ofb(0.227) and also defines the susceptibility
critical exponent asg= 2.2, the latter falling rea-
sonably in the range estimated from the high-
temperature series expansions for the 2D-XY
model,g= 2.4 ± 0.3 ( 45 ). However, although
the linear fits and the evolution of the inter-
cepts are reasonable for this set of critical expo-
nents, the Arrott-plot analysis is not as accurate
as the temperature-dependent magnetization
to determineTc(i.e., the high-field data of 12.5 K
and 13 K fall under the same fitting range). [See
( 34 ) for more details about issues in the deter-
mination of the susceptibility exponentgof
2D-XY systems]. These results have been repro-
duced on a second sample with a slightly dif-
ferentTcbutshowingthesameXYuniversality
scaling, demonstrating that monolayer CrCl 3
grown by MBE is an easy-plane magnet (see
table S1 and fig. S8 for the additional datasets).
The very good agreement between the crit-
ical exponentband the theoretically expected
value is attributed to the 2D-XY features of our
samples: vanishing in-plane crystalline anisot-
ropy fields, negligible substrate interaction, and
a relatively large magnetic coherence sizeLof
the CrCl 3 monolayer owing to a homogeneous,
atomically flat morphology on the graphene
substrate. (Other relevant 2D universality scaling
models fail to describe our data; see fig. S9.) The
observed 2D-XY ordering in monolayer CrCl 3
suggests that the nature of the phase transi-
tion is of the BKT type. This universal phase
transition has been observed in other physi-
cal systems such as superconductors ( 46 , 47 ),
atomic surface reconstructions ( 48 ), and quasi-
condensates of atomic gases ( 49 ). In magnetic
systems, this transition has been argued to
occur in metallic monolayers grown on crys-
talline substrates ( 50 , 51 ) and in layered bulk
magnets ( 52 ). However, the strong substrate
interaction in the first case, and interlayer
exchange in the second case, might cause a
departure from ideal 2D-XY behavior where
the BKT transition is expected. We believe
that our CrCl 3 system, a quasi–free-standing
van der Waals monolayer, is a more suitable
setting for a magnetic BKT transition to take
place. Further studies on finite-size effects
and exponential scaling of the magnetic cor-
relation length are needed to fully assess this
conjecture. In a very recent theoretical work,
a transport signature of the BKT transition
in magnetic easy-plane systems has been for-
mulated ( 53 ), which perfectly applies to our
CrCl 3 monolayer and will yield additional
insights on the spin transport phenomena of
2D easy-plane magnets, which are expected
to reach the spin superfluidity regime ( 54 ).
We have shown that a CrCl 3 monolayer, fea-
turing van der Waals coupling to the graphene
substrate and hexagonal symmetry in the
plane but without strict single-crystalline long-
range order, constitutes a nearly ideal realiza-
tion of a 2D-XY magnetic system. The van der
Waals nature at the CrCl 3 /substrate interface
minimizes effects such as hybridization, bond-
ing, and substrate-driven crystalline anisot-
ropy fields; these factors can drive the system
into an Ising or anisotropic Heisenberg type, or
may even cause a departure from 2D behavior
by strong substrate interaction. The in-plane
hexagonal crystal symmetry (XYh6) of CrCl 3 ,
on the other hand, is the least perturbative
for the XY model ( 6 ) and is additionally dimin-
ished in our experimental system as a result of
the in-plane twisting of crystalline domains.
As compared with bulk layered magnets, our
monolayer system has no interplanar exchange
couplingJex,inter, which is also a perturbation
of ideal 2D-XY behavior and dimensionality. A
follow-up study of possible interest would con-
sist of gently turning on in-plane anisotropy
fields by choosing different rigid substrates
with strong crystalline fields or a given step
terrace morphology, and seeing how this af-
fects the 2D-XY behavior of the monolayer. In
that way, recipes to attain a crossover to Ising-
type (uniaxial anisotropy) behavior may be
developed, offering a useful pathway to the
design of on-demand magnetic anisotropies
for functional spintronic devices based on 2D
materials. On a more fundamental side, the
finite-size effects of the BKT phase transition
can be studied by modifying the grain size
and percolation behavior of the MBE-grown
monolayers. Moreover, an epitaxy-controlled
trigonal distortion could be used as an exper-
imental parameter to set the balance between
single-ion anisotropy and dipolar interaction
in CrCl 3 , which is crucial for stabilizing topo-
logical spin textures such as merons ( 55 , 56 ) in
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ACKNOWLEDGMENTS
A.B.-P. thanks the HZB and CELLS-ALBA for the allocation of
synchrotron radiation beamtime under proposals 192-08773-ST and
202-09917-ST (HZB) and 2019-093862 (CELLS-ALBA). We thank
F. Küster for assistance with the LT-STM measurements and C. Luo,
K. Chen, S. Thakur, and S. Rudorff for technical support at BESSY.
Funding:F.R. and A.B.-P. acknowledge financial support for the
VEKMAG project and for the PM2-VEKMAG beamline by the German
Federal Ministry for Education and Research (BMBF 05K10PC2,
05K10WR1, 05K10KE1) and by HZB. M.V. and P.G. acknowledge
additional beamtime through ALBA IHR and proposal ID
2019023487-2, and funding via grants FIS2016-78591- C3-2-R
(AEI/FEDER, UE) and FlagEra Sograph MEM PCI2019- 111908-2.
K.C. was funded by National Natural Science Foundation of China
(grant 12074038).Author contributions:A.B.-P., K.C., and S.S.P.P.
conceived of the study, and A.B.-P. was the lead researcher. A.B.-P.
carried out the magnetic characterization by XAS/XMCD, analyzed the
data, and wrote the manuscript. J.-R.J. grew the samples for the
beamtimes and performed the in situ RHEED and STM characterization.
K.C. initiated and optimized the substrate preparation and epitaxial
growth. P.S. performed the low-temperature STM characterization.
J.-R.J., A.K.P., J.M.T., and F.R. assisted with the XMCD measurements
in BESSY; P.G. and M.V. assisted and performed part of the XAS/
XMCD experiments in ALBA. All authors discussed the data and
commented on the manuscript. S.S.P.P. supervised the entire project.
Competing interests:The authors declare no competing interests.
Data and materials availability:All data discussed in the main text or
the supplementary materials are uploaded in Zenodo ( 57 ).SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abd5146
Materials and Methods
Supplementary Text
Figs. S1 to S12
Table S1
References ( 58 – 67 )
25 June 2020; resubmitted 6 February 2021
Accepted 15 September 2021
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