatures. That is to say, 𝜒 of 𝑣 = 1 and 2/3 show non-monotonic dependence
MCD h
not only versus 𝐸, but also versus 𝑇 (see supplementary Fig. S3 for additional data from D(3.0°)
and D(3.1°)).

To see the 𝑇 dependence of 𝜒 clearer, MCD versus 𝐵 at selective 𝑇 were measured at 𝑣 = 1,
MCD h
2/3 and 𝐸 = 0 (Fig. 2b-c). The zero-field MCD slopes at 𝑣 = 1 and 2/3 first increase and then
h
decrease with increasing 𝑇 , showing clear non-monotonic T dependence of 𝜒 . Similar
MCD
behavior is also observed in D(3.0°) (Fig. S4). Moreover, we observed clear suppression of 𝜒
MCD
at small 𝐵 at low 𝑇, at 𝑣 = 1 (Fig. 2b), which gradually disappeared with elevated 𝑇. The non-
h
monotonic 𝐸 and 𝑇 dependences here are in sharp contrast to devices with larger (𝜃 ≥ 3.4°) or
smaller (𝜃 ≤ 2.7°) twist angles, in which monotonic 𝐸 and 𝑇 dependences are observed both in
our measurements (Fig. S3) and earlier reports15,16,25. The non-monotonic 𝜒 −𝑇 dependence
MCD
and the suppression of 𝜒 at small magnetic are characteristic features of antiferromagnetism26,
suggesting AFM ground states of D(3.15°) at 𝑣 = 1 and 2/3 at 𝐸 = 0.
h

Fig. 2d shows 𝑅 versus 𝐵 at selective 𝑇 of 𝑣 = 1 at 𝐸 = 0. We observed no Hall signal at zero
xy h
𝐵, and clear suppression of Hall slope at 1.6 K. The Hall suppression gradually disappeared with
elevated 𝑇 , showing non-monotonic 𝑇 dependence of zero-field 𝑅 slope, consistent with the
xy
h
MCD observation. Moreover, 𝑅 saturates to the quantized value of at critical 𝐵 (𝐵 ),
xy 𝑒2 c
demonstrating a magnetic field-induced AFM-ICI phase transition. It is worth noting that 𝑇 = 7 K
shows the best quantization at finite 𝐵 , i.e., 𝐵 is the smallest, compared with both lower and
c
higher T, consistent with the expectation of the AFM ground state of 𝑣 = 1 at 𝐸 = 0. Fig. 2e
h
shows 𝑅 versus 𝐵 at selective 𝑇 of 𝑣 = 2/3 at 𝐸 = 0 . The observations are qualitatively
xy h
similar to 𝑣 = 1, while 𝑅 saturates to the quantized value of 3ℎ at finite 𝐵 , demonstrating a
xy 2𝑒2 c
magnetic field-induced AFM-FCI phase transition. Again, we find 𝐵 is the smallest at temperature
c
~2.5−3.5 K, consistent with the expectation of the AFM ground state of 𝑣 = 2/3 at 𝐸 = 0.
h

Emergent ferromagnetism and Chern states
Fig. 3a and 3b show the MCD versus 𝐵 as a function of 𝐸 at 𝑣 = 1 and 2/3, respectively. The
h
zero-field slopes at 𝑣 = 1 and 2/3 are initially enhanced by increasing 𝐸, reaching maximums at
h
~𝐸 , and then suppressed by further increasing 𝐸 , showing clear non-monotonic 𝐸 field
c
dependences (see supplementary Fig. S4 for additional data from D(3.0° )). Surprisingly, we
observed appreciable hysteresis loop emerged at 𝐸 slight smaller than 𝐸 of layer polarization,
FM c
signifying the FM order. Supplementary Fig. S5a and S3c show the MCD versus 𝐵 at selective 𝑇 at
𝑣 = 1 , 2/3 at 𝐸 , respectively. The small-field slopes decrease with increasing 𝑇 , showing
h FM
monotonic 𝑇 dependence of 𝜒 . The monotonic 𝜒 −𝑇 dependences at 𝐸~𝐸 are in sharp
MCD MCD c
contrast to the non-monotonic 𝜒 −𝑇 dependences observed at 𝐸 = 0, consistent with the FM
MCD
order of 𝑣 = 1 and 2/3 at 𝐸 . The above result demonstrates a pure electric-field-induced
h FM
AFM-FM transition. Although electric-field-tuning of AFM-FM switching field has been
demonstrated in 2D magnet CrI 27, and FM to paramagnetic Mott insulator with AFM exchange
3
has been demonstrated in TMD moiré systems11,12,28, a pure electric-field-induced AFM-FM
transition has never been observed in moiré systems and any other material systems, to the best of
our knowledge. The emergence of FM order near 𝐸 also reflects the deep connection between the
c
FM exchange mechanism and electronic lattice symmetry.

We also analyze the nature of the magnetic states at representative electric fields by an Arrott plot
(that is, 𝑀2 versus 𝐻/𝑀, using MCD in place of 𝑀) in supplementary Fig. S6. Here a curve with a
positive low-field slope and positive y-intercept is FM-ordered, that with a positive x-intercept and
a positive slope is PM, and that with a negative low-field slope is AF-ordered.29–32 The Mott state
(the 𝐸 = 29 mV nm−1 curve) is PM. Although the superexchange interaction, as reflected by a
negative Curie–Weiss temperature 𝑇 (Fig. S9), favors an AFM-ordered state, the geometric
w
frustration from a triangular lattice greatly suppresses the ordering temperature. This behavior is
in contrast to the 𝐸 = 0 mV nm−1 state. Here the negative low-field slope in the Arrott plot shows
its AFM-ordering, which directly correlates with the suppressed 𝜒 at small magnetic fields.
MCD
Because geometric frustration is absent in the bipartite honeycomb lattice at small 𝐸, and finite
temperature AF-ordering is favored. The AFM state at small displacement fields is compatible with
the unfrustrated collinear z‑AFM on the effective honeycomb lattice, in contrast to the
geometrically frustrated triangular lattice in the layer‑polarized regime. However, our present
measurements do not uniquely fix the detailed spin configuration, other AFM patterns, including
non‑collinear 120°‑like states, cannot be rigorously excluded (see Supplementary Section 19).
The slop sign change at large magnetic field reflects the field polarizing process. At intermediate
𝐸 (the 𝐸 = 23 mV nm−1 curve), a positive slope with positive y-intercept is observed, signifying
the emergent FM-order.

Inspired by the above observation in the MCD measurements, we further performed transport
measurements in device D(3.15°) to examine the topological properties of this system as a function
of 𝐸 . Fig. 3d show 𝑅 and 𝑅 versus 𝐵 at selective 𝐸 fields at 𝑣 = 1 , 𝑇 = 1.5 K. A
xy xx h
Qualitatively similar trend is observed, consistent with the MCD measurements. No Hall signal is
observed at zero 𝐵, while 𝑅 saturates to the quantized value of ℎ at 𝐵 of ~200 mT at 𝐸 = 0.
xy 𝑒2 c
𝐵 decreases with increasing 𝐸 , down to 100 mT at 𝐸 of 23 mV nm−1 . An appreciable
c FM
hysteresis loop is observed, confirming its FM order. Another interesting feature is 𝑅 shows an
xx
anomalous positive magnetoresistance (MR) at small 𝐵 at 𝐸 = 0, and the positive MR gradually
evolves into a negative MR at larger 𝐸 near 𝐸 4,31.
c

Fig. 3e shows 𝑅 and 𝑅 versus 𝐵 at selective 𝐸 fields at 𝑣 = 2/3 of D(3.15° ) at 𝑇 = 1.5 K .
xy xx h
We observed no Hall signal at zero 𝐵 , while 𝑅 saturates to the quantized value of 3ℎ at
xy 2𝑒2
𝐵 ~200 mT at 𝐸 = 0 , and 𝐵 decreases with increasing 𝐸 , down to 20 mT at around 𝐸 of
s c FM
~11 mV nm−1 . A small but resolvable hysteresis loop is observed, while it is much more
pronounced in MCD measurement. We attribute the discrepancy to the fact that the optical
measurement is a more local measurement with sub-micro-sized light spot (See methods). In
contrast, the transport measurement involves a much larger area (Fig.S1), thus more affected by
spatial inhomogeneity. The spatial inhomogeneity effect combined with the smaller exchange
energy scale of 𝑣 = 2/3 could smear out the intrinsic hysteresis effect.
h

𝑅 also shows an anomalous positive MR at small 𝐵 at small 𝐸 at 𝑣 = 2/3. Similar to 𝑣 = 1,
xx h h
the positive MR gradually evolves into a negative MR at larger 𝐸. The observation of positive MR
at small 𝐵 at 𝑣 = 1 and 2/3 at 𝐸 = 0 also excludes one possible artifact: the absence of MCD
h
and Hall response here is caused by the formation of nano-sized FM domains, i.e.,
superparamagnetic state, which could smooth and smear out the magnetic hysteresis. If that is the
case, we would expect to see negative MR near 𝐵 = 0 (or coercive field if there is hysteresis), as
applying 𝐵 polarizes the magnetic domains and helps the development of chiral edge states, as
observed in all QAH and FQAH systems7,13,14,33–35. Therefore, we conclude that the anomalous
positive MR at small 𝐵 is closely correlated with the AFM order. The sign inversion of MR at large
𝐵 signifies a 𝐵-induced AFM-ICI(FCI) transition. On the other hand, we indeed observed negative
MR at all temperatures at 𝐸~𝐸 at 𝑣 = 2/3 (Fig. 3f), which is consistent with the typical
c h
behavior of the QAH and FQAH, confirming the ICI and FCI are the zero-field ground states of
𝑣 = 1 and 2/3 at ~𝐸 , respectively.
h FM

The combined optical and transport measurements above show that the magnetic order of 𝑣 = 1
h
and 2/3 are closely connected to their topological properties. It's expected to show more robust
FM order and possibly better zero-field quantization near 𝐸 at lower temperatures. However, the
c
worsened device contact at lower temperatures prevents us from performing reliable magneto-
transport measurements at mK temperature, which could be improved with better device quality
in the future.

To study the electronic ground state of 𝐸 = 0 state, we performed dielectric sensing measurements
on this system, which effectively measures the compressibility of the system.36. Here we show the
sensing signal of WSe versus 𝑣 at 𝐸 = 0 in Fig.S7. A pronounced feature of resonance-
2 h
energy-shift is observed at 𝑣 = 1, signifying an incompressible state at 𝐸 = 0. Unfortunately, we
h
didn’t see resolvable features of 𝑣 = 2/3, likely due to its much smaller gap which is beyond the
h
sensitivity of our measurement16. We have also performed temperature-dependent transport
measurement, where a non-monotonic behavior of 𝑅 as a function of 𝑇 is observed (Fig.S7).
xx
This might be due to the AFM order decreasing 𝑅 by freezing the magnetic fluctuations, and
xx
then the gap opening or disorder increasing 𝑅 at lower 𝑇 . Alternatively, the non-monotonic
xx
𝑅 −𝑇 behavior could also come from an in-gap quasiparticle peak, which vanishes when AFM
xx
order is developed37 (see section 17 of the supplementary materials for detailed discussion). By
the combined transport and dielectric sensing measurement, we conclude the 𝐸 = 0 state at 𝑣
h
=
1 is an insulator with a small gap (likely <6 K).

Magnetic phase diagrams
To map out the magnetic phase diagram of the system as a function of 𝑇 and 𝐸, we performed 𝑇
and 𝐸-dependent MCD measurements. Fig. 4a and 4b shows the MCD map and corresponding
𝜒 −𝑇 curves at representative 𝐸 at 𝑣 = 1 of D(3.15°) . Non-monotonic 𝜒 −𝑇 behavior
MCD h MCD
with a clear 𝜒 peak at around 7 K is observed at 𝐸 = 0. We assign the peak temperature to be
MCD
Neel temperature (𝑇 ), where the AFM order starts to develop26. Similar non-monotonic 𝜒 −
N MCD
𝑇 behaviors are also observed at finite 𝐸 fields below 𝐸 ≈ 25 mV nm−1, while 𝑇 decrease with
c N
increasing 𝐸. On the other hand, 𝜒 increases monotonically with decreasing 𝑇 at 𝐸 fields above
MCD
𝐸 , suggesting a different magnetic nature. Qualitatively similar behavior is also observed at 𝑣 =
c h
2/3, except 𝑇 are significantly lower, ~ 3.1 𝐾 at 𝐸 = 0, and 𝐸 of 11 mV nm−1, as shown in
N c
Fig. 4c and 4d (see supplementary Fig. S8 for additional data from D(3.0°)). We also performed 𝑇
and 𝐸-dependent 𝑅 measurements at 𝑣 = 1 and 2/3 in D(3.15°) at small 𝐵 (Fig. S7f and
xy h
S11a). Non-monotonic 𝑅 −𝑇 dependencies with 𝑅 peak temperature decreases with
xy xy
increasing 𝐸, are observed at 𝐸 fields below 𝐸 . For 𝐸 > 𝐸 , the sample becomes too insulating,
c c
preventing reliable 𝑅 measurements. The results are consistent with the MCD measurements,
xy
confirming the non-monotonic 𝜒 −𝑇 dependence at small 𝐸 is an intrinsic property of tMoTe
MCD 2
with intermediate 𝜃.

The magnetic phase diagrams are mapped out as a function of 𝐸 and 𝑇 based on the 𝜒 −𝑇
MCD
dependences. For 𝐸 < 𝐸 , 𝑇 is determined from the peak temperatures in 𝜒 −𝑇 curves26,
c N MCD
denoted by the arrows. For 𝐸 > 𝐸 , Curie–Weiss temperature 𝑇 can be extracted by analyzing
c w
𝜒 −𝑇 curves using Curie–Weiss law7,25,38,39. At high temperatures, the inverse MCD slope
MCD
follows the Curie–Weiss law, 𝜒 −1 ∝ 𝑇−𝑇 (dash lines) reasonably well (See supplementary
MCD w
Fig. S9 for Curie–Weiss analysis). 𝑇 is proportional to the effective spin-spin exchange
w
interaction40, and a negative (positive) 𝑇 reflects an AFM (FM) exchange interaction. The 𝐸
w
dependences of extracted 𝑇 and 𝑇 of 𝑣 = 1 and 2/3 of D(3.15°) are summarized in Fig. 4e and
N w h
4f. 𝑇 of ~7 K is obtained at 𝐸 = 0, which decreases monotonically with increasing |𝐸|. Negative
N
𝑇 of ~ −9 K at 𝐸 = 0 is obtained from Curie–Weiss fitting, in reasonable agreement with 𝑇 .
w N
This shows the system is AFM ordered at small 𝐸 , and the AFM order can be suppressed by
applying 𝐸 . For 𝐸 > 𝐸 , negative 𝑇 are obtained, showing a paramagnetic phase with AFM
c c w
interaction, consistent with the expectation of antiferromagnetic kinetic exchange in a half-filled
triangular lattice, as the earlier report in large twist angle device25. A positive maximum 𝑇 ~3.3 K
w
is obtained at 𝑣 = 1 around 𝐸 , coincides with the 𝜒 peak at 1.6 K, and is consistent with the
h c MCD
FM hysteresis loop observed around 𝐸 (Fig. 3a). 𝑣 = 2/3 shows qualitatively similar behavior
c h
as 𝑣 = 1, while the exchange energy scale is significantly smaller. The maximum 𝑇 is ~3 K at
h N
𝐸 = 0 , while 𝑇 maxima around 𝐸 is ~2.7 K . The above results demonstrate a cascade of 𝐸 -
w c
induced magnetic and topological phase transitions from AFM order (𝐸 < 𝐸 ) to FM-ordered
c
ICICFCI (𝐸~𝐸 ), and finally to paramagnetic phases (𝐸 > 𝐸 ).
c c

The pronounced zero Hall plateau and the non-monotonic 𝜒 −𝑇 behavior with a peak
MCD
at finite 𝑇 are fully consistent with the AFM ground state at 𝐸 = 0, while the in-plane FM state
can be ruled out: 𝜒 of in-plane FM should be constant all the way until saturation when the
MCD
magnetic field is applied along the hard axis (out-of-plane direction), and its 𝜒 −𝑇 behavior
MCD
should just saturate at 𝑇 < 𝑇 (see section 19 of the supplementary materials for detailed
c
discussion).

Methods
Device fabrication
Devices were fabricated using the standard tear-and-stack and dry transfer method. In all devices,
to facilitate good contact formation for hole doping in tMoTe , we use few-layer TaSe as contact
2 2
electrodes, taking advantage of its high work function. Thin flakes of hexagonal boron nitride (h-
BN), graphite (3−5 nm), monolayer MoTe and WSe (HQ Graphene), and TaSe (2−5 nm)
2 2 2
were first exfoliated from bulk crystals onto SiCSiO (285 nm) substrates. Flakes of appropriate
2
thickness were identified according to their reflectance contrast under an optical microscope. The
MoTe monolayer was mechanically cut into two parts using AFM tips. We handled MoTe flakes
2 2
inside a nitrogen-filled glovebox with oxygen and water levels below 0.01 ppm to minimize the
degradation of MoTe . The thickness of h-BN flakes is also measured using an atomic-force
2
microscope (AFM). The complete dual-gated structure was assembled using a polycarbonate
stamp within the N
2
glovebox environment. A high-precision rotation stage (Thorlabs PRM1Z8)
controls the targeted twist angle with a typical accuracy of 0.1º. For optical devices, the stack
was then released on the pre-patterned and cleaned gold electrodes of 20 nm thickness, such that
the graphite gates and TaSe
2
grounding contact were electrically connected to the deposited
contacts. For dielectric sensing devices, the moiré bilayer and the WSe
2
monolayer are separated
by an ultrathin h-BN layer with a thickness of approximately 1 nm. The complete dual-gated
allows for full h-BN encapsulation of the air-sensitive MoTe layers. The stamp polymer was
2
dissolved in anhydrous chloroform for 5 minutes in ambient conditions (see Fig.S1). For transport
devices, to achieve ohmic contacts irrespective of the applied electric fields, we fabricated the
dual-gated devices with SiO CSi global contact gates to heavily hole-dope the contact regions,
2
where tMoTe
2
overlaps with few-layer TaSe
2
flakes. To define the Hall bar geometry of the tMoTe
2
channel and eliminate the unavoidable monolayer MoTe region, we carried out extra EBL and
2
RIE processes, following a procedure similar to the one reported earlier14. The dual-gate geometry
allows independent control of 𝑣 and 𝐸 by the top gate voltage 𝑉 and bottom gate voltage 𝑉 . We
h t b
have measured in total 8 devices with twist angles ranging from 4.1° to 2.4° in this study, as
presented in the main figures and supplementary figures.

Optical measurements
The optical measurements were performed in reflection geometry in a home-built confocal optical
microscope system based on a closed-cycle helium cryostat (base temperature 1.6 K) equipped
with a superconducting magnet (9 T). A superluminescent light-emitting diode with a peak
wavelength of 1070 nm and full width at half-maximum bandwidth of 90 nm was used as the
light source. The output of the diode was coupled to a single-mode fiber and focused onto the
device under normal incidence by a low-temperature microscope objective (Attocube, 0.8
numerical aperture). The spot size of the excitation light, defined as the FWHM of the diffraction-
λ
limited beam spot, can be calculated as FWHM = 0.51 ~0.7 µm. A combination of a linear
NA
polarizer and an achromatic quarter-wave plate was used to generate the left and right circularly
polarized light. To avoid perturbing the system, the incident intensity on the sample was kept
below 30 nW μm−2 (see section 15 of the supplementary materials for more information). The
reflected light of a given helicity was spectrally resolved by a spectrometer coupled to a liquid
nitrogen-cooled InGaAs one-dimensional array sensor (Princeton Instruments PyLoN-IR 1.7).
The reflectance contrast spectrum was obtained by comparing the reflected light spectrum from the
sample with the reference spectrum measured on a heavily doped condition (which is featureless
in the spectral region of interest).

In Fig. 1c, the two crossed optical resonances on the right side of the neutral-exciton-like resonance
disperse almost linearly with 𝐸-field, which is a typical behavior of Stark shift of interlayer exciton
transitions, as also reported in earlier work25. The other two optical resonances on the left side of
the layer-polarized exciton resonance are attributed to the bonding and anti-bonding branch of the
layer-hybridized exciton resonances, as reported in earlier work16.

The MCD spectrum is defined as MCD(𝐸) =
𝑅+(𝐸)−𝑅−(𝐸)
, where 𝑅+(𝐸) and 𝑅−(𝐸) denote the
𝑅+(𝐸)+𝑅−(𝐸)
reflection intensity spectrum of the left and right circularly polarized light. To analyze the MCD
as a function of tuning parameters such as 𝜈, 𝐸, 𝐵, and 𝑇, we integrate the MCD modulus over a
spectral range that covers most of the spectrum range of the MCD signal. We have performed
integration that covers different ranges of the MCD spectrum, and the results are qualitatively the
same, confirming the validity of our analysis (see Figure S17). The integrated MCD (referred to
simply as the MCD below) reflects the difference in occupancy between the K and K′ valleys in
MoTe . Because of spin-valley locking, the signal is proportional to the out-of-plane
2
magnetization12,25,38,39,49. For simplicity, the MCD measured under a constant small 𝐵 (𝜒 ) is
MCD
𝜕𝑀
approximated as proportional to magnetic susceptibility 𝜒 = (see section 16 of the
𝜕𝐵
supplementary materials for detailed discussion). In the MCD map and MCD susceptibility
MCD(+𝐵)−MCD(−𝐵)
measurements, the results are averaged by positive and negative 𝐵, i.e., MCD = .
2

For dielectric sensing measurement, a halogen lamp serves as a white light source, the output of
which is first collected by a single-mode fiber and collimated by a ×10 objective. The beam on the
sample has a power below 1 nW.

Determination of doping density and electric field
The carrier density 𝑛 and electric field 𝐸 on the sample are converted from the top (bottom) gate
voltage 𝑉 (𝑉 ) using a parallel plate capacitor model: 𝑛 =
𝑉t𝐶t+ 𝑉
b
𝐶
b and 𝐸 =
1
(
𝑉t
−
𝑉
b)−
t b
𝑒 2 𝑑t 𝑑
b
𝐸 , where 𝑒 is the electron charge, and 𝜀 is the vacuum permittivity and 𝐶 and 𝐶 are the top
offset 0 t b
and bottom gate capacitance obtained from the top and bottom h-BN thickness 𝑑 and 𝑑
t b
measured by atomic force microscopy (Asylum Research Cypher S). The offset electric field likely
arises from the structure asymmetry and is determined from the symmetric axis of the dual-gate
MCD map. The obtained doping density from the capacitor model can then be used to calculate
the twist angle from the assigned filling factors in the reflection contrast measurements in optical
devices.

For transport devices, the twist angle can be more accurately calibrated from the 𝑅 map and
xx
Landau fan diagrams. Supplementary Fig. S10 presents the 𝐵 and filling dependences of 𝑅 .
The
xx
Landau fan diagram, denoted by dashed lines, highlights a series of minima in 𝑅 corresponding
xx
to the different Landau levels. Upon complete filling of 𝑁th Landau levels with hole carriers, the
hole carrier density (𝑛 ) can be expressed by 𝑛 = 𝑁|𝐵|/𝜙, where 𝜙 = ℎ/𝑒 (ℎ is Planck's
h h
constant). The hole carrier density difference (Δ𝑛 ) between neighboring Landau levels is given
h
by Δ𝑛 = 𝐵/𝜙 . By determining the number of filling factors corresponding to these hole carrier
h
densities, moiré density can be obtained. When 𝐵 reaches 10 Tesla, a change of 0.086 in the
filling factor is observed, so the moiré density 𝑛 is established to be 2.8×1012 cm−2. Finally,
M
the twist angle 𝜃 is calculated to be 3.15° using 𝜃 =
𝑎√3
𝑛 , where 𝑎 denotes the MoTe lattice
M 2
2
constant, approximately 3.5 Å.

Transport measurements
Electrical transport measurements were performed in a closed-cycle 4He cryostat (Oxford
TeslatronPT) equipped with a 12 T superconducting magnet. Electrical transport measurements
were performed using standard low-frequency lock-in techniques. The bias current is limited
within 2 nA to avoid the disturbance of fragile quantum states. Finite longitudinal-transverse
coupling occurs in our devices that mixes the longitudinal resistance 𝑅 and Hall resistance 𝑅 .
xx xy
To correct this effect, we used the standard procedure to symmetrize [
𝑅xx(𝐵)+𝑅xx(−𝐵)
] and anti-
2
symmetrize [ 𝑅xy (𝐵)−𝑅xy(−𝐵) ] the measured 𝑅 and 𝑅 under positive and negative magnetic
xx xy
2
fields to obtain accurate values of 𝑅 and 𝑅 , respectively. The measurements were carried out
xx xy
without any optical excitation.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a detailed study of tMoTe2 by tuning the twisting angle and vertical electric field, along with changing temperatures and magnetic fields, probed by both optical and electrical approaches. They focus on the magnetic states for samples of different conditions. The data sets are rich. There are a few major aspects the authors can improve before further consideration of this manuscript.\n1. tMoTe2 is a system being intensively studied in the scientific field. What are the missing parts this work can contribute to? From both abstract and introduction, it is unclear what the new things this work brought to the community. The authors started with a brief introduction in abstract and introduction that tMoTe2 is a rich system in support of AQHE, but suddenly switched to talk about magnetism they found in this work. Some missing parts need to be provided so the readers can appreciate this work in the context of what has been and not been achieved in the field.\n2. The readability of most figures is still low. It seems that figure 1d-f and 1g-I have one-to-one corresponding relationship. However, from these sub-figures themselves, it is hard to read since g and h have the same legend yet different curves. The same issue is for Figure b and c (these two sub-figures have the same noted curves), d and e. It is good to add brief legends to indicate the different conditions, based on which these data were acquired.\n3. Mechanism. The authors suggest “charge transfer” as the mechanism. What are the charge transfer coming from? It is transferred from metal electrode to the tMoTe2, or self doping by transfer between the two layers of tMoTe2? Why is it not because of electric field effect? The authors have top and bottom electrodes, which allow them to separate electric field and electrostatic doping effects by tuning the top and bottom electrodes separately. They should do this experiment and analysis.\n4. It is possible that the AFM magnetization orientation is out of plane, as the author speculated. But the author’s argument for this speculation appears problematic. The authors thought if it is in-plane, the MCD should keep constant while B field is applied out of plane, which is not true. If the magnetic anisotropy is in-plane, it is likely the out of plane B field would gradually increase the MCD, and it is also likely that out of plane B field would cause spin flop effect suddenly at a certain B field.\n5. Multiple typos need to be fixed. “inplane” is not a word, should be in plane or in-plane. “our-of-plane” should be out-of-plane. “Honeycomb” (main text) and “Magnetic” (figure 1 caption) should not be capitalized in sentences.\n6. Finally, the authors for a few times stressed the “unexpected” AFM states. Why is it unexpected? I felt the field of study has reported such magnetic states many times in different twisting systems. If I am wrong, please correct or clarify.\n7. In summary paragraph, please explain in a more clear manner what are the major finding and proved mechanism, instead of only simply re-stating the experimental observation.", "reviewer_2": "In the manuscript “Evidence of competing ground states between fractional Chern insulator and antiferromagnetism in moiré MoTe2”, Chang et. al. present a surprising result in the now famous twisted MoTe2 heterostructure device platform. Rather than fabricating devices in the ~3.7 degree range where the fractional quantum anomalous Hall effect was first discovered, the authors study dual gated devices with a twist angle of ~3 degrees. Unlike 3.7deg devices at hole doping of 1 hole per moiré unit cell, which present spontaneous symmetry breaking and an induced ferromagnetic state, they observe signatures of antiferromagnetic order, such as vanishing MCD signals and Hall resistivity at zero magnetic field. Further, the authors show that they can use electric fields to fully tune the AFM-FM transition in the device as well as an AFM to Chern insulating transition. I think the results are very exciting and open the door to another set of interesting phenomena in this rich system. The accessible interplay here between AFM, FM, and topological orders is an interesting one that warrants future work. However, I have reservations about recommending the manuscript for publication in its current form. The manuscript is lacking in many details and definitions that renders it unintelligible for any reader who is not already extremely knowledgeable about tMoTe2. Further exacerbating the problem, there is a heavy use of acronyms and shorthand that, again, might make the manuscript difficult to parse for a non-expert. I think that the data quality and analysis of the work is highly appropriate for Nature Communications and I think the results will be interesting and exciting to those working in condensed matter physics and 2D materials. As such, I recommend that the manuscript be accepted after major revisions of the written text to improve clarity. Please see my comments below.\n-(Page 1, line 23) the authors have not defined what ν_h is. They should clarify that this is the hole filling factor for non-experts who read the manuscript.\n-(Page 2, line 38) The manuscript never references Figure 1b\n-(Page 3, line 1) The manuscript has not defined RC\n-(Page 3, line 1) The authors are relatively unclear about whether they are tuning the hole doping of the system or the displacement field. I think simply mentioning ‘electric field’ is not enough given their dual-gated device geometry, they should be more specific.\n-(Page 4, line 4) While the authors define Tw in the caption of ED fig. 9 and on page 7 they do not define it before its use here\n-(Figure 1) the size and shape of the antiferromagnetic region in panel e is of a very similar size and shape as that of the ferromagnetic region in panel f and the bottom panel of figure 2a. Is there a connection here between the mechanisms that give rise to each magnetic ground state?\n-(Figure 2) It would be very helpful for readers to label the filling factor on the panels of Figs. 2 b-e, in addition to where the authors have defined them in the caption, similarly to Fig. 3.\n-(Page 4 line 7) The authors have left out the MCD subscript on chi\n-(Page 4 line 10) In the hall resistivity data at v=1 filling, there still seems to be an appreciable plateau at 4K which seems to be missing from the MCD data. How do the authors explain this discrepancy?\n-(Page 4 line 35) The claim here about the first pure electric field control of an AFM-FM transition may be true, but the result is similar in spirit to that of (Huang, B., Clark, G., Klein, D.R. et al. Electrical control of 2D magnetism in bilayer CrI3. Nature Nanotech 13, 544–548 (2018)). The authors should reference the article and provide the distinction between the works.\n-(Figure 3) Panels d-e have no units on the field numbers of each panel. These plots should be readable without the caption and at present they are not.\n-(Figure 4) again, no units on the E field values on panels b and d\n-(Page 6 line 29) The authors repeatedly reference the critical field of switching the moire symmetry Ec but never state that value or indicate it on any of their plots. I think having a reference line on the plots or, at the very least, a statement of the field value of interest here would be helpful for readers so that they can understand the results without consulting the references.\n-Throughout the paper, I found the use of abbreviations and lack of definitions/labels very hard to follow. I suggest the authors go through the manuscript carefully to ensure that all abbreviated names, commonly used letters and symbols, and figures are well defined/labeled.", "reviewer_3": "This manuscript investigates the correlated states of twisted MoTe2 (tMoTe2) for twist angles 2.4 – 4.1 using a combination of magnetic circular dichroism (MCD), reflection contrast (RC), exciton sensing and transport. The authors find an intermediate region of twist angle around 3 degrees where the valley-polarized ferromagnetic (VP-FM) integer and fractional Chern insulators at filling 1 and 2/3 filling are suppressed at small displacement fields E. Close to the displacement field Ec that layer polarizes the system, the VP-FM reemerges before transitioning to a layer polarized Mott insulator at E> Ec. The authors propose a charge-transfer mechanism to explain the emergence of this VP-FM close to Ec. The VP-FM state at filling 1 also reappears at smaller twist angles. Based on the M-H and \\chi-T behavior, the authors propose that the ground state at intermediate angle and E is an out-of-plane antiferromagnet (VP-AFM).\nWhile I believe this manuscript presents extensive novel experiments that will be of great interest to the community, I have some issues regarding the clarity of the arguments and calculations that I feel should be addressed before publication in Nature Communications.\n1. Ref. [https://arxiv.org/abs/2507.22354] has performed nanoSQUID-on-tip on tMoTe2 for twist angles 2.1 to 3.7, finding VP-FM phases at filling 1 for all the angles, with a “triangular-like” shape of the VP-FM region similar to the one obtained in this study at angle 4.1 (which also contrasts with the 2.4 angle device of this work). What do the authors attribute these different phase diagrams to? Is there any clear difference in the samples, e.g.: what is the distance to the gates in each device? Can the authors estimate the disorder for the different twist angles?\n2. Personally, I feel that, until reading the SI section 7, it is not clear that the authors propose that the AFM state has out-of-plane spins (it is VP-AFM), in contrast to the much more understood IVC-AFM with in-plane spins (see e.g. Refs. [10.1103/PhysRevX.13.041026], [10.1103/PhysRevB.109.L041106] for tMoTe2, and [arXiv:2503.09689], [10.1103/m6c2-yd5j] for tWSe2). I would suggest the authors to clarify this point better along the paper.\nTo the best of my knowledge, the VP-AFM is a new state which has not been observed in experiments or theoretical calculations of tTMDs. The signatures that the authors use to support the VP-AFM with respect to the IVC-AFM (and the IVC-FM) are based on two experimental measures: (1) The magnetization has a plateau at small H and then increases suddenly, and (2) The susceptibility peaks at a finite temperature. I agree with the authors that these signatures are not compatible with a collinear antiferromagnet with magnetic field applied perpendicular to the easy axis, but I’m wondering whether the same applies for an in-plane 120 antiferromagnet with strong Ising SOC (a positive magnetorresistance has also been observed for the IVC-AFM phase in tWSe2 [https://doi.org/10.1038/s41586-024-08381-1]). I would appreciate if the authors could provide further comments or references for this.\n3. The authors propose a charge transfer mechanism to explain the reemergent VP-FM close to the layer polarization transition at intermediate angles. However, at smaller and larger angles, the strongest VP-FM occurs at E=0, following the exchange mechanism. Is there any reason why intermediate angles are special?\n4. Related to questions 2 and 3, in the discussion paragraph 18, I would suggest to clarify which type of AFM is predicted by the theory outside the VP-FM region; is it an IVC-AFM? If so, if the experimental ground state is really VP-AFM, this might have some implications for the exchange interactions / microscopic model assumed; would you expect these to change the charge transfer induced VP-FM? Are there any parameters in the phase diagram where the VP-AFM is the ground state?\n5. Is it possible to determine whether the reemergent VP-FM state at the smallest twist angle is topological or trivial? Refs. [10.1103/PhysRevX.13.041026], [10.1103/PhysRevB.109.L041106] predicted a transition from the Chern insulator to a trivial VP-FM state at small twist angles at filling 1.\n6. In page 4, lines 36-37, the authors state that “a pure electric-field-induced AFM-FM transition, which has never been observed in moiré systems and any other material systems, to the best of our knowledge”. A similar electric-field-induced trivial insulator to QAH transition has been observed in AB-MoTe2/WSe2 heterobilayers [https://doi.org/10.1038/s41586-021-04171-1, 10.1103/PhysRevX.14.011004] (although it is true that it is not clear whether whether the trivial insulator is a Mott insulator or it has already ordered as an AFM at the experimental temperatures).\n7. I was wondering whether it is possible to locate the (split) van Hove line in the density-displacement field diagram, and in this case whether its location coincides with the fillings 2/3 and/or 1 at the angles where the VP-FM disappears.\n8. In SI 5 (see also Fig. 7e), the authors suggest that the non-monotonic behavior of Rxx as a function of T might be due to the AFM order decreasing Rxx by freezing the magnetic fluctuations, and then the gap opening or disorder increasing Rxx at lower T. I was wondering whether the measured Rxx could also be compatible with the scenario proposed in Ref. [10.1103/PhysRevX.12.021064], where Rxx decreases due to the appearance of an in-gap quasiparticle peak, which the magnetic ordering kills when it onsets at lower T.\n9. 4. The meaning of RC (reflectance contract) should be defined before using it on page 3 line 1.\n10. 5. While I understand that the authors refer to the layer polarization crossover/transition by “superlattice symmetry transition”, I think it might be a bit confusing, since the C2 symmetry that relates MX and XM is already broken by a finite displacement field. I would suggest changing this term by “layer polarization”, which is more commonly used in the literature, or explaining this terminology before using it (e.g. in the abstract).\n11. In SI 1 page 2, I believe there is an errata: I think it should be t1 ~ sqrt(t2 U) instead of t2 ~ sqrt(t1 U). Also, in the Eq. At the top of page 2, I would suggest defining the interactions Ua, Ub beforehand. It would also be great if the authors could also explicitly say that \\Delta ~ U."}, "author_response": "Response to Reviewers' comments\nWe sincerely thank all three reviewers for carefully reviewing our work and for\nproviding highly insightful and constructive comments. Please find our detailed point-\nby-point responses below.\nReviewer #1 (Remarks to the Author):\nOverall comment:\nThe authors present a detailed study of tMoTe2 by tuning the twisting angle and vertical\nelectric field, along with changing temperatures and magnetic fields, probed by both\noptical and electrical approaches. They focus on the magnetic states for samples of\ndifferent conditions. The data sets are rich. There are a few major aspects the authors\ncan improve before further consideration of this manuscript.\nOverall Response: We sincerely thank the reviewer for the positive assessment of our\nwork and for the expert comments that have helped to improve the clarity, rigor, and\npresentation of our manuscript. Below, we carefully address the reviewer’s insightful\nquestions/comments point-by-point.\nComment #1: tMoTe2 is a system being intensively studied in the scientific field. What\nare the missing parts this work can contribute to? From both abstract and introduction,\nit is unclear what the new things this work brought to the community. The authors\nstarted with a brief introduction in abstract and introduction that tMoTe2 is a rich\nsystem in support of AQHE, but suddenly switched to talk about magnetism they found\nin this work. Some missing parts need to be provided so the readers can appreciate this\nwork in the context of what has been and not been achieved in the field.\nResponse #1: We thank the reviewer for the comments and suggestions that help to\nimprove our manuscript. Below, we summarize our principal advances:\n1). Discovery of antiferromagnetic (AFM) ground states at 𝑣 = 1 and 2/3 in twisted\n(cid:2918)\nMoTe at intermediate twist angles (θ ≈ 3.0°). While robust (Chern) ferromagnetism is\n2\nreported in devices with large twist angle (≈3.4–4.0°) and smaller (≤2.4°) at half and\nfractional fillings, the magnetic ground state at intermediate twist angles 𝜃~3° is\nunexplored. Our study bridges the previously unexplored intermediate-angle regime\nbetween robust FM/Chern phases (≈3.4–4.0° and ≤2.4°), discovering an unexpected\nantiferromagnetic (AFM) ground state and demonstrating that the magnetic ground\nstates in tMoTe is sensitive to the twist angle. To our knowledge, AFM order at these\n2\nfractional fillings in tMoTe has not been observed. Moreover, this is the first time that\n2\nan AFM-ordered phase has been observed in moiré material systems (also see\nResponse #6).\n2). Demonstration of a purely electric‑field (displacement‑field) driven sequence AFM\n→ FM (with integer/fractional Chern insulator, ICI/FCI) → paramagnet at fixed filling\n(v = 1, 2/3), with combining optical, transport, and Arrott analysis. This continuous\n(cid:2918)\nelectric control of AFM → FM within a single device has not been observed in other\nmaterial systems. See Main Fig. 3 and 4; ED Fig. 6 and 9.\nWe have rewritten the abstract to foreground these points, add explicit comparison with\nprior tMoTe studies, thereby clarifying what was “missing” and what we newly\n2\ncontribute. We hope that with the additional discussion presented above, the reviewer\nis more convinced of the novelty of our study.\nChanges in the manuscript:\nIn our revised manuscript, we have rewritten the abstract to emphasize what we newly\ncontribute according to the reviewer’s suggestion.\nComment #2: The readability of most figures is still low. It seems that figure 1d-f and\n1g-i have one-to-one correspondence. However, from these sub-figures\nthemselves, it is hard to read since g and h have the same legend yet different curves.\nThe same issue is for Figure b and c (these two sub-figures have the same noted curves),\nd and e. It is good to add brief legends to indicate the different conditions, based on\nwhich these data were acquired.\nResponse #2: We thank the reviewer for the comments and suggestions that help to\nimprove our manuscript. It’s true that figure 1d-f and 1g-i have one-to-one\ncorrespondence. We agree with the reviewer that we should add legends to better show\nthe correspondence and indicate the measurement conditions.\nChanges in the manuscript:\nIn our revised manuscript, we have updated Figure 1-3, and added extra legends to\nindicate show the correspondence and indicate the measurement conditions according\nto the reviewer’s suggestion.\nComment #3: Mechanism. The authors suggest “charge transfer” as the mechanism.\nWhat are the charge transfer coming from? It is transferred from metal electrode to the\ntMoTe2, or self doping by transfer between the two layers of tMoTe2? Why is it not\nbecause of electric field effect? The authors have top and bottom electrodes, which\nallow them to separate electric field and electrostatic doping effects by tuning the top\nand bottom electrodes separately. They should do this experiment and analysis.\nResponse #3: We thank the reviewer for raising this question, and we are sorry to\ncause this confusion. “Charge transfer” here refers to intra-moiré charge redistribution\nbetween the two layers of tMoTe , i.e., the two inequivalent moiré orbital centers (MX\n2\nand XM) sublattices induced by pure electric field 𝐸 at fixed total density (𝑣 ), not\n(cid:2918)\nextrinsic carrier injection from metal contacts. Our dual‑gate geometry already allows\nindependent control of filling (𝑣 ) and 𝐸-field through the linear combinations of the\n(cid:2918)\ntop (bottom) gate voltages. Specifically, the carrier density 𝑛 and electric field 𝐸 on the\nsample are converted from the top (bottom) gate voltage 𝑉 (𝑉 ) using a parallel plate\n(cid:2930) (cid:2912)\ncapacitor model: 𝑛 (cid:3404)\n(cid:3023)(cid:3178)(cid:3004)(cid:3178)(cid:2878) (cid:3023)\n(cid:3160)\n(cid:3004)\n(cid:3160) and 𝐸 (cid:3404)\n(cid:2869)\n(cid:4672)\n(cid:3023)(cid:3178)\n(cid:3398)\n(cid:3023)\n(cid:3160)(cid:4673)(cid:3398)𝐸 , where 𝑒 is the electron\n(cid:2925)(cid:2916)(cid:2916)(cid:2929)(cid:2915)(cid:2930)\n(cid:3032) (cid:2870) (cid:3031)(cid:3178) (cid:3031)\n(cid:3160)\ncharge, and 𝜀 is the vacuum permittivity and 𝐶 and 𝐶 are the top and bottom gate\n(cid:2868) (cid:2930) (cid:2912)\ncapacitance, 𝑑 and 𝑑 are the top and bottom h-BN thicknesses (see Methods section\n(cid:2930) (cid:2912)\n‘Determination of doping density and electric field’ for details). Therefore, the electric\nfield and electrostatic doping effects are already separated throughout our experiment\nand analysis. We have added a brief description to emphasize this point.\nChanges in the manuscript:\nIn our revised manuscript, we have added a brief description to clarify this issue (Page\n3, line 3) according to the reviewer’s suggestion.\nComment #4: It is possible that the AFM magnetization orientation is out of plane, as\nthe author speculated. But the author’s argument for this speculation appears\nproblematic. The authors thought if it is in-plane, the MCD should keep constant while\nB field is applied out of plane, which is not true. If the magnetic anisotropy is in-plane,\nit is likely the out of plane B field would gradually increase the MCD, and it is also\nlikely that out of plane B field would cause spin flop effect suddenly at a certain B field.\nResponse #4: We thank the reviewer for the comments and suggestions that help to\nimprove our manuscript. We wish to clarify that:\n1) Our statements concern the 𝜒 (cid:3404) 𝑑(cid:4666)𝑀𝐶𝐷(cid:4667)/𝑑𝐵, i.e., the slope of MCD-B at small\n(cid:2897)(cid:2887)(cid:2888)\nB, not the absolute MCD. For an in-plane collinear AFM under out-of-plane B (hard-\naxis), 𝜒 is expected to be approximately constant in the low-field regime, which\n(cid:2897)(cid:2887)(cid:2888)\noriginates from the spin canting process as mentioned by the reviewer (see Line 37,\nPage 7, and section 7 of the supplementary materials for details).\n2) Spin flop in an antiferromagnet happens only when an external magnetic field is\napplied along its easy axis; therefore, we would not expect to see the spin flop in an in-\nplane AFM under out-of-plane B field (see Figure S6c in section 7 of the supplementary\nmaterials).\nWe hope that with the above discussion, the reviewer will find our work clearer and\nmore convincing.\nComment #5: Multiple typos need to be fixed. “inplane” is not a word, should be in\nplane or in-plane. “our-of-plane” should be out-of-plane. “Honeycomb” (main text) and\n“Magnetic” (figure 1 caption) should not be capitalized in sentences.\nResponse #5: We thank the reviewer for pointing out these problems that help to\nimprove our manuscript. We are sorry for our carelessness. We have tried our best to\ncorrect the typos in our revised manuscript.\nChanges in the manuscript:\nIn our revised manuscript, all specified typos are corrected: “in-plane”, “out-of-plane”,\nlower‑case “honeycomb”, “magnetic”, etc.\nComment #6: Finally, the authors for a few times stressed the “unexpected” AFM\nstates. Why is it unexpected? I felt the field of study has reported such magnetic states\nmany times in different twisting systems. If I am wrong, please correct or clarify.\nResponse #6: We thank the reviewer for raising this question. Here we explain why we\nsay it's “unexpected” and clarify the essential differences between our observation and\nprevious works:\n1) It is known that integer and fractional QAH was observed in twisted bilayer\nMoTe with large twist angles (𝜃 ∼ 3.4°(cid:3398)3.9°), confirming the ferromagnetic\n2\n(FM)/Chern insulator states as their ground states. A recent study also reports the\nFM/Chern insulator state as the ground state in tMoTe with small twist angles 𝜃 (cid:3404)\n2\n2.1° [Nature 628, 522-526]. Therefore, it was previously widely assumed in the\ncommunity that the FM/Chern insulator states are the ground states in tMoTe within\n2\nthe fairly large relevant twist angle range (~2°(cid:3398)4°)[Nat Rev Mater 9, 460 (2024)].\nHowever, the magnetic and electronic ground states of tMoTe with intermediate twist\n2\nangle (𝜃~3°) remain largely unexplored, owing to the challenges in high-quality device\nfabrication and transport characterization. Therefore, the discovery of AFM ground\nstates at 𝑣 = 1 and 2/3 in twisted MoTe at intermediate twist angles (θ ≈ 3.0°) is in\n(cid:3035) 2\ncontrast to the previously established robust Chern ferromagnetism at larger (≈3.4–\n4.0°) and smaller (≤2.4°) angles, which is the reason we say it's “unexpected”\n2) To the best of our knowledge, an AFM-ordered phase has not been observed before\nin moiré material systems. The earlier works didn’t observe the AFM-ordered phase.\nWhat they reported is a paramagnetic phase with AFM exchange interaction. As the\nreviewer may notice, a paramagnetic phase with AFM exchange has been observed in\nseveral different moiré material systems [for example, Science 381, 325; Nature 597,\n350; Nature 579, 353; Nat Nanotechnol 18, 233]. However, none of them show AFM\norder, which is consistent with the geometric frustration in a triangular lattice, which is\nknown to suppress AFM order significantly. On the other hand, we have observed AFM\norders at both integer (𝑣 (cid:3404) 1) and fractional (𝑣 (cid:3404) 2/3) fillings in devices with\n(cid:3035) (cid:3035)\nintermediate twist angles 𝜃~3°. This is consistent with that the geometric frustration is\nabsent in the bipartite honeycomb lattice at small E, and finite temperature AF-ordering\nis favored.\nWe hope that with the additional discussion presented above, the reviewer is more\nconvinced of the novelty of our study.\nComment #7: In summary paragraph, please explain in a more clear manner what are\nthe major finding and proved mechanism, instead of only simply re-stating the\nexperimental observation.\nResponse #7: Again, we thank the reviewer for the comments and suggestions that\nhave helped us improve our manuscript. We have rewritten the summary paragraph to\nemphasize our main results and corresponding significances according to the reviewer’s\nsuggestion.\nChanges:\nIn our revised manuscript, we have rewritten the summary paragraph according to the\nreviewer’s suggestion.\nReviewer #2 (Remarks to the Author):\nOverall comment:\nIn the manuscript “Evidence of competing ground states between fractional Chern\ninsulator and antiferromagnetism in moiré MoTe2”, Chang et. al. present a surprising\nresult in the now famous twisted MoTe2 heterostructure device platform. Rather than\nfabricating devices in the ~3.7 degree range where the fractional quantum anomalous\nHall effect was first discovered, the authors study dual gated devices with a twist angle\nof ~3 degrees. Unlike 3.7deg devices at hole doping of 1 hole per moiré unit cell, which\npresent spontaneous symmetry breaking and an induced ferromagnetic state, they\nobserve signatures of antiferromagnetic order, such as vanishing MCD signals and Hall\nresistivity at zero magnetic field. Further, the authors show that they can use electric\nfields to fully tune the AFM-FM transition in the device as well as an AFM to Chern\ninsulating transition. I think the results are very exciting and open the door to another\nset of interesting phenomena in this rich system. The accessible interplay here between\nAFM, FM, and topological orders is an interesting one that warrants future work.\nHowever, I have reservations about recommending the manuscript for publication in its\n its\ncurrent form. The manuscript is lacking in many details and definitions that renders it\nunintelligible for any reader who is not already extremely knowledgeable about tMoTe2.\nFurther exacerbating the problem, there is a heavy use of acronyms and shorthand that,\nagain, might make the manuscript difficult to parse for a non-expert. I think that the\ndata quality and analysis of the work is highly appropriate for Nature Communications\nand I think the results will be interesting and exciting to those working in condensed\nmatter physics and 2D materials. As such, I recommend that the manuscript be accepted\nafter major revisions of the written text to improve clarity. Please see my comments\nbelow.\nOverall Response: We sincerely thank the reviewer for recommending the publication\nof our work and for providing many expert comments that have helped to improve our\nmanuscript. Below, we carefully address the reviewer’s insightful questions/comments\npoint-by-point.\nComment #8: -(Page 1, line 23) the authors have not defined what ν_h is. They should\nclarify that this is the hole filling factor for non-experts who read the manuscript.\nResponse #8: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript.\nChanges:\nIn our revised manuscript, we have added the definition of 𝜈 (Page 2, line 17)\n(cid:2918)\naccording to the reviewer’s suggestion.\nComment #9: -(Page 2, line 38) The manuscript never references Figure 1b\nResponse #9: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript.\nChanges:\nIn our revised manuscript, we have referenced and added a brief description of Figure\n1b (Page 3, line 1) according to the reviewer’s suggestion.\nComment #10: -(Page 3, line 1) The manuscript has not defined RC\nResponse #10: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We had defined RC in the caption of Fig. 1.\nHowever, we agree with the reviewer that it would be helpful for readers to define RC\nalso in the main text.\nChanges:\nIn our revised manuscript, we have added the definition of RC in the main text (Page 3,\nline 6).\nComment #11: -(Page 3, line 1) The authors are relatively unclear about whether they\nare tuning the hole doping of the system or the displacement field. I think simply\nmentioning ‘electric field’ is not enough given their dual-gated device geometry, they\nshould be more specific.\nResponse #11: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We have added a brief description to clarify that 𝐸\nand 𝜈 are tuned independently.\n(cid:3035)\nChanges:\nIn our revised manuscript, we have added a brief description to clarify this issue (Page\n3, line 3) according to the reviewer’s suggestion.\nComment #12: -(Page 4, line 4) While the authors define Tw in the caption of ED fig.\n9 and on page 7 they do not define it before its use here\nResponse #12: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript.\nChanges:\nIn our revised manuscript, we have added the definition of 𝑇 (Page 5, line 12)\n(cid:3050)\naccording to the reviewer’s suggestion.\nComment #13: -(Figure 1) the size and shape of the antiferromagnetic region in panel\ne is of a very similar size and shape as that of the ferromagnetic region in panel f and\nthe bottom panel of figure 2a. Is there a connection here between the mechanisms that\ngive rise to each magnetic ground state?\nResponse #13: We thank the reviewer for raising this interesting question. The\nsimilarity between Fig. 1e and Fig. 2a is due to the fact that the darkest region in Fig.\n1e represents the AFM state with the strongest exchange interaction. The stronger\nexchange interaction will give a larger magnetic susceptibility at temperatures above\nthe Neel temperature than a pure paramagnet, as each sublattice of spins in the AFM\ncan be regarded as FM ordered [for example, the 2L CrI case, Nat. Mat. 17, 406].\ncurrently, we propose that it could be related to the fact that both the AFM phase and\nthe FM phase boundaries are governed by layer polarization evolution, i.e., the\ngeometric similarity reflects the same underlying competition between\nsublattice‑balanced direct exchange and emerging charge‑transfer processes.\nComment #14: -(Figure 2) It would be very helpful for readers to label the filling factor\non the panels of Figs. 2 b-e, in addition to where the authors have defined them in the\ncaption, similarly to Fig. 3.\nResponse #14: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript.\nChanges:\nIn our revised manuscript, we have added labels of the filling factors in Figure 2\naccording to the reviewer’s suggestion.\nComment #15: -(Page 4 line 7) The authors have left out the MCD subscript on chi\nResponse #15: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript.\nChanges:\nIn our revised manuscript, we have corrected 𝜒 to 𝜒 where it’s used as magnetic\n(cid:3014)(cid:3004)(cid:3005)\nsusceptibility according to the reviewer’s suggestion.\nComment #16: -(Page 4 line 10) In the hall resistivity data at v=1 filling, there still\nseems to be an appreciable plateau at 4K which seems to be missing from the MCD\ndata. How do the authors explain this discrepancy?\nResponse #16: We thank the reviewer for raising this interesting question. Although\nwe do not have an exact answer, we propose two possible mechanisms:\n1) It could be related to the fact that different spatial regions are involved in these\ntwo measurements: MCD is a local probe (≈0.7 μm spot) while transport\naverages a much larger (possibly inhomogeneous) area of the sample.\n2) It could be related to the fact that the MCD detection is involved in some forms\nof photoexcitation effects, which could potentially affect the spin flipping\ndynamics (for example, the domain motion), that could result in the slightly\ndifferent M-B behavior measured by magneto-optics and electric transport.\nComment #17: -(Page 4, line 35) The claim here about the first pure electric field\ncontrol of an AFM-FM transition may be true, but the result is similar in spirit to that\nof (Huang, B., Clark, G., Klein, D.R. et al. Electrical control of 2D magnetism in bilayer\nCrI3. Nature Nanotech 13, 544–548 (2018)). The authors should reference the article\nand provide the distinction between the works.\nResponse #17: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We have referenced this article and provided the\ndistinction between the works according to the reviewer’s suggestion.\nChanges:\nIn our revised manuscript, we have referenced this article and added a brief description\nof the difference between the works (Page 4, line 41).\nComment #18: -(Figure 3) Panels d-e have no units on the field numbers of each panel.\nThese plots should be readable without the caption and at present they are not.\n-(Figure 4) again, no units on the E field values on panels b and d\nResponse #18: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We have fixed these issues according to the\nreviewer’s suggestion.\nChanges:\nIn our revised manuscript, we have added the units on the field numbers of Fig.3d-e\nand Fig.4b and 4d.\nComment #19: -(Page 6 line 29) The authors repeatedly reference the critical field of\nswitching the moire symmetry Ec but never state that value or indicate it on any of their\nplots. I think having a reference line on the plots or, at the very least, a statement of the\nfield value of interest here would be helpful for readers so that they can understand the\nresults without consulting the references.\nResponse #19: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We would like to point out that we have indicated\nthe value of 𝐸 in Fig. 1c and its caption as ‘The white dashed lines denote 𝐸 that\n(cid:3030) (cid:3030)\nseparate the layer-hybridized and layer-polarized regions.’ However, we agree with the\nreviewer that it would be helpful for readers to re-emphasize it in the main text.\nChanges:\nIn our revised manuscript, we have added the value of 𝐸 (Page 7, line 2) accordingly.\n(cid:3030)\nComment #20: -Throughout the paper, I found the use of abbreviations and lack of\ndefinitions/labels very hard to follow. I suggest the authors go through the manuscript\ncarefully to ensure that all abbreviated names, commonly used letters and symbols,\nand figures are well defined/labeled.\nResponse #20: We thank the reviewer for pointing out these problems that help to\nimprove our manuscript. We are sorry for our carelessness. We have tried our best to\ncorrect these issues in our revised manuscript.\nReviewer #3 (Remarks to the Author):\nOverall comment:\nThis manuscript investigates the correlated states of twisted MoTe2 (tMoTe2) for twist\nangles 2.4 – 4.1 using a combination of magnetic circular dichroism (MCD), reflection\ncontrast (RC), exciton sensing and transport. The authors find an intermediate region\nof twist angle around 3 degrees where the valley-polarized ferromagnetic (VP-FM)\ninteger and fractional Chern insulators at filling 1 and 2/3 filling are suppressed at small\ndisplacement fields E. Close to the displacement field Ec that layer polarizes the system,\nthe VP-FM reemerges before transitioning to a layer polarized Mott insulator at E> Ec.\nThe authors propose a charge-transfer mechanism to explain the emergence of this VP-\nFM close to Ec. The VP-FM state at filling 1 also reappears at smaller twist angles.\nBased on the M-H and \\chi-T behavior, the authors propose that the ground state at\nintermediate angle and E is an out-of-plane antiferromagnet (VP-AFM).\nWhile I believe this manuscript presents extensive novel experiments that will be of\ngreat interest to the community, I have some issues regarding the clarity of the\narguments and calculations that I feel should be addressed before publication in Nature\nCommunications.\nOverall Response: We sincerely thank the reviewer for the positive assessment of our\nwork and for the expert comments that have helped to improve our manuscript. We are\nthrilled to see that the reviewer found “…this manuscript presents extensive novel\nexperiments that will be of great interest to the community…”. Below, we carefully\naddress the reviewer’s insightful questions/comments point-by-point.\nComment #21: Ref. [https://arxiv.org/abs/2507.22354] has performed nanoSQUID-\non-tip on tMoTe2 for twist angles 2.1 to 3.7, finding VP-FM phases at filling 1 for all\nthe angles, with a “triangular-like” shape of the VP-FM region similar to the one\nobtained in this study at angle 4.1 (which also contrasts with the 2.4 angle device of\nthis work). What do the authors attribute these different phase diagrams to? Is there any\nclear difference in the samples, e.g.: what is the distance to the gates in each device?\nCan the authors estimate the disorder for the different twist angles?\nResponse #21: We thank the reviewer for raising this interesting question. Although\nwe do not have an exact answer currently, we propose several potential mechanisms\naccounting for the differences:\n1) As pointed out by the reviewer, it could be related to the different thickness of the\ndielectric layer. Typically, we use relatively thin hBN <10 nm for better optical contrast\nand larger (n, E) tuning range [Nature 600, 641]. Specifically, for the main device\nstudied here, we used hBN ~8 nm. This is close to the moire lattice constant of ~ 7 nm,\nwhere the dielectric screening could start to play a role. It has been demonstrated that\nthe change in dielectric environment could significantly affect the spin-exchange\ninteraction in the strongly correlated moire systems, both experimentally [Nat. Nano.\n18, 233] and theoretically [PRB 104, 214403; PRX.13.041026]. The similar shape of\nthe phase diagrams is also observed in the earlier work [Extended Data Fig. 8, Nature\n622, 69], where thin hBN (6-7 nm) is used. The dielectric screening effect on the\nstrongly correlated phases in tMoTe is certainly an interesting direction to explore for\n2\nour feature studies.\n2) It could be related to the difference in the twisted angle and the angle calibration\nmethod. In our study, the AFM state is found in a relatively narrow twist angle range\naround 3°. However, the closest angle studied in the arXiv paper is 3.3°, which is\nalready considerably deviated. Moreover, instead of using the more-accurate in-situ\nparameter-free calibration of the twist angle based on the Landau fan diagrams, as in\nour case [also see: Nature 622, 69; Nature 637, 839; Nature 637, 833; Nature 556, 80;\nNature 556, 43], their twist angle calculation depends on the atomic force microscope-\nmeasured hBN thickness and the adopted hBN dielectric constant, both of which are\nknown to have a certain margin of error. For example, based on a well-cited study, the\nstatic out-of-plane dielectric constant 𝜖 of bulk hBN is 3.76 [npj 2D Mater Appl 2, 6\n(cid:2884),(cid:2868)\n(2018)], instead of 3 adopted in the arxiv paper. This discrepancy of the hBN dielectric\nconstant will cause a significant deviation in the calculated twist angle (~0.4° difference\nbetween 𝜖 =3 and 3.76). Considering the 3.4° [Nature 622, 69] and 3.5° [Extended\n(cid:2884),(cid:2868)\nData Figure 3c,d of our manuscript] have already been demonstrated to have the FM\nground state, it is possible that the nominal 3.3° device studied in the arXiv paper is\nalready close to the larger angle scenario.\n3) It could be related to the different levels of the lattice structure reconstruction level\nin the small twist angle devices. Note that lattice structure relaxation/reconstruction\neffect becomes much more significant in moiré devices with smaller twist angles\n[Nature 602, 41 (2022)]. Moreover, the relaxation/reconstruction is strongly affected\nby the device fabrication process. This is one of the main reasons why the small twist-\nangle device, which in principle hosts stronger electronic correlation and thus exotic\nquantum phases, is so hard to fabricate or reproduce (for example, the Fractional\nquantum spin hall in the 2.1° device is still under debate. Nature 628, 522). The different\nshape of the FM phase of the 2.4° device could possibly align with this scenario.\nWe currently do not have a practical method to obtain the disorder density of the devices.\nHowever, the quantum mobility 𝜇 and disorder strength in our transport device can be\n(cid:3044)\nroughly estimated based on the onset magnetic field of quantum oscillations at low\ntemperatures in the transport measurement. When the disorder-induced Landau level\nbroadening is comparable with the Landau level spacing (gap), i.e., 𝛥𝐸 ~ ℎ𝑤 (cid:3404)\n𝑐\nℎ𝑒𝐵/𝑚∗, the quantum oscillations become unresolvable. As shown in Extended Data\nFig. 9, the onset magnetic field for quantum oscillations at 𝐸 (cid:3404) 57 𝑚𝑉/𝑛𝑚 at 1.5 𝐾\nis about 6(cid:3398)7 𝑇, corresponding to 𝜇 ~1500 𝑐𝑚(cid:2870)/𝑉𝑠 and 𝛥𝐸 ~ ℎ𝑤 ~ 0.5 𝑚𝑒𝑉~6 𝐾,\n(cid:3044) 𝑐\nassuming the band effective mass at 𝐸 (cid:3404) 57 𝑚𝑉/𝑛𝑚 is close to that of monolayer\nMoTe (~ 𝑚 ). Unfortunately, it's experimentally challenging to fabricate transport\n2 (cid:2868)\ndevices with smaller twist angles with decent quality.\nComment #22: Personally, I feel that, until reading the SI section 7, it is not clear that\nthe authors propose that the AFM state has out-of-plane spins (it is VP-AFM), in\ncontrast to the much more understood IVC-AFM with in-plane spins (see e.g. Refs.\n[10.1103/PhysRevX.13.041026], [10.1103/PhysRevB.109.L041106] for tMoTe2, and\n[arXiv:2503.09689], [10.1103/m6c2-yd5j] for tWSe2). I would suggest the authors to\nclarify this point better along the paper. To the best of my knowledge, the VP-AFM is\na new state which has not been observed in experiments or theoretical calculations of\ntTMDs. The signatures that the authors use to support the VP-AFM with respect to the\nIVC-AFM (and the IVC-FM) are based on two experimental measures: (1) The\nmagnetization has a plateau at small H and then increases suddenly, and (2) The\nsusceptibility peaks at a finite temperature. I agree with the authors that these signatures\nare not compatible with a collinear antiferromagnet with magnetic field applied\nperpendicular to the easy axis, but I’m wondering whether the same applies for an in-\nplane 120 antiferromagnet with strong Ising SOC (a positive magnetorresistance has\nalso been observed for the IVC-AFM phase in tWSe2 [https://doi.org/10.1038/s41586-\n024-08381-1]). I would appreciate if the authors could provide further comments or\nreferences for this.\nResponse #22: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We agree with the reviewer that while we can rule\nout the in-plane FM and in-plane collinear AFM but may not be able to rule out the\nIVC-AFM based on the discussion in SI section 7. As the reviewer may have noticed,\nwe only try to rule out the possibility of the in-plane FM phase in the main text (Page\n7, line 23 of the original version), and did not claim a definitive determination of VP-\nAFM in the main text, mainly for the following reasons:\n1) Theoretically, as also pointed out by the reviewer, the IVC-AFM is the more\nexpected candidate based on the theoretical works mentioned by the review and our\ncalculation [section 1 of the supplementary materials].\n2) Experimentally, although we think our experimental observation (the susceptibility\npeaks at a finite temperature and the magnetization plateau at small H) is more\nconsistent with VP-AFM, we cannot fully exclude potential counterexamples leading\nto IVC-AFM. For example, tWSe is believed to host the in-plane 120 IVC-AFM phase\n2\nin the earlier works mentioned by the reviewer [also arXiv:2412.14296]. However, a\nrecent experiment also observed the susceptibility peaks at a finite temperature [Fig. 2\nof arXiv:2508.02662, Nature in press], leaving it an open theoretical question whether\na susceptibility peak at a finite temperature is strong enough evidence to claim VP-\nAFM, instead of IVC-AFM.\nWith the above discussion, we hope the reviewer can understand why we are reluctant\nto make a strong claim of definitive determination of VP-AFM here. Spin-resolved\nscanning probe technic with nanometer-scale spatial resolution might be needed to fully\nreveal the spin texture of the AFM state, which is of great experimental challenge and\nbeyond the scope of this study.\nChanges:\nIn our revised manuscript, we have included the above discussion in SI section 7 and\nmodified our statement accordingly in SI section 7.\nComment #23: The authors propose a charge transfer mechanism to explain the\nreemergent VP-FM close to the layer polarization transition at intermediate angles.\nHowever, at smaller and larger angles, the strongest VP-FM occurs at E=0, following\nthe exchange mechanism. Is there any reason why intermediate angles are special?\nResponse #23: We thank the reviewer for this thoughtful question. In tMoTe , the\n2\nmagnetic order is governed by the competition between kinetic exchange and intersite\nHund’s coupling (the latter favoring ferromagnetism). At both very small and very large\ntwist angles, Hund’s coupling dominates and the ground state is ferromagnetic. At\nintermediate angles (≈3°), the kinetic-exchange contribution prevails, likely due to a\ntopological transition between the second and third bands, changing their Chern\nnumbers from (1,1) at large angles to (1,−1) near 3° [Communications Physics 7, 262\n(2024)].\nComment #24: Related to questions 2 and 3, in the discussion paragraph 18, I would\nsuggest to clarify which type of AFM is predicted by the theory outside the VP-FM\nregion; is it an IVC-AFM? If so, if the experimental ground state is really VP-AFM,\nthis might have some implications for the exchange interactions / microscopic model\nassumed; would you expect these to change the charge transfer induced VP-FM? Are\nthere any parameters in the phase diagram where the VP-AFM is the ground state?\nResponse #24: We thank the reviewer for this insightful question. Our calculations\nindicate that, outside the VP–FM region, an intervalley-coherent antiferromagnet\n(IVC–AFM) is energetically favored. In twisted tMoTe strong Ising spin–orbit\n2,\ncoupling locks spin to valley, so any valley-polarized state is necessarily spin-polarized;\naccordingly, we do not find a VP–AFM ground state anywhere in the phase diagram\nwe explored. Beyond the 120 AFM (stabilized by intravalley Fock exchange that\npromotes valley coherence), a natural competitor is an out-of-plane (z-axis) AFM,\nwhich can become the ground state if the intravalley Fock exchange is sufficiently\nweakened. That said, as noted in Response #22, current experimental data are\ninsufficient to determine the spin configuration of the AFM state unambiguously.\nComment #25: Is it possible to determine whether the reemergent VP-FM state at the\nsmallest twist angle is topological or trivial? Refs. [10.1103/PhysRevX.13.041026],\n[10.1103/PhysRevB.109.L041106] predicted a transition from the Chern insulator to a\ntrivial VP-FM state at small twist angles at filling 1.\nResponse #25: We thank the reviewer for raising this interesting question. As pointed\nout by the reviewer, earlier theoretical works predict a Chern insulator to a trivial VP-\nFM state at a critical twist angle of ~2.5°. To the best of our knowledge, the smallest\ntwist angle that is systematically studied is 2.1°, where Fractional quantum spin hall\nhas been reported [Nature 628, 522]. Chern insulator is observed at filling 1at this angle,\nmeaning the Chern insulator to a trivial VP-FM transition, if there is, should happen at\na smaller twist angle. As discussed in Response #21, it is of great experimental change\nto fabricate high quality tMoTe device with smaller twist angle than 2.1°, because the\n2\nlattice structure relaxation/reconstruction effect becomes much more significant in\nmoiré devices with twist angles [Nature 602, 41 (2022)], and that’s one of the main\nreasons why the Fractional quantum spin hall in the 2.1° device has not been reproduced\nby any other groups. Therefore, although the transition from the Chern insulator to a\ntrivial VP-FM state at small twist angles at filling 1 is a very interesting direction to\nexplore, performing this experimental study is highly challenging and beyond the scope\nof this study.\nComment #26: In page 4, lines 36-37, the authors state that “a pure electric-field-\ninduced AFM-FM transition, which has never been observed in moiré systems and any\nother material systems, to the best of our knowledge”. A similar electric-field-induced\ntrivial insulator to QAH transition has been observed in AB-MoTe2/WSe2\nheterobilayers [https://doi.org/10.1038/s41586-021-04171-1,\n10.1103/PhysRevX.14.011004] (although it is true that it is not clear whether whether\nthe trivial insulator is a Mott insulator or it has already ordered as an AFM at the\nexperimental temperatures).\nResponse #26: We thank the reviewer for the comments and suggestions that help to\nimprove our manuscript. We wish to point out the essential differences between our\ncurrent observation and the observation in MoTe /WSe heterobilayer (which happens\n2 2\nto be our earlier work).\n1) As the reviewer also noticed, no evidence of AFM order is observed in MoTe /WSe .\n2 2\nWhat is reported in MoTe /WSe is a paramagnetic Mott insulator with AFM exchange\n2 2\ninteraction. In fact, paramagnetic Mott insulators with AFM exchange interaction have\nalso been observed in other moiré material systems [for example, WSe /WS\n2 2\nheterobilayers, Nature 579, 353; Nat Nanotechnol 18, 233], as well as in our tMoTe\n2\ndevice at 𝐸 (cid:3408) 𝐸 . However, none of them show AFM order. This is consistent with the\n(cid:3030)\ngeometric frustration in a triangular lattice, which is known to suppress AFM order\nsignificantly. On the other hand, we have observed AFM orders at both integer (𝑣 (cid:3404)\n(cid:3035)\n1) and fractional (𝑣 (cid:3404) 2/3) fillings in devices with intermediate twist angles 𝜃~3°.\n(cid:3035)\nThis is consistent with the fact that the geometric frustration is absent in the bipartite\nhoneycomb lattice at small E, and finite temperature AF-ordering is favored.\n2) The underlying physical mechanisms of these two cases are different. The\nparamagnetic Mott insulators with AFM exchange interaction reported in MoTe /WSe\n2 2\nare observed when charges are polarized on one sublattice, forming a half-filled\ntriangular lattice. The AFM exchange interaction, in this case, is expected theoretically\nby the triangular-lattice Hubbard model, i.e., antiferromagnetic superexchange\ninteraction of 𝐽 ∼ 𝑡(cid:2870)/𝑈 [Rev. Mod. Phys. 90, 025003; PRL. 121, 026402; PRB 73,\n(cid:2870)\n235107; PRB 89, 161118]. On the other hand, the AFM order observed in our device\nappears at ~𝐸 (cid:3404) 0, where the system is effectively a quarter-filled honeycomb lattice\nwithout geometric frustration.\n3) The FM-AFM transition in these two cases also has different underlying\nmechanisms. In MoTe /WSe , the FM-AFM transition is induced by the layer\n2 2\npolarization transition, i.e., from Hund’s FM in the honeycomb lattice to AFM\nexchange in the triangular lattice. As a result, the magnetic phase transition and layer\npolarization share the same critical 𝐸 field. In our case, the magnetic phase transition\nis induced by the minority charges transferred into the 𝐵 sublattice, which happens\nbefore charges are fully polarized on one layer. Therefore, they do not share the same\ncritical 𝐸 field.\nWe hope that with the above discussion, the reviewer is more convinced of the novelty\nof our study. However, we do understand the reviewer’s concern, and we added a brief\ndescription of the essential differences between these two cases in the revised version.\nChanges:\nIn our revised manuscript, we have included the above references, added a brief\ndescription of the essential differences between these two cases, and modified the above\nstatement accordingly.\nComment #27: I was wondering whether it is possible to locate the (split) van Hove\nline in the density-displacement field diagram, and in this case whether its location\ncoincides with the fillings 2/3 and/or 1 at the angles where the VP-FM disappears.\nResponse #27: In transport measurements, the van Hove singularity is typically\ncharacterized by a local peak in Rxx and a concomitant vanishing of 𝑅 . In the present\n(cid:2934)(cid:2935)\ndevice with a twist angle of approximately 3.15 degrees, we didn’t observe the van\nHove line at or below filling factor 1.\nComment #28: In SI 5 (see also Fig. 7e), the authors suggest that the non-monotonic\nbehavior of Rxx as a function of T might be due to the AFM order decreasing Rxx by\nfreezing the magnetic fluctuations, and then the gap opening or disorder increasing Rxx\nat lower T. I was wondering whether the measured Rxx could also be compatible with\nthe scenario proposed in Ref. [10.1103/PhysRevX.12.021064], where Rxx decreases\ndue to the appearance of an in-gap quasiparticle peak, which the magnetic ordering kills\nwhen it onsets at lower T.\nResponse #28: We thank the reviewer for the suggestions that helped improve our\nmanuscript. At a finite displacement field, the Wannier centers of the lowest two bands\nform a honeycomb lattice consisting of two triangular sublattices. Under a large\nsublattice potential difference, the honeycomb lattice reduces to a triangle lattice, and\nthe Hubbard model proposed in PhysRevX.12.021064 provides an effective description\nof the system. As predicted in that work, a quasiparticle peak appearing inside the\nHubbard gap can account for the experimentally observed decrease of 𝑅 with\n(cid:2934)(cid:2934)\nlowering temperature above ~6 K, explaining the experimental observations. Once\nmagnetic order develops at lower temperatures, the system becomes fully gapped,\nleading to an increase in 𝑅 —again consistent with experimental observations. While\n(cid:2934)(cid:2934)\nin our data, the behavior of resistance first decreasing and then increasing with lowering\n𝑇 is most evident at small displacement fields, it remains possible that the same\nmechanism contributes more generally.\nChanges:\nIn our revised manuscript (Page 6, line 27) and SI 5, we have included the above\nreferences, mentioning the possibility that the resistivity contributed by the in-gap\nquasiparticle peak in high temperature.\nComment #29: The meaning of RC (reflectance contract) should be defined before\nusing it on page 3 line 1.\nResponse #29: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We have defined RC in the caption of Fig. 1.\nHowever, we agree with the reviewer that it could be helpful for readers to define RC\nalso in the main text.\nChanges:\nIn our revised manuscript, we have added the definition of RC in the main text (Page 3,\nline 6) according to the reviewer’s suggestion.\nComment #30: While I understand that the authors refer to the layer polarization\ncrossover/transition by “superlattice symmetry transition”, I think it might be a bit\nconfusing, since the C2 symmetry that relates MX and XM is already broken by a finite\ndisplacement field. I would suggest changing this term by “layer polarization”, which\nis more commonly used in the literature, or explaining this terminology before using it\n(e.g. in the abstract).\nResponse #30: We thank the reviewer for the comments and suggestions that have\nhelped us improve our manuscript. We agree with the reviewer that ‘layer polarization’\nis more rigorous than ‘superlattice symmetry transition’, considering the intermediate\ndisplacement field case.\nChanges:\nIn our revised manuscript, we have replaced ‘superlattice symmetry transition’ with\n‘layer polarization’ according to the reviewer’s suggestion.\nComment #31: In SI 1 page 2, I believe there is an errata: I think it should be t1 ~\nsqrt(t2 U) instead of t2 ~ sqrt(t1 U). Also, in the Eq. At the top of page 2, I would\nsuggest defining the interactions Ua, Ub beforehand. It would also be great if the\nauthors could also explicitly say that \\Delta ~ U.\nResponse #31: We apologize for the confusion caused here. It should indeed be 𝑡 ∼\n(cid:2869)\n(cid:3493)|𝑡 |𝑈. We clarify that 𝑈 ,𝑈 represent the on-site Hubbard interaction on sites\n(cid:2870) (cid:3028) (cid:3029)\nbelonging to A and B sublattices, respectively: 𝐻 (cid:3404) 𝑈 ∑ 𝑛 𝑛 (cid:3397)\n(cid:3022) (cid:3028) (cid:3036)∈(cid:3002) (cid:3036)↑ (cid:3036)↓\n𝑈 ∑ 𝑛 𝑛 . We also add the condition where our formalism remains in the\n(cid:3029) (cid:3036)∈(cid:3003) (cid:3036)↑ (cid:3036)↓\nperturbative regime: 𝑈 ≫ 𝑡 ,𝛥 ∼ 𝑈 ∼ 𝑈 , and 𝑡 ∼ (cid:3493)|𝑡 |𝑈 .\n(cid:2870) (cid:3028) (cid:3029) (cid:2869) (cid:2870) (cid:3028)\nChanges:\nIn our revised SI section 1, we fixed the typo, added the definition of 𝑈 ,𝑈 , and\n(cid:3028) (cid:3029)\nclarify the regime where perturbative theory remains valid."}, {"round": 2, "reviewer_comments": {"reviewer_2": "MY issues have been sufficiently addressed in the revised manuscript and I am happy to recommend the manuscript be published in Nature Communications in its current form.", "reviewer_3": "I thank the authors for their detailed responses and appropriate changes to the manuscript. I recommend publication in Nature Communications once these minor comments are addressed.\n1. The authors associate that the AFM at small displacement fields is ordered thanks to the absence of geometric frustration in the honeycomb lattice, in contrast to the triangular lattice paramagnetic insulator at the layer polarized regime (see e.g. lines 13-18 in page 5). As far as I understand, the absence of geometric frustration in the honeycomb lattice applies to the possibility of a collinear AFM, but the 120 AFM is frustrated. As the authors carefully explained in the response and added to the SM, it is difficult to discard the later (also the in-plane collinear AFM seems less likely according to their arguments in SM section 7). The experimental results are very interesting and worth publishing even if the particular order of the AFM is not fully settled. Therefore, I would suggest to be more honest and explain this (it is ok to mention the arguments in the SM and the frustration to say that maybe a collinear z-AFM is more compatible, but other options cannot be discarded). Along these lines, I would also mention this in figure 12, where the left image of panel (a) and the caption indicate collinear AFM order.\n2. As the authors carefully explained in the response and page 5, the electric-field tuned FM to paramagnetic insulator was previously realized by the authors in Mote2/WSe2, as well as in other tMoTe2 experiments. However, the abstract says that both the AFM-FM (which as explained by the authors is new in moiré systems) and the FM-paramagnet electric-field tuned transitions are new in moire systems. I would suggest highlighting that only the former is new.", "reviewer_4": "Regarding the charge transfer mechanism and AFM magnetization orientation, I think the authors have provided a convincing response. Specifically:\nFirst, the authors clearly point out that charge transfer refers to intra-moire charge redistribution between the two layers of tMoTe₂, not extrinsic carrier injection from metal contacts. Meanwhile, the dual-gate structure allows them to independently tune the charge carrier density and the displacement field, which has been discussed in the main text, SI, and the response letter. The authors’ response is reasonable and clear.\nSecond, the authors have a detailed discussion on the AFM magnetization orientation in the SI. In the response letter, they have pointed out that χ_MCD, rather than the MCD signal itself, is expected to be approximately constant in the low-field regime for in-plane collinear AFM, which directly addresses Reviewer 1’s question. The reviewer’s statement about the spin-flop transition was incorrect. The authors also note that the reviewer’s description was inaccurate, and they have provided the correct interpretation.\nOverall, I think the authors' response is convincing and clear."}, "author_response": "Response to Reviewers' comments\nWe sincerely thank all three reviewers for carefully reviewing our work and for\nproviding highly insightful and constructive comments. Please find our detailed point-\nby-point responses below.\nReviewer #2 (Remarks to the Author)\nMy issues have been sufficiently addressed in the revised manuscript and I am happy\nto recommend the manuscript be published in Nature Communications in its current\nform.\nOverall Response: We sincerely thank the reviewer for recommending the publication\nof our work and for providing many expert comments that have helped to improve our\nmanuscript.\nReviewer #3 (Remarks to the Author)\nOverall comment:\nI thank the authors for their detailed responses and appropriate changes to the\nmanuscript. I recommend publication in Nature Communications once these minor\ncomments are addressed.\nOverall Response: We sincerely thank the reviewer for recommending the publication\nof our work and for providing many expert comments that have helped to improve our\nmanuscript. Below, we carefully address the reviewer’s insightful questions/comments\npoint-by-point.\nComment #1: The authors associate that the AFM at small displacement fields is\nordered thanks to the absence of geometric frustration in the honeycomb lattice, in\ncontrast to the triangular lattice paramagnetic insulator at the layer polarized regime\n(see e.g. lines 13-18 in page 5). As far as I understand, the absence of geometric\nfrustration in the honeycomb lattice applies to the possibility of a collinear AFM, but\nthe 120 AFM is frustrated. As the authors carefully explained in the response and added\nto the SM, it is difficult to discard the later (also the in-plane collinear AFM seems less\nlikely according to their arguments in SM section 7). The experimental results are very\ninteresting and worth publishing even if the particular order of the AFM is not fully\nsettled. Therefore, I would suggest to be more honest and explain this (it is ok to\nmention the arguments in the SM and the frustration to say that maybe a collinear z-\nAFM is more compatible, but other options cannot be discarded). Along these lines, I\nwould also mention this in figure 12, where the left image of panel (a) and the caption\nindicate collinear AFM order.\nResponse #1: We thank the reviewer for this very thoughtful and fair comment. We fully agree\nthat our experimental data establish the presence of an AFM‐like insulating state, but do not\nuniquely fix the detailed spin configuration. In the revised manuscript, we have therefore\nsoftened the wording and clarified our interpretation accordingly.\nChanges:\nIn our revised manuscript, we have added brief discussion accordingly in Line 8 page\n5, read:\n‘The AFM state at small displacement fields is compatible with the unfrustrated\ncollinear z‑AFM on the effective honeycomb lattice, in contrast to the geometrically\nfrustrated triangular lattice in the layer‑polarized regime. However, our present\nmeasurements do not uniquely fix the detailed spin configuration, other AFM patterns,\nincluding non‑collinear 120°‑like states, cannot be rigorously excluded (see\nSupplementary Section 7).’\nAnd in the caption of ED Fig. 12, read:\n‘The left image is a schematic illustration of one possible collinear z‑AFM\nconfiguration on the effective honeycomb lattice at small displacement field. The\nschematic highlights that such a state can avoid geometric frustration on the honeycomb\nlattice. The present experiments, however, do not uniquely determine the detailed AFM\nspin pattern, and other AFM configurations (e.g. non‑collinear states) cannot be\nexcluded.’\nComment #2: As the authors carefully explained in the response and page 5, the\nelectric-field tuned FM to paramagnetic insulator was previously realized by the authors\nin Mote2/WSe2, as well as in other tMoTe2 experiments. However, the abstract says\nthat both the AFM-FM (which as explained by the authors is new in moiré systems) and\nthe FM-paramagnet electric-field tuned transitions are new in moire systems. I would\nsuggest highlighting that only the former is new.\nResponse #2: We thank the reviewer for pointing out this important clarification\nregarding what is genuinely new in our work. We fully agree that electric‑field–tuned\ntransitions between a ferromagnet and a paramagnetic insulator have already been\nreported in MoTe₂/WSe₂ heterobilayers and in other tMoTe₂ experiments. What is new\nin the present study is the electric‑field–driven transition between an antiferromagnetic\ninsulating state and a Chern ferromagnetic state in a moiré system, together with their\ndirect competition at fixed filling.\nChanges:\nIn our revised manuscript, we have revised the corresponding sentence in the Abstract,\nnow read:\n‘We observe a pure electric‑field–driven transition between an antiferromagnetic\ninsulating state and an integer/fractional Chern ferromagnetic state at fixed filling\nfactors ( = 1, 2/3), revealing a new type of magnetic ground states competition in\nmoiré systems.’\n𝑣𝑣h\nReviewer #4 (Remarks to the Author):\nRegarding the charge transfer mechanism and AFM magnetization orientation, I think\nthe authors have provided a convincing response. Specifically:\nFirst, the authors clearly point out that charge transfer refers to intra-moire charge\nredistribution between the two layers of tMoTe₂, not extrinsic carrier injection from\nmetal contacts. Meanwhile, the dual-gate structure allows them to independently tune\nthe charge carrier density and the displacement field, which has been discussed in the\nmain text, SI, and the response letter. The authors’ response is reasonable and clear.\nSecond, the authors have a detailed discussion on the AFM magnetization orientation\nin the SI. In the response letter, they have pointed out that χ_MCD, rather than the MCD\nsignal itself, is expected to be approximately constant in the low-field regime for in-\nplane collinear AFM, which directly addresses Reviewer 1’s question. The reviewer’s\nstatement about the spin-flop transition was incorrect. The authors also note that the\nreviewer’s description was inaccurate, and they have provided the correct interpretation.\nOverall, I think the authors' response is convincing and clear.\nOverall Response: We sincerely thank the reviewer for the positive assessment of our\nwork."}]

Decision letter