# Resonant Raman Scattering of Few Layers CrBr3

Łucja Kipczak<EMAIL_ADDRESS>Institute of Experimental Physics,
Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland  Arka Karmakar
Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
02-093 Warsaw, Poland  Magdalena Grzeszczyk  Institute for Functional
Intelligent Materials, National University of Singapore, 117544, Singapore
Róża Janiszewska  Department of Semiconductor Materials Engineering, Faculty
of Fundamental Problems of Technology, Wrocław University of Science and
Technology, 50-370 Wrocław, Poland  Tomasz Woźniak  Department of
Semiconductor Materials Engineering, Faculty of Fundamental Problems of
Technology, Wrocław University of Science and Technology, 50-370 Wrocław,
Poland  Institute of Theoretical Physics, Faculty of Physics, University of
Warsaw, 02-093 Warsaw, Poland  Zhaolong Chen  Institute for Functional
Intelligent Materials, National University of Singapore, 117544, Singapore
Department of Materials Science and Engineering, National University of
Singapore, 117575, Singapore  Jan Pawłowski  Institute of Experimental
Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
Kenji Watanabe  Research Center for Electronic and Optical Materials, National
Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan  Takashi
Taniguchi  Research Center for Materials Nanoarchitectonics, National
Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan  Adam
Babiński  Institute of Experimental Physics, Faculty of Physics, University of
Warsaw, 02-093 Warsaw, Poland  Maciej Koperski  Institute for Functional
Intelligent Materials, National University of Singapore, 117544, Singapore
Department of Materials Science and Engineering, National University of
Singapore, 117575, Singapore  Maciej R. Molas<EMAIL_ADDRESS>Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
02-093 Warsaw, Poland

###### Abstract

We investigate the vibrational and magnetic properties of thin layers of
chromium tribromide (CrBr3) with a thickness ranging from three to twenty
layers (3 L to 20 L) revealed by the Raman scattering (RS) technique.
Systematic dependence of the RS process efficiency on the energy of the laser
excitation is explored for four different excitation energies: 1.96 eV, 2.21
eV, 2.41 eV, and 3.06 eV. Our characterization demonstrates that for 12 L
CrBr3, 3.06 eV excitation could be considered resonant with interband
electronic transitions due to the enhanced intensity of the Raman-active
scattering resonances and the qualitative change in the Raman spectra.
Polarization-resolved RS measurements for 12 L CrBr3 and first-principles
calculations allow us to identify five observable phonon modes characterized
by distinct symmetries, classified as the A${}_{\textrm{g}}$ and
E${}_{\textrm{g}}$ modes. The evolution of phonon modes with temperature for a
20 L CrBr3 encapsulated in hexagonal boron nitride flakes demonstrates
alterations of phonon energies and/or linewidths of resonances indicative of a
transition between the paramagnetic and ferromagnetic state at Curie
temperature ($T_{\textrm{C}}\approx 50$ K). The exploration of the effects of
thickness on the phonon energies demonstrated small variations pronounces
exclusively for the thinnest layers in the vicinity of 3 - 5 L. This
observation is attributed to strong localization in the real space of
interband electronic excitations, limiting the effects of confinement for
resonantly excited Raman modes to atomically thin layers.

## Introduction

The recent discovery of magnetism in two-dimensional van der Waals (vdW)
materials at the limit of atomically thin monolayers opens capabilities to
study the fundamental aspects of magnetism at varied dimensionalities. From
the practical perspective, the realization of magnetism down to monolayers
pushes the limits of device minaturization, which becomes increasingly
relevant for the development of spintronics [1, 2], valleytronics, and
nanoelectronics [3, 4]. The family of layered magnetic materials (LMMs) grows
rapidly motivated by the search for materials that host stable magnetic orders
under a variety of physical conditions, including temperature [5, 6, 7],
magnetic or electric field [6, 8, 9], and pressure [10]. These intense
research efforts lead to theoretical predictions of hundreds of LMM systems,
of which dozens have been synthesized and characterized. The largest groups of
LMMs include di- and trihalides ($e.g.$, CrBr3 and CrI3) [11, 12], transition
metal dichalcogenides ($e.g.$, 1T-VS2) [13, 14], tri- and tetrachalcogenides
($e.g.$ FePS3 and CrPS4) [15, 16, 17, 18, 19, 20], and metal-chalcogene-
halides ($e.g.$, CrSBr) [21, 22].

Herein, we investigate the vibrational properties of CrBr3, which belongs to
the family of chromium trihalides (CrX3, X = I, Br, Cl). The three materials
exhibit an intralayer ferromagnetic coupling within a monolayer, however, they
differ in the easy-axis magnetization exhibiting in-plane (CrCl3) or out-of-
plane spin orientations (CrBr3 and CrI3) [3, 23]. The interlayer coupling is
more complex, displaying thickness- and/or gate-dependent ferromagnetic or
antiferromagnetic characteristics [24, 3, 11, 25, 26]. For CrBr3, the
interlayer coupling is mostly ferromagnetic, however, contributions from
antiferromagnetic coupling have been observed in bulk crystals via inspection
of magneto-resistance in vertical tunnelling junctions [27].

From the perspective of studying lattice dynamics, the Raman scattering (RS)
technique has been established as a pivotal tool to uncover the physics of the
vibrational and electronic properties of layered vdW materials, as well as a
method to identify the exact number of layers [28, 29, 30, 31]. Particularly,
the RS characterization of CrBr3 revealed a chiral character of the lattice
excitations in a rather complex elementary cell [7]. These phonon modes are
coupled to the magnetic order, predominantly driven by modifications of the
exchange coupling between neighboring Cr3+ ions due to vibrational motion of
the lattice [32].

In this work, we further explore the interplay between vibrational,
electronic, and magnetic characteristics of thin CrBr3 layers through
systematic polarization-resolved RS characterization as a function of the
energy of laser excitation, temperature, and the thickness of the magnetic
layers. We concluded that for 12 L CrBr3 3.06 eV excitation energy creates
resonant conditions characterized by enhanced RS efficiency at the cryogenic
temperature $T$ = 5 K. Five Raman peaks were identified in the polarization-
sensitive resonant RS spectra, characterized by the A${}_{\textrm{g}}$(out-of-
plane) and E${}_{\textrm{g}}$(in-plane) symmetries, as confirmed by first-
principles calculations. Curie temperature ($T_{\textrm{C}}$) for CrBr3 is
determined to be $\sim$50 K from the measured sudden energy redshift of the
Raman resonances triggered by the increase of temperature above the critical
point, where the ferromagnetic order collapses in favor of the paramagnetic
response. Moreover, the effect of thicknesses on the phonon energies reveals a
notable change in phonon energy only for the thinnest layers (3 - 5 L CrBr3),
indicative of the strong spatial localization of excitons [33] which are
expected to be responsible for the resonant characteristics of the enhanced
vibrational response.

## Results and discussion

(a)

Figure 1: The schamatic representation of (a) a side view and (b) a top view
the atomic structure of the CrBr3 crystal in rhombohedral configuration. The
orange parallelepiped represents the unit cell, which consists of three
molecular layers including two Cr atoms (blue) and six Br atoms (green) per
layer.

CrBr3 crystallizes in a rhombohedral BI3 structure of R$\bar{3}$ symmetry. The
schematic representation of the atomic structure of the CrBr3 crystal is shown
in Fig. 1. Within each layer, Cr atoms form a hexagonal crystal lattice, with
each atom bonded to its six neighboring Br atoms, forming an octahedral
configuration. The CrBr3 layers are stacked along the $c$ axis and are held
together by vdW interactions [34, 35, 36]. CrBr3 exibit the rhombohedral
arrangement at low and ambient temperatures, [37, 32] unlike its counterparts,
CrI3 and CrCl3, which undergo a structural transition from the monoclinic
AlCl3 phase of C2/m symmetry at ambient temperature towards rhombohedral
R$\bar{3}$ structure at low temperature. The transition was identified to
occur at 210 K and 240 K for CrI3 and CrCl3, respectively [38, 39]. The
rhombohedral primitive cell belongs to space group no. 148 with Cr and Br
atoms in 6c and 18f Wyckoff positions, respectively. It gives rise to eight
Raman-active modes, classified as: $\Gamma$ = 4Ag \+ 4Eg, where the Eg modes
are doubly degenerate [40, 37, 32]. We calculated the dispersion of the phonon
modes for bulk CrBr3 with ferromagnetic order in the density functional theory
(DFT) framework, as illustrated in Fig. 2. The superscripts in the labels of
the peaks describe additional numbering due to their increased Raman shift.
The optimized lattice constant of rhombohedral cell, $a$=7.128Å, corresponds
to $a$=6.352Åin hexagonal cell, in good agreement with the experimental value
of 6.302Å [37].

(a)

Figure 2: Phonon dispersion of bulk CrBr3 crystal in rhombohedral primitive
cell with ferromagnetic order. The $\Gamma$ point corresponds to the center of
the Brillouin zone.

(a)

Figure 3: (a) Raman Scattering (RS) spectra of 12 L of CrBr3 measured at 5 K
with different excitation energies: 1.96 eV, 2.21 eV 2.41 eV and 3.06 eV,
using excitation power 50 $\mu W$. Spectra were shifted vertically for better
visual representation. (b) Low-temperature ($T$ = 5 K) RS spectra of the same
flake measured in co- (light-blue) and cross-linear (dashed dark pink)
configurations of polarized light using 3.06 eV excitation energy and power 50
$\mu$W. Insert represents a schematic illustration of the sample cross-
section.

The representative low temperature ($T$=5 K) unpolarized RS spectra of a
mechanically exfoliated 12 L CrBr3 deposited on Si/SiO2 substrate are
demonstrated in Fig. 3(a). We comparatively inspect the dependence of the RS
resonances on the laser energy, utilizing 1.96 eV, 2.21 eV, 2.41 eV, and 3.06
eV excitations. There are five distinct RS peaks in the spectra, and these
peaks can be attributed to the in-plane E${}_{\textrm{g}}$ and out-of-plane
A${}_{\textrm{g}}$ modes [40, 37, 7, 32, 41]. Specifically, four phonon modes,
apparent at 110 cm-1, 146 cm-1, 156 cm-1, and 187 cm-1, are observed under all
the used excitation energies, while the fifth one at 282 cm-1 is seen
exclusively when excited with a 3.06 eV energy. DFT calculations yield
frequencies of 110 cm-1, 137 cm-1, 142 cm-1, 177 cm-1 and 266 cm-1,
respectively, which agree well with the measured values. We also measured
polarization-resolved Raman spectra on the 12 L CrBr3 flake in two
configurations of linearly polarized excitation and detection: co- (light
blue) and cross-linear (dashed dark pink), see Fig. 3(b), which is consistent
with the symmetry analysis of phonon modes at the $\Gamma$ point. As can be
seen in Fig. 3(a), the intensities of the Raman peaks reduce monotonically
with the decrease of the excitation energy, leading to about their two times
change in transition between the 1.96 eV and 3.06 eV excitations. A similar
variation in the intensity of the RS spectra under different excitations was
reported in Ref. [32], where the Raman spectra of the CrBr3 monolayer were
investigated using two different excitation energies, $i.e.$ 1.65 eV and 2.09
eV. They also found that the observation of the 282 cm-1 mode strongly depends
on the used excitation energy.

It is well established that the intensity of the RS signal in vdW materials is
significantly dependent on the applied excitation energy [42]. In the simplest
approach, the resonant conditions of RS, related to the electron-phonon
coupling in a material, occur when the excitation energy of the RS processes
is in the vicinity of a given transition ($e.g.$ electronic or excitonic) in
the material [43]. Therefore, the observed enhancement of the RS intensity
measured in CrBr3 under the 3.06 eV excitation should be associated with a
specific transition occurring in this compound. As the optical response of
CrX3 materials is determined by localized (Frenkel) excitons with large
binding energies of about $\sim 2-3$ eV [44], identification of the transition
can be a difficult task. A detailed analysis of the experimental low
temperature ($T\sim 2-4$ K)absorption spectra of CrBr3 [45, 46, 47, 48, 49,
50] along with the corresponding theoretical predictions of the imaginary part
of the dielectric function [44] reveal that CrBr3 absorption is dominated by
three significant resonances at energies of about 1.7 eV, 2.2 eV, and 3.0 eV.
The highest energy absorption band apparent at about 3 eV probably is
responsible for the observed resonant conditions of the RS spectra under the
3.06 eV excitation (see Fig. 3(a)).

(a)

Figure 4: (a) Schematic representation of the investigated sample. The 16 L
flake of CrBr3 was encapsulated in hBN and coated with an optically inactive
polymer and placed on silicon substrate. (b) Temperature evolution of RS
spectra of CrBr3 measured at selected temperature between 5 K and 200 K under
the 3.06 eV excitation and $P$=100 $\mu$W. Temperature dependence of (c) - (f)
Raman shifts, (g) - (j) FWHMs and (k) - (n) integrated intensities obtained of
the A${}^{1}_{\textrm{g}}$, E${}^{1}_{\textrm{g}}$, E${}^{2}_{\textrm{g}}$,
and A${}^{2}_{\textrm{g}}$ phonon modes. The shaded grey rectangle represents
the ferromagnetic region, while the border delineates the Curie temperature
($T_{\textrm{C}}$).

Most LMMs undergo different types of degradation, such as photocatalysis and
photochemical or photothermal oxidation, which are substantially dependent on
various factors such as light exposure and temperature [51, 52, 53, 54, 55,
56]. During our investigation, we also observed that exfoliated thin CrBr3
flakes on Si/SiO2 substrates are subjected to the degradation process under
laser illumination, particularly at higher temperatures, close to room
temperature. Therefore, we performed the temperature-dependent RS spectra on
16 L flake encapsulated in hBN layers, and the structure was also covered by a
thin layer of optically inactive polymer to add additional protection (see
Methods for details) to avoid degradation (see Fig. 4(a)). The temperature
evolution of the Raman spectra of the CrBr3 flake is presented in Fig. 4(b).
Note that we were able to carry out the measurements only up to 200 K due to
the degradation caused by the elevated temperature. There are three effects of
the increased temperature on a given Raman peak that are revealed: red shift
of energy, broadening of linewidth, and variation of intensity. To investigate
the temperature effect in more detail, we fitted the observed phonon modes
with Lorentzian functions. The obtained temperature evolutions of the peak
energies, full widths at half maximum (FWHMs), and intensities for four phonon
modes, $i.e.$, A${}^{2}_{\textrm{g}}$, E${}^{2}_{\textrm{g}}$,
E${}^{3}_{\textrm{g}}$, A${}^{3}_{\textrm{g}}$, are shown in Figs. 4(c)-(f),
(g)-(j), and (k)-(n), respectively.

While the Raman shift of the A${}^{2}_{\textrm{g}}$ mode is relatively
insensitive to temperature changes, three other modes (E${}^{2}_{\textrm{g}}$,
E${}^{3}_{\textrm{g}}$, and A${}^{3}_{\textrm{g}}$) gradually redshift with
increasing temperature. Especially, in between 40 K to 60 K the energies
undergo significant redshifts, followed by nearly linear decreases at higher
temperatures. These abrupt reductions were observed in the literature and
identified as a fingerprint of the transition from the ferromagnetic phase at
low temperature to the paramagnetic phase at higher temperatures [40, 37, 7,
32]. We estimate the Curie temperature ($T_{\textrm{C}}$) for CrBr3 to be
around 50 K. The determined $T_{\textrm{C}}$ value is in very good agreement
with the recent result obtained for the exfoliated CrBr3 flake (47 K [7]), but
is much bigger value as compared to the one for a single crystal (33 K [49]
and 27 K [37]) or in a monolayer limit (25 K [32]). The difference between the
found $T_{\textrm{C}}$ for the exfoliated flakes and the single crystal of
CrBr3 can be explained by the influence of stress, which can modulate the
transition temperature between the ferromagnetic and paramagnetic phases [57].

(a)

Figure 5: (a) Optical image of 8 L flake of CrBr3. Dashed white cube
corresponds to an area scanned using AFM. (b) AFM image of flake. A horizontal
line represents the (c) profile of this flake. (d) Raman shift as a function
of number of layers. The solid points represents the average Raman shift
values, while the open, lighter points correspond to values of Raman shift for
each layer. Dark yellow bars indicate the error bars. (e) Energy difference
between the most prominent A${}^{2}_{g}$ Raman mode and the remaining modes.
The dark yellow bars represents the associated error bars.

For FWHMs, we observe a chaotic distribution of the FWHMs for the
A${}^{2}_{\textrm{g}}$ and E${}^{2}_{\textrm{g}}$ modes, whereas the
corresponding dependences for E${}^{3}_{\textrm{g}}$, and
A${}^{3}_{\textrm{g}}$ are monotonic with their slow growth at higher
temperatures. There is no significant signature of the ferro-to-paramagnetism
transition in the temperature evolutions of the shown FWHMs, in contrast to
the results reported in Refs. [37, 7]. However, Kozlenko $et$ $al.$ [37]
demonstrated that the mode linewidths are reduced within the ferromagnetic
phase, reaching a minimum at $T_{\textrm{C}}$ and are followed by their
monotonic growth at higher temperatures. On the other hand, Yin $et$ $al.$ [7]
showed similar linewidth behaviors, but the minimum of phonon FWHMs was
identified at lower temperature than $T_{\textrm{C}}$. Our results accompanied
by the literature [37, 7] indicate that the analysis of the phonon linewidths
in CrBr3 is burdened with greater uncertainty in assigning the Curie
temperature.

The analysis of the temperature dependence of the phonon intensities is the
most intriguing, as there can be two competing transition processes:
nonresonant versus resonant conditions of RS and ferro- versus paramagnetic
order. The intensities of the A${}^{2}_{\textrm{g}}$ and
E${}^{3}_{\textrm{g}}$ modes exhibit a seemingly random distribution, while
the corresponding ones for the E${}^{2}_{\textrm{g}}$ and
A${}^{3}_{\textrm{g}}$ are described by more organized trends. Particularly,
the A${}^{3}_{\textrm{g}}$ intensity is reduced of about 40$\%$ between 5 K
and 50 K, and then its intensity stabilizes at almost a fixed level. This
result indicates that the intensity can also be used to distinguish the
transition temperature between different magnetic phases, as reported for
other LMMs, $e.g.$, CrSBr [58] and Cr2Ge2Te6 [59].

The final part of our work is devoted to the examination of the thickness
influence on the RS spectra of thin CrBr3 exfoliated on the Si/SiO2
substrates. We investigate 25 flakes with thicknesses ranging from 3 L to 20
L. Knowing that CrBr3 degradation is quite slow in the ambient atmosphere,
compared to its photocatalytic oxidation [55], the flakes thicknesses were
determined using the AFM technique and then subjected to Raman spectroscopy
characterization. Figs. 5(a) and (b) show the optical and atomic force
microscopy (AFM) images of the selected CrBr3 flake, respectively. Its
thickness is estimated to be about 5 nm (see Fig. 5(c)), which corresponds to
8 L (the experimental thickness of a single layer of CrBr3 equals 6
$\mathrm{\SIUnitSymbolAngstrom}$ [50]). Fig. 5(d) represents the thickness
dependency of the Raman shifts of four phonon modes. The open points represent
the phonon energies measured on the each thickness of the individual flakes,
whereas the solid points denote the mean values calculated for a particular
layer thickness. A discernible tendency of the phonon energies as a function
of the layer thickness is apparent in the figure. However, the dependence of
the Raman shifts, which is only from 0.4 cm-1 to 0.8 cm-1 in the investigated
range of thicknesses, is hidden by their substantial random variations also
within the same number of layers. To better visualize the thickness effect,
Fig. 5(e) illustrates the energy differences between the most prominent
A${}^{3}_{g}$ peak and others (A${}^{2}_{\textrm{g}}$, E${}^{2}_{\textrm{g}}$,
and E${}^{3}_{\textrm{g}}$). The observed dependences can be divided into two
groups: 3 - 5 L and 6 -20 L. While an evident reduction in the energy
difference between the A${}^{3}_{\textrm{g}}$ and E${}_{\textrm{g}}$
(E${}^{2}_{\textrm{g}}$ and E${}^{3}_{\textrm{g}}$) modes is observed when the
number of layers increases from 3 to 5 layers, there is no similar behavior
for the two A${}_{\textrm{g}}$ peaks (A${}^{2}_{\textrm{g}}$ and
A${}^{3}_{\textrm{g}}$). For the 6 - 20 L range, all the energy differences
between the phonon modes are not affected by the thickness and stay almost at
the same level. Our results, shown in Fig. 5, are in agreement with the
thickness dependences previously observed for thin layers of transition metal
dichalcogenides, $e.g.$ MoS2 [28, 60], MoTe2 [61, 29], and ReSe2 [30]. The
energy differences between the A${}_{\textrm{g}}$ and E${}_{\textrm{g}}$ modes
are established to be the result of the interaction of the interlayer and
surface effects [60, 61]. In the case of thin layers of CrCl3, Cheng $et$
$al.$ [62] demonstrated a significant difference in Raman shifts for 1 - 3 L
and bulk. It may be indicative of the strong spatial localization of excitons
[33], which are expected to be responsible for the resonant characteristics of
the enhanced vibrational response.

## Summary

The vibrational and magnetic properties of the thin layers of CrBr3 were
investigated using Raman scattering spectroscopy. We found that the resonant
RS for CrBr3 is observed at low temperature under the 3.06 eV excitation,
which agrees with the reported absorption spectra of this material.
Furthermore, the temperature dependence of the phonon energies in a 20 L CrBr3
encapsulated in hBN flakes was analyzed to determine its Curie temperature of
about 50 K. Finally, it was established that the effect of thickness on phonon
energies is pronounced only for the thinnest layers in the vicinity of 3 to 5
layers of CrBr3.

## Methods

Most of the samples investigated in this work were thin flakes of CrBr3
exfoliated directly on SiO2/Si substrates with a thickness of 90 nm or 300 nm
of SiO2 from the bulk CrBr3 crystal purchased from HQ Graphene. For the
temperature dependence measurements, we used a sample prepared from a CrBr3
flake and hBN flakes that were exfoliated directly on a 285 nm SiO${}_{2}/Si$
substrate in an inert gas glovebox (O2 < 1 ppm, H2O < 1 ppm). Then, a
poly(bisphenol A carbonate)/polydimethylsiloxane, referred to as a polymer
stamp on a glass slide was used to pick up 50 nm hBN, 10 nm CrBr3 and 50 nm
hBN, respectively at 80∘C with the assistance of the transfer stage in the
glovebox. The polymer was left on the structure for protection. CrBr3 flakes
of interest were first identified by visual inspection under an optical
microscope and then subjected to atomic force microscopy to obtain their
thickness.

Raman scattering spectra were measured under laser excitations of $\lambda$ =
405 nm (3.06 eV), $\lambda$ = 515 nm (2.41 eV), $\lambda$ = 561 nm (2.21 eV),
and $\lambda$ = 633 nm (1.96 eV) on samples placed on a cold finger of a
continuous-flow cryostat, which allows experiments to be carried out as a
function of temperature from about 5 K to room temperature. The excitation
light was focused by means of a 50$\times$ long-working-distance objective
with a 0.55 numerical aperture (NA) producing a spot of about 1 $\mu$m
diameter. The signal was collected via the same objective (backscattering
geometry), sent through a 0.75-m monochromator, and then detected using a
liquid nitrogen-cooled charge-coupled device (CCD). The polarization-resolved
Raman spectra were analyzed by a motorized half-wave plate and a fixed linear
polarizer mounted in the detection path.

The first-principles calculations were performed within density functional
theory (DFT) in the Vienna ab-initio simulation package (VASP) [63, 64, 65,
66]. The projector augment wave (PAW) potentials and general gradient
approximation (GGA) of Pedew-Burke-Ernzerhof (PBE) [67] with D3 van der Waals
correction [68] were used. Spin-orbit coupling was not included due to its
insignificant impact on lattice relaxation and phonon dispersion in this
compound, as shown by Pandey $et$ $al.$ in Ref. [69]. The unit cell and atomic
positions have been optimized until forces on atoms were lower than 10-5 eV/Å
and stress tensor components were lower than 0.1 kbar. A plane wave basis set
cutoff of 500 eV and a $\Gamma$-centered k-mesh 6$\times$6$\times$6 were
sufficient to converge the lattice constants with precision of 0.001 Å. An
energy tolerance of 10-8 eV was used to in self-consistent loop. The phonon
dispersion was calculated using the finite displacement method as implemented
in Phonopy package [70, 71]. 2$\times$2$\times$2 supercells were found to
assure convergence of the phonon frequencies at $\Gamma$ point. All the
calculations were performed at temperature of 0 K.

## Acknowledgments

The work was supported by the National Science Centre, Poland (grant no.
2020/37/B/ST3/02311), the Ministry of Education (Singapore) through the
Research Centre of Excellence program (grant EDUN C-33-18-279-V12, I-FIM) and
under its Academic Research Fund Tier 2 (MOE-T2EP50122-0012), and the Air
Force Office of Scientific Research and the Office of Naval Research Global
under award number FA8655-21-1-7026. The calculations were carried out with
the support of the Interdisciplinary Centre for Mathematical and Computational
Modelling University of Warsaw (ICM UW) under computational allocation no
G95-1773. K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant
Numbers 21H05233 and 23H02052) and World Premier International Research Center
Initiative (WPI), MEXT, Japan.

## Author contributions

Ł.K., performed the measurements of the Raman scattering. R.J. and T.W.
carried out DFT calculations. Ł.K., A.K., and M.G. fabricated the samples with
CrBr3 thin flakes on the Si/SiO2 substrates. Z.C. fabricated the sample of
CrBr3 encapsulated in hBN and covered by the polymer. T.T and K.W provide the
hBN crystals. Ł.K., A.K., and J.P. carried out the AFM imaging. A.B. and
M.R.M. participated in the measurements of the Raman spectra. M.K. and M.R.M.
supervised the project. Ł.K. and M.R.M. analyzed the data. Ł.K., A.K., M.G.,
M.K. and M.R.M wrote the manuscript with input from all coauthors.

## Competing interests

The authors declare no competing interests.

## Data availability

The datasets obtained during the experiments and analyzed for the current
study are available from the corresponding authors on reasonable request.

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