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ACKNOWLEDGMENTS
We thank F. Sterl and F. Mörz for contributions to the experimental
setup and L.-S. Hornberger and B. Gompf for contributions to the
ellipsometry measurements.Funding:We acknowledge financial
support from Baden-Wuerttemberg-Stiftung (Opterial), the European
Research Council (ERC Advanced Grant Complexplas and ERC PoC
Grant 3DPrintedOptics), Bundesministerium für Bildung und
Forschung, Deutsche Forschungsgemeinschaft (SPP1839 Tailored
Disorder and GRK2642 Photonic Quantum Engineers), the Institute
of Quantum Science and Technology (IQST), the University of
Stuttgart (Terra Incognita), the Carl Zeiss Foundation, and the Vector
Foundation.Author contributions:J.K., M.H., and H.G. conceived
the project. J.K. and M.U. fabricated the samples. J.K. and M.F.
performed the measurements. J.K. carried out the data analysis.
C.D., C.M., and T.S. contributed to the experimental setup, sample
fabrication, and measurements. H.G., M.H., and S.L. supervisedthe project. All authors discussed the results and contributed to
manuscript writing.Competing interests:J.K., M.H., and H.G. have
filed an international patent related to the topic of this work
(PCT/EP2021/069202).Data and materials availability:All data
needed to evaluate the conclusions in the paper are present in
the paper and/or the supplementary materials.SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abj3433
Materials and Methods
Figs. S1 to S7
Reference ( 34 )
Movie S1
10 July 2021; accepted 13 September 2021
10.1126/science.abj3433MAGNETISM
Intrinsic 2D-XY ferromagnetism
in a van der Waals monolayer
Amilcar Bedoya-Pinto^1 †, Jing-Rong Ji^1 †, Avanindra K. Pandeya^1 , Pierluigi Gargiani^2 ,
Manuel Valvidares^2 , Paolo Sessi^1 , James M. Taylor^3 , Florin Radu^3 , Kai Chang^1 , Stuart S. P. Parkin^1 *
The physics and universality scaling of phase transitions in low-dimensional systems has historically been a
topic of great interest. Recently, two-dimensional (2D) materials exhibiting intriguing long-range magnetic
order have been in the spotlight. Although an out-of-plane anisotropy has been shown to stabilize 2D
magnetic order, the demonstration of a 2D magnet with in-plane rotational symmetry has remained elusive.
We constructed a nearly ideal easy-plane system, a single CrCl 3 monolayer on graphene/6H-SiC(0001),
and observed robust ferromagnetic ordering with critical scaling characteristic of a 2D-XY system. These
observations indicate the realization of a finite-size Berezinskii-Kosterlitz-Thouless phase transition in
a large-area, quasiÐfree-standing van der Waals monolayer magnet with an XY universality class. This offers a
material platform to host 2D superfluid spin transport and topological magnetic textures.
H
ow reduced dimensionality affects phys-
ical properties is a question that has fas-
cinated researchers for decades. Recent
technological advances have enabled the
study of truly one- and two-dimensional
systems. In this context, theoretical models
of low-dimensional magnetism have been
revisited. It was recognized early that the
absence of long-range magnetic order in a
low-dimensional system (d< 3) with contin-
uous symmetry, postulated by Mermin and
Wagner ( 1 , 2 ), could be remedied by the exis-
tence of a sizable magnetic anisotropy. In 2D
systems with easy-plane anisotropy, an unusual
long-range order is expected to emerge as a
result of the formation of magnetic vortex-
antivortex or chirally opposing domain wall–
bound pairs, theoretically described by the
Berezinskii-Kosterlitz-Thouless (BKT) formal-
ism ( 3 – 5 ). This implies the occurrence of a
phase transition even in a 2D magnetic sys-
tem with continuous rotational symmetryO(2).
This theory was later adapted to account for
symmetry-breaking fields ( 6 – 8 ),finite size
effects ( 9 , 10 ), and spin-wave interactions with
magnetic vortices ( 11 ).The work in ( 6 ), ( 7 ), ( 9 ),
and ( 11 ) allowed the quantification of the order
parameters and critical scaling near the phase
transition for each scenario. A renormalization
group approach was used to show that the
magnetization of finite-sized 2D easy-plane
systems—also called 2D-XY—scales with a crit-
ical exponent ofb=3p^2 /128≈0.231, defining a
fingerprint of the XY universality class ( 9 , 12 ).
Perturbations to the rotational invariance of
the spins in the plane—such as the symmetry
and strength of magnetocrystalline fields—have
been shown to strongly influence the critical
exponents and the universality class. Whereas a
uniaxial in-plane anisotropy (XYh 2 ) drives the
system into an Ising-type behavior (b= 0.125),
the effect of a four-fold symmetry (XYh 4 ) is
highly dependent on the crystal field strength,
with critical exponents ranging between Ising
and XY universality classes ( 13 ). In contrast, the
hexagonal symmetry (XYh 6 ) barely affects the
magnetic behavior ( 4 , 6 , 7 ) even in the limit of
strong crystal fields ( 13 ), such that the system
remains in the XY class, thereby enabling the
observation of a BKT-type phase transition.A large number of experiments on quasi-2D
magnetic systems, such as monolayers on crys-
talline metallic surfaces or bulk layered magnets
with small interplanar exchange interactions,
have contributed to the assessment of the afore-
mentioned theories [see ( 13 , 14 ) for reviews].
However, in those cases, the substrate interac-
tion through bonding and hybridization (mono-
layers on surfaces) and the small amount of
interplanar exchange (layered magnets) were
conditions that precluded the realization of an
ideal 2D system. Recent advances in the isola-
tion and preparation of crystalline monolayers
from innately layered magnets, via exfoliation
( 15 – 17 ) or molecular beam epitaxy (MBE) ( 18 ),
allow for more detailed investigations of low-
dimensional critical phenomena. So far, ferro-
magnetic ordering has been demonstrated in
CrI 3 , CrBr 3 , and Fe 3 GeTe 2 monolayers ( 15 , 16 , 18 ),
all of them stabilized by a substantial out-of-plane
uniaxial anisotropy that places them close to
the Ising universality class, as discussed in recent
reviews ( 19 – 22 ). A careful analysis of some of
these systems, such as ferromagnetic CrBr 3 ( 23 )
or antiferromagnetic NiPS 3 ( 24 ), rather sug-
gests XXZ-type magnetic behavior, the latter
losing magnetic ordering in the monolayer re-
gime. CrCl 3 , on the other hand, is an in-plane
antiferromagnet in the bulk form ( 25 , 26 ), re-
sulting from an alternation between the mag-
netic moments in each individual CrCl 3 layer,
which are ferromagnetically aligned in-plane.
This leads to the question of whether a single-
layer CrCl 3 would order ferromagnetically—or
order magnetically at all—given its weak an-
isotropy and the lack of interplanar exchange
in the monolayer limit.
Recent reports on the magnetic properties
of CrCl 3 exfoliated flakes reach down to the
bilayer regime ( 27 – 30 ), where the antiferro-
magnetic interlayer exchange is still preserved,
whereas the determination of the magnetic
properties of a monolayer has remained elu-
sive. One reason is that the magnetic charac-
terization of the monolayer flakes relies on
indirect methods, which require device fabrica-
tion for tunneling magnetoresistance ( 27 – 30 )
or Hall-micromagnetometry experiments ( 23 ).
Direct methods such as the magneto-optical616 29 OCTOBER 2021•VOL 374 ISSUE 6567 science.orgSCIENCE
(^1) NISE Department, Max Planck Institute of Microstructure
Physics, Halle, Germany.^2 ALBA Synchrotron Light Source,
Barcelona, Spain.^3 Helmholtz-Zentrum für Materialien und
Energie, Berlin, Germany.
*Corresponding author. Email: [email protected]
(A.B.-P.); [email protected] (K.C.); stuart.parkin@mpi-halle.
mpg.de (S.S.P.P.)
†These authors contributed equally to this work.
RESEARCH | REPORTS