# Atomic Layer Molecular Beam Epitaxy of Kagome Magnet RMn6Sn6 (R = Er, Tb)
Thin Films

Shuyu Cheng  Department of Physics, The Ohio State University, Columbus, Ohio
43210, United States  Igor Lyalin  Department of Physics, The Ohio State
University, Columbus, Ohio 43210, United States  Wenyi Zhou  Department of
Physics, The Ohio State University, Columbus, Ohio 43210, United States
Roland K. Kawakami<EMAIL_ADDRESS>Department of Physics, The Ohio State
University, Columbus, Ohio 43210, United States

###### Abstract

Kagome lattices have garnered substantial interest because their band
structure consists of topological flat bands and Dirac cones. The RMn6Sn6 (R =
rare earth) compounds are particularly interesting because of the existence of
large intrinsic anomalous Hall effect (AHE) which originates from the gapped
Dirac cones near the Fermi level. This makes RMn6Sn6 an outstanding candidate
for realizing the high-temperature quantum anomalous Hall effect. The growth
of RMn6Sn6 thin films is beneficial for both fundamental research and
potential applications. However, most of the studies on RMn6Sn6 have focused
on bulk crystals so far, and the synthesis of RMn6Sn6 thin films has not been
reported so far. Here we report the atomic layer molecular beam epitaxy
growth, structural and magnetic characterizations, and transport properties of
ErMn6Sn6 and TbMn6Sn6 thin films. It is especially noteworthy that TbMn6Sn6
thin films have out-of-plane magnetic anisotropy, which is important for
realizing the quantum anomalous Hall effect. Our work paves the avenue toward
the control of the AHE using devices patterned from RMn6Sn6 thin films.

††preprint: APS/123-QED

Materials with layered kagome structures provide an ideal platform for
studying the interplay between band structure and magnetism. In momentum
space, a two-dimensional kagome lattice manifests Dirac cones at the K points
Kuroda  _et al._ (2017); Ye  _et al._ (2018), saddle points at the M points
Kang  _et al._ (2022); Teng  _et al._ (2023), and a flat band across the
Brillouin zone Kang  _et al._ (2020a, b). The introduction of magnetism and
spin-orbital coupling further opens a gap at the band touching points, leading
to topologically nontrivial electronic states Sun  _et al._ (2011); Guo and
Franz (2009); Bolens and Nagaosa (2019). In real space, non-trivial spin
textures (e.g. magnetic skyrmions) have been observed in kagome magnets Hou
_et al._ (2017); Li  _et al._ (2023).

Recently, RMn6Sn6 (R = rare earth) compounds have emerged as a new family of
topological kagome magnets Yin  _et al._ (2020); Ma  _et al._ (2021). The Mn
atoms in RMn6Sn6 form Mn3 kagome layers and the spin ordering of the Mn3
layers is largely affected by the R atoms. Previous studies on bulk crystals
report that R = Gd, Tb, Dy, and Ho give rise to ferromagnetic coupling of Mn
spins, while R = Er, Tm, and Lu lead to antiferromagnetic coupling of Mn spins
at zero field Venturini, El Idrissi, and Malaman (1991); Malaman  _et al._
(1999); Clatterbuck and Gschneidner Jr (1999). Rare earth elements in RMn6Sn6
compounds also provide one additional knob for tuning the magnetocrystalline
anisotropy (MCA) which is connected to the Dirac gap opening Cheng  _et al._
(2023). Large Berry-curvature-induced intrinsic anomalous Hall effect (AHE)
may originate from the gapped Dirac cones close to the Fermi level, because
the intrinsic anomalous Hall conductivity (AHC) is connected to the Dirac gap
opening $\Delta$ and the Dirac cone position $E_{D}$ through Sinitsyn  _et
al._ (2007):

$\sigma^{int}=\frac{e^{2}}{h}\frac{\Delta}{2E_{D}}$ (1)

Notably, TbMn6Sn6 bulk crystals exhibit out-of-plane magnetic anisotropy,
which leads to a 34 meV Dirac gap opening at 130 meV above the Fermi level Yin
_et al._ (2020), and band structure calculations predict the quantum anomalous
Hall effect (QAHE) if the Fermi level could be tuned into the gap.
Experimentally, the observation of a giant intrinsic AHC of
$\sigma^{int}$=0.14 e2/$h$ per kagome layer in TbMn6Sn6 bulk crystals Yin  _et
al._ (2020) makes the RMn6Sn6 family of materials attractive for QAHE. To this
end, the growth of RMn6Sn6 thin films provides opportunities for tuning the
band structure and Fermi level through epitaxial strain, chemical doping, or
voltage gating. However, all of the reported works have focused on bulk
crystals of RMn6Sn6, while studies on their thin film counterparts have been
missing. Therefore, the development of epitaxial RMn6Sn6 thin films is highly
desired.

In this paper, we report the growth of (0001)-oriented thin films of ErMn6Sn6
and TbMn6Sn6 using atomic layer molecular beam epitaxy (AL-MBE) and
characterize their magnetic and transport properties. The films are grown on
Pt(111) buffer layers on Al2O3(0001) substrates. Various methods are employed
to characterize the structure of our samples, including in-situ reflection
high energy electron diffraction (RHEED), X-ray diffraction (XRD), and atomic
force microscopy (AFM). We demonstrate that the magnetic properties of RMn6Sn6
thin films can be tuned through the selection of rare earth element $R$.
ErMn6Sn6 thin films favor in-plane (IP) magnetization, while TbMn6Sn6 thin
films undergo an out-of-plane (OOP) to IP spin-reorientation transition (SRT)
as the temperature increases above 300 K. Lastly, we find that the
longitudinal resistance of RMn6Sn6/Pt bilayers do not follow a simple parallel
resistor model but instead depends on the electron mean free path and can be
explained qualitatively by the Fuchs-Sondheimer model.

(a)

(b)

(c)

(d)

Figure 1:  AL-MBE Growth of RMn6Sn6 thin films. (a). Lattice structure of
RMn6Sn6 viewed from the side. In each unit cell, RMn6Sn6 consists of
alternating stacking of RSn2, Mn3, Sn1, Sn2, Sn1, Mn3 layers (from bottom to
top) along c-axis. (b). In-plane lattice structure of kagome Mn3 (top left),
triangular Sn1 (top right), honeycomb Sn2 (bottom left), and RSn2 (bottom
right) layers. (c, d). in-situ RHEED pattern of 20 nm ErMn6Sn6 sample grown on
Pt(111) buffer layer on Al2O3(0001) substrate. (d). in-situ RHEED pattern of
20 nm TbMn6Sn6 sample grown on Pt(111) buffer layer on Al2O3(0001) substrate.

The crystal structure of RMn6Sn6 is displayed in Fig. 1, featuring a hexagonal
lattice (space group $P6/mmm$, lattice constants a = 5.5 Å and c = 9.0 Å) with
atomic layers stacked along the c-axis Malaman, Venturini, and Roques (1988).
In each unit cell, there are two kagome Mn3 layers closely neighboured by two
Sn1 layers, with one honeycomb Sn2 layer inserted between two Sn1 layers, and
one RSn2 layer inserted between Mn3 kagome layers. Inspired by this stacking
sequence, we develop an AL-MBE recipe to grow ErMn6Sn6 and TbMn6Sn6 thin films
on epitaxial Pt(111) buffer layers on Al2O3(0001) substrates. In AL-MBE,
atomic layers are grown sequentially by opening and closing the appropriate
MBE source shutters with precise timing. A similar growth strategy allowed us
to synthesize thin films of another kagome magnet, Fe3Sn2, which also has a
hexagonal layered lattice structure Cheng  _et al._ (2022).

The base pressure of the growth chamber is 1$\times$10-9 Torr. The Al2O3(0001)
substrates (MTI corporation) are annealed in air at 1000 ∘C for 3 hours, then
degassed in-situ at 500 ∘C for 30 minutes to prepare a flat and clean surface.
A 5 nm epitaxial Pt(111) buffer layer is subsequently grown on Al2O3(0001)
following the recipe described in our previous work Cheng  _et al._ (2022).
The ErMn6Sn6(0001) and TbMn6Sn6(0001) thin films are grown on Pt(111) buffer
layers at 100 ∘C and 80 ∘C, respectively using the AL-MBE recipe described
below. First, the kagome Mn3 layer and hexagonal Sn1 layer are co-deposited
with flux ratio Mn:Sn = 3:1, then the honeycomb RSn2 is deposited with flux
ratio Er:Sn (or Tb:Sn) = 2:1, then another hexagonal Sn1 layer and kagome Mn3
layer are co-deposited, then one Sn2 layer is deposited. The aforementioned
shutter growth sequence is repeated until the desired thickness (typically 20
nm) of RMn6Sn6 is achieved. Typical deposition rates are 1.6 Å/min, 1.6 Å/min,
3.9 Å/min, and 2.8 Å/min for Er, Tb, Mn, and Sn, respectively. After growth, a
5 nm CaF2 layer is deposited to prevent sample oxidation.

The in-situ RHEED patterns of ErMn6Sn6 and TbMn6Sn6 are monitored during the
growths. The RHEED patterns of a 20 nm ErMn6Sn6 thin film and a 20 nm TbMn6Sn6
thin film along Al2O3[11$\bar{2}$0] direction are shown in Fig. 1c and 1d,
respectively. The RHEED patterns are generally streaky, suggesting the
morphology of our RMn6Sn6 thin films is dominated by two-dimensional terraces
with finite sizes, although some three-dimensional features also exist as
spots. The RHEED pattern suggests the in-plane lattice constants for our
samples are $a_{ErMn_{6}Sn_{6}}$= 5.47 Å, and $a_{TbMn_{6}Sn_{6}}$= 5.56 Å,
respectively, and the in-plane epitaxial relationship is
RMn6Sn6[1$\bar{1}$00]$\parallel$Pt[110]$\parallel$Al2O3[11$\bar{2}$0].

(a)  (b)  (c)

(d)

Figure 2:  Structural characterizations of RMn6Sn6 thin films. (a). XRD data
of ErMn6Sn6(20 nm)/Pt(5 nm) sample. (b). AFM image of ErMn6Sn6(20 nm)/Pt(5 nm)
sample. (c). XRD data of TbMn6Sn6(25 nm)/Pt(5 nm) sample. (d). AFM image of
TbMn6Sn6(25 nm)/Pt(5 nm) sample.

We perform XRD measurements to confirm the crystallographic structures of
ErMn6Sn6 and TbMn6Sn6 thin films. The X-ray is from the Cu-K$\alpha$
radiation, with a wavelength of 1.5406 Å. Fig. 2a shows the XRD data of a 20
nm ErMn6Sn6 thin film. Next to the substrate peaks at 41.57∘ and 90.60∘, two
major peaks are found at 39.78∘ and 85.46∘, respectively. These peaks are
attributed to Pt(111) and Pt(222) peaks because their 2$\theta$ angles convert
to out-of-plane lattice constants of 2.275 Å and 2.270 Å, respectively. These
values are close to the out-of-plane lattice constant of Pt along (111)
direction ($\sqrt{3}/3\times$3.923 Å= 2.265 Å) Rooksby and Lewis (1964).
ErMn6Sn6(0004) and ErMn6Sn6(0008) peaks appear as nearby shoulder peaks at
40.36∘ and 87.63∘, respectively. The out-of-plane lattice constant of ErMn6Sn6
extracted from (0004) peak is 8.93 Å, which is close to but slightly smaller
than the reported bulk value of 9.0006 Å Clatterbuck, Lange, and Gschneidner
Jr (1999).

For TbMn6Sn6 thin film, the general characteristics of the XRD data are
similar to ErMn6Sn6. To the right of Pt(111) peak which is at 39.88∘, the
TbMn6Sn6(0004) peak is found as a shoulder peak (see Fig. 2c). A double
Gaussian peak fitting yields TbMn6Sn6(0004) peak position of 40.26∘, which
corresponds to an out-of-plane lattice of c = 8.95 Å. This is also smaller
than the reported bulk value of 9.0208 Å Clatterbuck, Lange, and Gschneidner
Jr (1999).

We characterize the surface morphology of ErMn6Sn6 and TbMn6Sn6 thin films
using AFM. Fig. 2b shows the AFM image of a 20 nm ErMn6Sn6 sample grown at
100∘C. The film has a continuous and flat surface with sub-micron grain size.
The root-mean-square (rms) roughness of the 20 nm ErMn6Sn6 sample is 1.02 nm.
Fig. 2b shows the AFM image of a 20 nm TbMn6Sn6 sample grown at 80∘C. The rms
roughness of the 20 nm TbMn6Sn6 sample is 1.45 nm.

(a)  (b)  (c)  (d)

(e)  (f)

Figure 3:  Magnetic properties of ErMn6Sn6 and TbMn6Sn6 thin films. (a - c).
Magnetic properties of 20 nm ErMn6Sn6 thin film measured with out-of-plane
(OOP, red) and in-plane (IP, blue) geometries. (a). M vs. H hysteresis loops
measured at T=300 K. (b). M vs. H hysteresis loop measured at T=5 K. (c). M
vs. T curve. (d - f). Magnetic properties of 20 nm TbMn6Sn6 thin film measured
with out-of-plane (OOP, red) and in-plane (IP, blue) geometries. (d). M vs. H
hysteresis loops measured at T=300 K. (e). M vs. H hysteresis loop measured at
T=5 K. (f). M vs. T curve, showing uniaxial anisotropy for T¡300 and an OOP-
to-IP spin reorientation at T=300 K.

To investigate the magnetic properties of the RMn6Sn6 thin films, we perform
SQUID magnetometer measurements. Fig. 3a shows the IP (blue) and OOP (red)
hysteresis loops of a 20 nm ErMn6Sn6 thin film. The IP hysteresis loop has a
smaller saturation field of 0.2 Tesla, while the OOP hysteresis loop has a
larger saturation field of 1.7 Tesla, indicating ErMn6Sn6 has easy-plane
anisotropy at room temperature. The saturation magnetization of ErMn6Sn6 thin
film is 5.4 $\mu_{B}$/f.u. (212 kA/m) at room temperature. The IP and OOP
hysteresis loops of ErMn6Sn6 at T = 5 K are shown in Fig. 3b. At T = 5 K, both
IP and OOP hysteresis loops show much larger coercive fields and larger
saturation fields, while the saturation field of the OOP hysteresis loop is
still larger than the IP hysteresis loop. The IP loop exhibits a sharper
switching behavior, with the coercive field of 0.47 Tesla. Meanwhile, the OOP
hysteresis loop becomes narrower near zero field and wider at higher fields.
The coercive field of the OOP hysteresis loop is 0.30 Tesla.

We also measure the temperature-dependence of remanence magnetization of the
ErMn6Sn6 thin film, as shown in Fig. 3c. For both OOP (the red curve) and IP
(the blue curve) measurements, the sample is cooled down under 7 Tesla applied
field, and measured at low field while heating up. A 30 mT field is applied to
set the polarity of the magnetization. From the temperature-dependent
magnetization curve, the Curie temperature of the 20 nm ErMn6Sn6 thin film is
determined to be 353 K, signified by a drop of magnetization to zero. This
Curie temperature is consistent with the reported value of 350 K on ErMn6Sn6
bulk crystals Clatterbuck and Gschneidner Jr (1999).

Compared to ErMn6Sn6 thin films, TbMn6Sn6 thin films show different magnetic
properties. Fig. 3d and 3e show the hysteresis loops of a 25 nm TbMn6Sn6 thin
film at 300 K and 5 K, respectively. At T = 300 K, the OOP (red) and IP (blue)
hysteresis loops of TbMn6Sn6 are almost identical, with a saturation field of
0.6 Tesla (see Fig. 3d). The saturation magnetization of TbMn6Sn6 is 3.9
$\mu_{B}$/f.u. (154 kA/m) at room temperature. While cooling down to T = 5 K,
the OOP hysteresis loop of TbMn6Sn6 exhibits a square shape, with tails
extended to 5 Tesla, as shown in Fig. 3e Meanwhile, the IP hysteresis loop
shows a gradual switching behavior. At zero field, the OOP remanence
magnetization is much larger than the IP remanence magnetization, suggesting
that TbMn6Sn6 favors OOP at T = 5 K.

The perpendicular magnetic anisotropy is highly unusual for epitaxial kagome
magnet thin films, as most of the previously reported kagome magnet thin films
have easy-plane anisotropy Taylor  _et al._ (2020); Hong  _et al._ (2020);
Khadka  _et al._ (2020); Cheng  _et al._ (2021, 2022); Fujiwara  _et al._
(2023). Even for epitaxial Fe3Sn2 whose bulk form has MCA along the c-axis,
the MCA is overcome by the magnetic shape anisotropy (MSA) which favors easy-
plane anisotropy. As a result, both MBE-grown and sputtered Fe3Sn2 thin films
manifest easy-plane anisotropy Khadka  _et al._ (2020); Cheng  _et al._
(2022). However, in TbMn6Sn6 thin films, the MCA is strong enough to overcome
the MSA and leads to an easy-axis anisotropy at low temperatures. It is
noteworthy that such large magnetocrystalline anisotropy along the c-axis
opens a gap at the Dirac cone, leading to a large intrinsic AHE Yin  _et al._
(2020); Ma  _et al._ (2021).

The perpendicular magnetic anisotropy of the TbMn6Sn6 thin film sample at low
temperatures is further confirmed by the temperature-dependent SQUID
measurements, as shown in Fig. 3f. A 20 mT field is applied to set the
polarity of the magnetization. Below 300 K, the OOP magnetization (red curve)
is always larger than the IP magnetization (blue curve). A crossover between
IP and OOP magnetization happens at T = 300 K above which the IP magnetization
becomes larger than the OOP magnetization. This crossover suggests an OOP-to-
IP SRT as the temperature increases above 300 K. A similar temperature-induced
SRT has been observed at 310 K in TbMn6Sn6 bulk crystals Clatterbuck and
Gschneidner Jr (1999) and is reported to be related to the formation of
magnetic skyrmions Li  _et al._ (2023). Both IP and OOP magnetization
eventually disappears above the Curie temperature which is determined to be
380 K. This Curie temperature is lower than the reported value of 423 K on
TbMn6Sn6 bulk crystals Venturini, El Idrissi, and Malaman (1991).

(a)  (b)  (c)

Figure 4:  Transport measurements of ErMn6Sn6/Pt and TbMn6Sn6/Pt bilayers.
(a). Resistance of 300 $\mu$m$\times$100 $\mu$m devices patterned from
TbMn6Sn6(25 nm)/Pt(5 nm) bilayer (red), TbMn6Sn6(5 nm)/Pt(5 nm) bilayer
(blue), ErMn6Sn6(20 nm)/Pt(5 nm) bilayer, and 5 nm Pt single layer (black,
dashed), respectively. (b). Anomalous Hall resistivity of ErMn6Sn6(20 nm)/Pt(5
nm) bilayer measured at different temperatures ranging from 2 K to 300 K. (c).
Anomalous Hall resistivity of TbMn6Sn6(25 nm)/Pt(5 nm) bilayer measured at
different temperatures ranging from 2 K to 300 K.

We next discuss the transport properties of ErMn6Sn6/Pt and TbMn6Sn6/Pt thin
films. The transport measurements are performed using Quantum Design Physical
Property Measurement System (PPMS) on 300 $\mu$m$\times$100 $\mu$m Hall bar
devices patterned from ErMn6Sn6/Pt and TbMn6Sn6/Pt thin films. The
longitudinal resistance of the Hall bar devices at zero field is shown in Fig.
4a. Comparing between TbMn6Sn6(25 nm)/Pt(5 nm) bilayer (the red curve) and
Pt(5 nm) single layer (the black dashed curve), the bilayer resistance is
lower than the Pt single layer resistance for higher temperatures (T$>$200 K).
This is consistent with the parallel resistor model in which the TbMn6Sn6 and
Pt layers are modeled as two resistors connected in parallel and therefore
have smaller resistance than the Pt layer alone. The parallel resistor model
has been widely used to extract the resistivity of kagome material thin films
grown on metallic buffer layers Hong  _et al._ (2020); Khadka  _et al._
(2020); Cheng  _et al._ (2021); Thapaliya  _et al._ (2021). However, at low
temperatures (T$<$150 K), the resistance of the TbMn6Sn6(25 nm)/Pt(5 nm)
bilayer is larger than that of the Pt(5 nm) single layer. This is the opposite
of what one would expect from the parallel resistor model. The comparison
between ErMn6Sn6(20 nm)/Pt(5 nm) bilayer (the green curve) and Pt(5 nm) single
layer shows a similar trend that the bilayer resistance is smaller than the Pt
single layer resistance for T$>$200 K and larger than the Pt single layer
resistance for T$<$100 K. The deviation from the parallel resistor model is
more pronounced for the bilayers with smaller kagome layer thicknesses. For
example, for TbMn6Sn6(5 nm)/Pt(5 nm) bilayer (the blue curve), the resistance
is larger than Pt(5 nm) single layer from T=5 K up to T=300 K.

The deviation from the parallel resistor model can be explained by Fuchs-
Sondheimer theory, in which the resistance of bilayers depends not only on the
bulk resistance of two materials but also the mean free path of electrons in
them Fuchs (1938); Sondheimer (1952). In the Fuchs-Sondheimer model, when the
electron mean free path is much smaller than the thickness of each layer, the
bilayer resistance is smaller than the resistance of individual layers. In
this case, the Fuchs-Sondheimer model converges to the parallel resistor
model. However, when the electron mean free path is much larger than the
thickness of each layer, the bilayer resistance is larger than the resistance
of individual layers, which is more similar to the series resistor model.
Especially in an infinite superlattice consisting of alternating stacking of
two materials with the same thickness, in the thin layer limit and under the
assumption that the electron densities in two materials are identical, the
averaged resistivity of the superlattice is exactly equal to the average value
of the bulk resistivity of the two materials Misra  _et al._ (1999). In our
RMn6Sn6/Pt bilayer samples, the scattering length is shorter than the
individual layer thickness at high temperatures, therefore the bilayer
resistance is smaller than the resistance of Pt layer, similar to the parallel
resistor model. Meanwhile, at low temperatures or with smaller thicknesses,
the mean free path becomes longer than the individual layer thickness, and the
bilayer resistance is larger than the resistance of Pt layer, similar to the
series resistor model. Due to the complexity of data analysis, extracting the
intrinsic longitudinal resistivity of ErMn6Sn6 and TbMn6Sn6 from bilayer
resistance is outside the scope of this paper.

We also measured the anomalous Hall effect (AHE) of ErMn6Sn6(20 nm)/Pt(5 nm)
and TbMn6Sn6(25 nm)/Pt(5 nm) bilayers, as shown in Fig. 4b and Fig. 4c,
respectively. Here, the anomalous Hall resistivity is calculated by
multiplying the anomalous Hall resistance by the thickness of the RMn6Sn6
layer. For ErMn6Sn6, the AHE hysteresis loop at $T=2$ K has a large remanence,
a low-field opening (with the coercive field of $\sim 1$ T) and a large
saturation field ($\sim 6$ T). The opening of the hysteresis loop decreases
quickly as the temperature increases, and almost disappears before the
temperature reaches 100 K. For TbMn6Sn6, the AHE hysteresis loops are
relatively square, with the coercive field decreasing as temperature
increases. For both materials, as temperature increases from 2 K to 300 K, the
amplitude of AHE first increases, reaches the maximum value between 200 K and
250 K, and then decreases. This behavior is understood as follows. The
anomalous Hall resistivity $\rho^{AH}$ scales with $\rho_{xx}^{\alpha}$ where
$\alpha$ is between $1$ and $2$. The intrinsic and side-jump contributions
yield $\alpha=2$ and skew-scattering yields $\alpha=1$. Tian, Ye, and Jin
(2009) Since $\rho_{xx}$ increases with temperature (Figure 4a), this scaling
explains the enhancement of $\rho^{AH}$ with temperature as observed below 200
K. On the other hand, the reduction of AHE resistivity at higher temperatures
can be attributed to the decrease in magnetization as the temperature
approaches the Curie temperature.

In conclusion, this study demonstrates the synthesis of $c$-plane ErMn6Sn6 and
TbMn6Sn6 thin films using atomic layer molecular beam epitaxy. A combination
of RHEED, XRD, and AFM confirms the structure of the samples. Magnetization
measurements show that ErMn6Sn6 has easy-plane anisotropy from 5 K to room
temperature, while TbMn6Sn6 has perpendicular magnetic anisotropy at low
temperature and an OOP-to-IP spin reorientation as the temperature increases
above 300 K. Transport measurements at low temperatures show that the
longitudinal resistance of the RMn6Sn6/Pt bilayer is larger than that of the
Pt layer alone, which is inconsistent with the parallel resistance model. On
the other hand, such behavior is qualitatively explained by the Fuchs-
Sondheimer model. Lastly, since both ErMn6Sn6 and TbMn6Sn6 are synthesized
under similar conditions, other members of the RMn6Sn6 family could likely be
grown using similar AL-MBE recipes. These results create a solid foundation
for future research and applications based on RMn6Sn6 thin films.

## Acknowledgments

We acknowledge Daniel Halbing, Katherine Robinson, and Xueshi Gao for their
assistance in the construction of the evaporation cells. S.C. was supported by
NSF Grant No. CHE-1935885. I.L. was supported by the Center for Emergent
Materials, an NSF MRSEC, under Grant No. DMR-2011876. W.Z. was supported by
AFOSR MURI 2D MAGIC Grant No. FA9550-19-1-0390 and the US Department of Energy
Grant No. DE-SC0016379.

## Author Declarations

### Conflict of Interest

The authors declare no conflicts of interest to disclose.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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