first-principles calculations of a CrCl 3 mono-
layer ( 32 , 37 , 38 ), which range from 0.031 to
0.055 meV/Cr, and also turn out to be slightly
larger than the critical field anisotropy in the
antiferromagnetic bulk (0.3 to 0.5 T) ( 26 , 33 )
and in bilayer CrCl 3 (0.23 T) ( 29 ). A stable fer-
romagnetic ordering was not expected a priori
when reducing the dimensionality of the few-
layer antiferromagnetic system down to the
monolayer, as it was unclear whether the re-
moval of the interlayer exchange interaction
would leave the intralayer ferromagnetic be-
havior intact. In fact, the magnitudes of the
calculated magnetic anisotropy energies for a
single CrCl 3 monolayer were so low that some
calculations ( 32 , 37 ) even predict a marginally
favorable perpendicular magnetic anisotropy
instead of the expected in-plane one. Our ob-
servation of a clear in-plane easy axis in mono-
layer CrCl 3 provides a decisive answer to this
puzzle and consolidates its classification as a
two-dimensional in-plane ferromagnet. The en-
hanced magnetic anisotropy (0.09 to 0.11 meV)
cannot be simply understood by a dominant
shape anisotropy [upper bound of 0.052 meV
calculated in ( 39 )]—asisthecaseinfew-layer
exfoliated CrCl 3 samples—but rather is ex-
plained by sizable contributions of the single-
ion anisotropy (DESI) and magnetic exchange
terms (DEME)( 40 , 41 ).In this regard, we found
a detectable orbital-moment anisotropy (DL=
0.04) using sum-rule evaluation of the XMCD
spectra at grazing and normal incidence (fig.
S4) as well as a substantial deviation of the Cr-
Cl-Cr bond plane angle (dq= 10°) via angle-
dependent x-ray absorption measurements (fig.
S5), the latter related to a trigonal distortion of
the ideal CrCl 3 octahedral environment. Both
factors have a direct impact on the magnitude
of the single-ion and magnetic exchange anisot-
ropy in CrCl 3 and thus lie at the origin of the
enhanced anisotropy [see ( 34 ) for an extended
discussion and qualitative estimation of the rel-
evant magnetic anisotropy terms]. We expect
that this substantial trigonal distortion and the
related orbital moment anisotropy are induced
during the nucleation and epitaxial growth pro-
cess of our monolayer samples. We note that our
few-layer CrCl 3 samples grown by MBE show
magnetic behavior similar to that reported in
exfoliated flakes ( 27 – 30 ), exhibiting signatures
of spin-flop transitions at low fields ( 30 ) and
giant interlayer exchange enhancement ( 28 , 30 )
in the form of large critical fields (fig. S6).
To characterize the magnetic behavior be-
low and above the Curie temperatureTcand to
gain insight into the nature of the phase
transition, we acquired the low-field depen-
dence of the CrL 3 edge XMCD between 12 K
and 15 K in the easy-axis direction (see fig. S7
for the detailed datasets close to the phase
transition). Concomitant with the disappear-
ance of the hysteresis at 13 K (Fig. 2D), theM(H)
curves evolve into a softer S-shape aboveTcand
move toward a linear dependence, entering
the paramagnetic regime. The magnetization
is a good order parameter and scales asM=
M 0 [1–(T/Tc)]b, wherebis the critical expo-
nent that determines the magnetic univer-
sality class. In two-dimensional systems, the
isotropic Heisenberg system (n= 3) does not
have any spontaneous order, and the Ising (n= 1)
and XY (n= 2) models are the relevant sce-
narios for CrCl 3 , wherenis the dimensionality
of the spin degree of freedom. Although often
understood in terms of an out-of-plane easy
axis, the Ising universality can also be found in
in-plane magnetized systems ( 42 , 43 ) as long
as there is only one preferred (uniaxial) mag-
netization direction. To perform the analysis
of the critical exponentb,werelyontheevolu-
tion of the remanent magnetic momentmr
[proportional to the XMCDL 3 intensity at zero
field ( 34 )] as a function of temperature (Fig.
3A). The inset shows the fitting of the data close
to the phase transition (12 to 13 K), yielding
values ofb= 0.227 ± 0.021 andTc= 12.95 ±
0.03 K, matching well with the expected value
(b= 0.231) of the 2D-XY model ( 9 ). If the ex-
ponentbis set to equal 0.125, corresponding
to Ising-type universality (Fig. 3B, green line),
the agreement with the experimental data israther poor. A better visualization of the tem-
perature region of critical behavior is given by
a log-log representation of the magnetization
versus reduced temperature [1–(T/Tc)], as
showninFig.3C.Theregionwherethecritical
scaling holds occurs in a range of reduced
temperatures between 0.1 and 0.003, a regime
typically used in critical phenomena studies
[see ( 14 ) for a compendium].
To further assess the 2D-XY behavior in our
samples, we carried out a second analysis pro-
cedure, the so-called Arrott-Noakes plots ( 44 ),
from the field- and temperature-dependent
XMCD data. In this representation, the magne-
tization and susceptibility power-law scaling are
visualized together across the phase transition,
and a consistent set of the critical exponentsb
andg, corresponding to the magnetization and
susceptibility, can be deduced. This approach is
widely used to distinguish between the various
magnetic interaction models (e.g., Heisenberg,
Ising, XY, Potts) in three and two dimensions,
each of which have a specific set of critical
exponents. The determination of the critical
exponentgby an Arrott-plot analysis of the
temperature-dependent XMCD data is shown
in Fig. 3D. The analysis of the Arrott plots is
consistent with the previously inferred valueSCIENCEscience.org 29 OCTOBER 2021•VOL 374 ISSUE 6567 619
Fig. 3. Scaling behavior and critical exponents.(A) XMCD values at zero magnetic field (remanence)
as a function of temperature, extracted from the hysteresis loops. Inset: The critical scaling fit close to the
phase transition determines the exponentb= 0.227. (B) The fits using the 2D Ising (green) and 2D-XY models
(red) are shown; the latter is consistent with our data. (C) Logarithmic representation of XMCD magnitude
versus reduced temperature [1Ð(T/Tc)], for an optimal visualization of the accuracy of the inferred critical
exponentband the definition of the critical temperature region. (D) Modified Arrott plots of the field-dependent
XMCD data at various temperatures (b= 0.227,g= 2.2), matching the 2D-XY model predictions.Mis the
magnetic moment, proportional to the XMCD intensity. Extrapolation of the linear fits at high fields is drawn as a
guide to the eye to visualize they-intercept evolution toward the phase transition (y=0atTc).RESEARCH | REPORTS