# Vapor transport growth of MnBi2Te4 and related compounds

J.-Q. Yan  Materials Science and Technology Division, Oak Ridge National
Laboratory, Oak Ridge, Tennessee 37831, USA<EMAIL_ADDRESS>Z. L. Huang
Department of Physics and Astronomy, Rutgers University, Piscataway, New
Jersey 08854, USA  W. D. Wu  Department of Physics and Astronomy, Rutgers
University, Piscataway, New Jersey 08854, USA  A. F. May  Materials Science
and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831, USA

###### Abstract

Motivated by fine tuning of the magnetic and topological properties of
MnBi2Te4 via defect engineering, in this work, we report the crystal growth of
MnBi2Te4 and related compounds using vapor transport method and crystal
characterization by measuring elemental ratio, magnetic and transport
properties, and scanning tunneling microscopy. For the growth of MnBi2Te4
single crystals, I2, MnI2 , MnCl2, TeCl4, and MoCl5 are all effective
transport agents; chemical transportation occurs faster in the presence of
iodides than chlorides. MnBi2Te4 crystals can be obtained in the temperature
range 500∘C-590∘C using I2 as the transport agent. We further successfully
grow MnSb2Te4, MnBi2-xSbxTe4, and Sb-doped MnBi4Te7 crystals. A small
temperature gradient $<$20∘C between the hot and cold ends of the growth
cmpoule is critical for the successful crystal growth of MnBi2Te4 and related
compounds. Compared to flux grown crystals, vapor transported crystals tend to
be Mn stoichiometric, and Sb-bearing compositions have more Mn/Sb site mixing.
The vapor transport growth provides a new materials synthesis approach to fine
tuning the magnetic and topological properties of these intrinsic magnetic
topological insulators.

##  I Introduction

MnBi2Te4was intensively investigated in the last few years after it was first
predicted and investigated as the first intrinsic antiferromagnetic
topological insulatorOtrokov  _et al._ (2019). MnBi2Te4 is one member of a
large family of compounds with a general formula $n$MnTe.$m$Bi2Te3 where both
integers $n$ and $m$ can vary. $n$ determines the thickness of the magnetic
slabs, and $m$ determines the nonmagnetic spacing between the magnetic slabs.
Varying m while keeping $n$=1 gives MnBi2Te4($m$=1), MnBi4Te7 ($m$=2),
MnBi6Te10 ($m$=3), and MnBi8Te13 ($m$=4) with various magnetic and topological
properties which were the focus of the community in the last three years.
Recently, Mn2Bi2Te5 ($n$=2, $m$=1) was successfully synthesizedCao  _et al._
(2021) as the first $n>$1 member in this large family. The Sb analogues,
MnSb2Te4 and MnSb4Te7, were found to existYan  _et al._ (2019a); Huan  _et
al._ (2021) which facilitates the fine tuning of the physical properties via
chemical substitutionYan  _et al._ (2019a); Chen  _et al._ (2019); Hu  _et
al._ (2021); Chen  _et al._ (2021); Shao  _et al._ (2021). This family of
compound provides an ideal materials playground for the study of intimate
coupling between magnetic and electronic topological properties and for exotic
quantum phenomena.

However, this family of compound, like other crystalline solids, has defects
in its crystal lattice that can affect both magnetic and topological
properties. Density functional theory calculations suggest that the formation
of Mn/Bi site mixing in MnBi2Te4 is driven by the lattice mismatch between
Bi2Te3 and MnTe slabsDu  _et al._ (2021). The nonstoichiometry of Te and the
site mixing between Bi and Te should also be considered depending on the
growth conditions. These are confirmed by the experimental observation of
lattice defects via single crystal x-ray and neutron diffraction, scanning
tunneling microscopy(STM), scanning transmission electron microscopy(STEM) Yan
_et al._ (2019b); Yuan  _et al._ (2020); Zhu  _et al._ (2020); Li  _et al._
(2020a); Zeugner  _et al._ (2019); Murakami  _et al._ (2019); Liu  _et al._
(2021); Huang  _et al._ (2020); Garnica  _et al._ (2021); Shikin  _et al._
(2021); Sitnicka  _et al._ (2021). We noticed in our flux-grown MnBi2Te4
crystals, while the concentration of MnBi (Mn at Bi site) is in the range of
2-4% in crystals from different batches, the concentration of BiMn (Bi at Mn
site) can vary in a wide range 4-15% which is rather sensitive to growth
parameters. In MnSb2Te4, more Mn/Sb site mixing can form due to the smaller
size difference between Mn and Sb. These lattice defects induce electronic
inhomogeneities, a complex ferrimagnetism in each septuple layer, and can
affect and even change the sign of inter-septuple-layer magnetic
interactions.Lai  _et al._ (2021); Murakami  _et al._ (2019); Liu  _et al._
(2021); Huang  _et al._ (2020) Recently, lattice disorder in MnBi2Te4 was
proposed to account for the experimentally observed high Chern number state in
MnBi2Te4 flakesLi  _et al._ (2021) and affect the gap size of the surface
statesGarnica  _et al._ (2021); Shikin  _et al._ (2021); Sitnicka  _et al._
(2021). Careful investigations on MnTe.$m$Bi2Te3 with $m>$1 found the above
mentioned lattice defects in both the quintuple and septuple layers, which
lead to diverse magnetic ground statesYan  _et al._ (2021); Hu  _et al._
(2021).

The presence and abundance of lattice defects make possible the defect
engineering of the magnetic and topological properties of this family of
compound. Considering the sign change of the inter-septuple-layer magnetic
interactions with increasing amount of MnSb (Mn at Sb site) in
MnSb2Te4Murakami  _et al._ (2019); Liu  _et al._ (2021), similar approach
might lead to ferromagnetic MnBi2Te4 with either increasing amount of MnBi or
partial substitution of Bi by other transition metal ions such as V or Cr.
This ferromagnetism will facilitate the realization of quantum anomalous Hall
effect (QAHE) if band inversion preserves in the presence of high
concentration of lattice defects. On the other hand, reducing the defect
concentration to be minimal is necessary for the intrinsic properties and
possibly quantized transport properties at even higher temperatures.
Thermodynamically, materials syntheses at lower temperatures helps reduce the
amount of site mixing while growths at higher temperatures are expected to
have an oppositive effect. The different growth mechanism and kinetics of
different growth approaches can be employed to fine tune the lattice defects
and nonstoichiometry and therefor the physical properties.

In the pioneer work by Otrokov et alOtrokov  _et al._ (2019), MnBi2Te4 single
crystals were grown by slow cooling of a melt mixture of MnTe and Bi2Te3 in a
narrow temperature window or by Bridgman method. Later, we developed the flux
growth of sizeable MnBi2Te4 crystals out of Bi2Te3 flux and this procedure can
also grow other members in the MnTe.$m$Bi2Te3 family including the Sb-doped
compositionsYan  _et al._ (2019b). The identification of Bi2Te3 as an
appropriate flux for the growth of sizable MnBi2Te4 single crystals
facilitates a thorough investigation of this interesting compound by multiple
probes including inelastic neutron scattering which normally requires a large
mass of samples. A careful inspection of MnBi2Te4 single crystals grown using
this protocol found about 2-4% MnBi and 4-15% BiMn; both depend on the growth
parameters especially the temperature profile and the composition of starting
materials. According to the Bi-Te binary phase diagram, varying the Bi/Te
ratio in the flux can slightly lower the growth temperature and can also fine
tune the charge carrier concentrationDu  _et al._ (2021). However, once the
flux composition is too far away from Bi2Te3, other competing phases
precipitate. This leads to limited variation of growth temperature and forces
us to consider new fluxes or other growth techniques such as chemical vapor
transport. Vapor transport growths are normally performed in a sealed ampoule
and chemical transportation occurs with the aid of a volatile substance named
transport agent. At elevated temperatures, the transport agent reacts with the
starting materials forming gaseous phases that can diffuse to the other end of
the ampoule, normally kept at a lower temperature and called cold end.
Crystals then deposit at the cold end and then the transport agent is
released. In principle, the growth temperature can be significantly lower than
the melting temperature of Bi2Te3, which makes possible the crystal growth of
MnBi2Te4 at much lower temperatures. Up to now, vapor transport growth of
MnBi2Te4 and related compounds has not been reported yet.

Motivated by purposely manipulating the concentration and distribution of
lattice defects for more intrinsic or exotic quantum phenomena, in this work,
we report the crystal growth of MnBi2Te4 and related compounds using vapor
transport method. For the growth of MnBi2Te4 single crystals, I2, MnI2, MnCl2,
TeCl4, or MoCl5 are all valid transport agents. A small temperature gradient
$<$20∘C is essential for the successful crystal growth of MnBi2Te4 and related
compounds. The lowest temperature that we managed to obtain MnBi2Te4 crystals
is 500∘C when I2 is used to assist the growth. Using I2 as the transport
agent, we also successfully grew single crystals of MnSb2Te4, MnBi2-xSbxTe4,
and Sb-doped MnBi4Te7. Compared to flux grown crystals, vapor transported
crystals tend to be Mn stoichiometric and the Sb-bearing compositions have
more Mn site mixing. These differences demonstrate that the physical
properties of MnBi2Te4 and related compounds can be engineered by using
different materials synthesis routes.

Table 1: Summary of the details of some selected growths mentioned in the text. Only the Sb content,$x$ in Mn2Bi2-xSbxTe5, is listed for the starting composition of the last four batches with Sb doping. The tube furnace used for the growths is a single zone tube furnace with a thermocouple to monitor the temperature at the cold end of the ampoule. The Neel temperature, TN, is defined as the temperature where a cusp was observed in the temperature dependence of magnetic susceptibility measured in a magnetic field of 1 kOe.  Batch # | starting composition | transport agent | T/time | furnace | EDS | TN/c | e/h($\times$1019cm-3)
---|---|---|---|---|---|---|---
#1164 | Mn:Bi:Te=2:2:5 | I2 | 585∘C, 10days | box | Mn0.94(2)Bi2.07(1)Te3.99(1) | 25.0 K | e, 3.1
#1174B | Mn:Bi:Te=2:2:5 | TeCl4 | 585∘C, 14days | box | Mn0.94(2)Bi2.05(2)Te4.01(3) | 24.6 K | e,7.3
#1178 | Mn:Bi:Te=2:2:5 | MnCl2 | 585∘C, 21days | box | Mn1.01(2)Bi1.99(2)Te4.00(2) | 25.2 K | e, 5.0
#1183B | Mn:Bi:Te=5:2:8 | I2 | 550∘C, 14days | tube | Mn1.01(1)Bi2.01(1)Te3.98(1) | 25.7 K | e, 3.3
#1198B | Mn:Bi:Te=2:2:5 | I2 | 550∘C, 14days | tube | Mn0.99(1)Bi2.00(1)Te4.01(1) | 25.7 K | e, 1.2
#1193A | Mn:Sb:Te=2:2:5 | I2 | 590∘C, 14days | box | Mn1.15(2)Sb1.95(1)Te3.90(1) | Tc=44 K | p,110
#1191A |  $x$ = 0.65 | I2 | 590∘C, 14days | box | Mn1.00(4)Bi1.34(3)Sb0.74(3)Te3.92(3) | 24.2 K | –
#1238 |  $x$ = 1.0 | I2 | 585∘C, 14days | box | Mn0.97(4)Bi1.04(1)Sb1.05(2)Te3.94(1) | 23.5 K | –
#1193B |  $x$ = 1.5 | I2 | 590∘C, 14days | box | Mn1.01(3)Bi0.50(3)Sb1.53(1)Te3.95(1) | Tc=26 K | –
#1193C |  $x$ = 1.0 | I2 | 590∘C, 12days | box | Mn0.88(1)Bi1.77(1)Sb2.39(1)Te6.96(1) | 13 K, 6 K | p,37
Figure 1: (color online) (a) Schematic picture of the chemical vapor transport
growth highlighting that a small temperature gradient $<$20∘C is essential for
the successful growth of MnBi2Te4 and related compounds regardless the
transport agents investigated in this work. (b) a rectangular-bar-shaped
MnBi2Te4crystal from #1164 on a millimeter grid. (c) a plate shaped
MnBi2Te4crystal from #1198B. (d) a mixture of rectangular-shaped crystals and
plate-like crystals at the cold end of the growth ampoule. (e) cluster of
plate-like crystals at the cold end of the growth ampoule. Crystals shown in
(b-e) are grown using I2 as the transport agent. (f) The droplets of Bi2Te3
melt and beautiful MnCl2 crystals condensed at the cold end of growth ampoule
for a vapor transport growth of MnBi2Te4 performed above 600∘C.

##  II Experimental details

Millimeter sized single crystals of MnBi2Te4, MnSb2Te4, MnBi2-xSbxTe4, and
MnBi4-xSbxTe7 were grown by vapor transport method. Table I lists the detailed
growth parameters of some selected growths. In a typical growth, 0.5 g
starting materials and 0.1 g transport agent were sealed in a quartz tube of
12 mm in inner diameter and 4 inches in length. The growth was performed in a
single zone tube furnace or a box furnace. When a tube furnace is used, an
extra thermocouple is placed right next to the growth ampoule to monitor the
temperature at the cold end. When a box furnace is used, the end pointing to
the door is called the cold end assuming the area near the furnace door has a
slightly lower temperature. The use of a box furnace is mainly due to the
small temperature gradient needed for the crystallization of MnBi2Te4 and
related compounds as presented later. After 2-3 weeks, single crystals are
normally found at the cold end but occasionally along the tube, most likely
due to the detailed temperature gradient. For the growth of MnBi2Te4, we
obtained millimeter sized crystals using I2, MnCl2, TeCl4, MnI2, or MoCl5 as
the transport agent.

The elemental analysis was performed on freshly cleaved surfaces using a
Hitachi TM-3000 tabletop electron microscope equipped with a Bruker Quantax 70
energy dispersive x-ray system. 00l reflections on cleaved surfaces were
measured to confirm the phases at room temperature using a PANalytical XPert
Pro diffractometer with Cu-Kα1 radiation. Magnetic properties were measured
with a Quantum Design (QD) Magnetic Property Measurement System in the
temperature range 2.0 K$\leq$T$\leq$ 300 K. The temperature and field
dependent electrical resistivity data were collected using a QD Physical
Property Measurement System (PPMS) in magnetic fields up to 140 kOe. The
scanning tunneling microscope (STM) and spectroscopy (STS) measurements were
performed in an Omicron UHV-LT-STM with a base pressure 1$\times$10-11mbar.
Electrochemically etched tungsten tips were characterized on Au (111) surface.

##  III Results and discussion

###  III.1 Vapor transport growth of MnBi2Te4

Halides were previously employed as the transport agent to grow MnBi2Se4Nowka
_et al._ (2017). We thus tested the growth of MnBi2Te4 using I2, MnI2, MnCl2,
TeCl4, or MoCl5 as the transport agent. Considering the slow transportation of
MnNowka  _et al._ (2017), we used Mn2Bi2Te5 as the starting materials. All
transport agents work well for the growth of MnBi2Te4 crystals. No difference
was observed between growths using I2 and MnI2 as transport agent. However,
they both are more effective transport agents than those chlorides. As shown
in Table I, growths using chlorides as transport agent require much longer
growth time in order to obtain crystals of comparable size.

Figure 1 (a) shows a schematic picture of the growth ampoule which highlights
that a small temperature gradient $<$20∘C is necessary for the successful
growth of MnBi2Te4 and related compounds. Once the temperature gradient is too
large, Bi2Te3, normally doped with 1-4% Mn, is always found at the cold end
leaving some small MnTe crystals at the hot end of the growth ampoule. For
growths performed inside of a tube furnace, plate-like crystals (see Fig. 1c)
are always obtained regardless the type of transport agent, the temperature of
the cold end, or the duration time. In contrast, for growths using a box
furnace, both plate-like and rectangular-bar-shaped crystals (see Fig. 1b) are
found inside of the growth ampoule. Figures 1 (d, e) show the pictures of the
cold end after the growth. There are more rectangular-bar-shaped crystals in
Fig. 1d. Most MnBi2Te4 crystals stay at the cold end while occasionally
crystals can be found in between the cold and hot ends along the tubes. This
suggests that the temperature gradient inside of a box furnace is not that
well defined as in a tube furnace. Despite the poorly defined temperature
gradient, all growths of MnBi2Te4, MnBi2-xSbxTe4, and MnSb2Te4 are
reproducible.

In addition to crystals of the desired composition, the following crystals can
be occasionally found inside of the ampoule: MnTe2, MnTe, Mn-doped Bi2Te3, and
Mn$X_{2}$ ($X$=Cl, I). Mn$X_{2}$ crystals are transparent and moisture
sensitive. The pyrite structured MnTe2 grows like truncated cubes and can be
easily identified by vision inspection under an optical microscope. The
hexagonal structured MnTe crystals are also plate-like but rather brittle. Mn-
doped Bi2Te3 and the targeted MnBi2Te4 and related compositions are quite
alike and we normally distinguish them by using elemental ratio and (00l)
reflections.

Figure 2: (color online) Temperature dependence of magnetization measured in a
field of 1kOe applied perpendicular (labelled as H//$ab$) and parallel to the
crystallographic c-axis. This MnBi2Te4crystals (#1164) was grown at 585∘C in a
box furnace using I2 as the transport agent.

Vapor transport growth using MnCl2 as the transport agent was specially
investigated with great details aiming to obtain crystals good for the
experimental realization of QAHE. The experimental realization of QAHE in
MnBi2Te4 flakes is one of the most exciting results on this intrinsic magnetic
topological insulatorDeng  _et al._ (2020). But it is yet to be reproduced. In
Ref. 25, MnBi2Te4 crystals used for the device exhibiting QAHE were grown out
of MnCl2 flux. If the quality of the starting MnBi2Te4 crystals is the sole
factor responsible for the absence of the spin flop transition and the
observation of QAHE in Ref. 25, crystal growth in the presence of MnCl2
deserves special attention. Considering the vapor pressure of MnCl2 and
possible reaction between MnCl2 and other starting materials at the growth
temperatures used in Ref. 25, one would expect that the vapor phases might
play an important role in the crystal growth. We first determined the
appropriate temperature range for the vapor transport growth of MnBi2Te4 with
0.1 gram of MnCl2 and 0.5 gram of Mn2Bi2Te5. All growths were performed in a
box furnace using the small natural temperature gradient. Mn-doped Bi2Te3
crystals were obtained when the growth temperature is lower than 550∘C and
Bi2Te3 liquids were observed at the cold end when the growth temperature is
over 600∘C (see Fig. 1(f)). We then fixed the growth temperature at 585∘C but
increased the amount of MnCl2 in the starting materials from 0.1 gram to 0.3
gram and then to 0.5 gram. With increasing amount of MnCl2 in the starting
materials, there are more transport pink colored MnCl2 single crystals at the
cold end after the crystal growth. However, Elemental analysis, magnetic
measurement, and room temperature Hall measurements found all MnBi2Te4
crystals from these growths are comparable to each other. Thus the amount of
MnCl2 in the starting materials does not seem to affect the physical
properties of MnBi2Te4 crystals obtained in the growths described above.

Figure 3: (color online) Temperature dependence of in-plane electrical
resistivity. The data for two batches of flux-grown crystals are also shown
for comparison. The high field magnetization of #1083A was reported in
Ref.[21]. Both batches of flux-grown crystals were used in the study of
quantum phase transitions in thin flakes [Refs 26; 27]. Figure 4: (color
online) (a) The topographic image of sample #1164 surface after room-
temperature cleaving. (b) The line profile along the blue dashed line in (a).
(c) and (d) are respectively the topographic images of sample #1198B surface
after room-temperature and cold cleaving. (e) and (g) are respectively the
topographic images of samples #1174B and #1178 surfaces after the sample is
cold cleaved, warmed up to 220K and inserted into the cold STM head. (f) and
(h) are respectively the topographic images of samples #1174B and #1178
surfaces after cold cleaving. Tunneling set points of topographic images: (a)
and (c) -1V, 30pA; (d) 1V, 100pA; (e) 1.5V, 30pA; (f) -0.8V, 100pA; (g) 1.5V,
30pA; (h) 1.5V, 20pA. Figure 5: (color online) Magnetic properties of
MnSb2Te4crystals. (a) Temperature dependence of magnetization with the
magnetic field of 100 Oe applied parallel (H$//$c) and perpendicular to the
crystallographic $c$-axis. (b) Field dependence of magnetization measured at 2
K.

All MnBi2Te4 crystals we obtained in this study exhibit an antiferromagnetic
order around TN = 25 K. Figure 2 shows the temperature dependence of the
magnetic susceptibility of one batch #1164 as an example. The anisotropic
temperature dependence agrees with previous report and suggests an
antiferromagnetic order at TN=25 K. It should be mentioned that the magnetic
data shown in Fig. 2 was collected without any cleaning after crystal growth.
The data show no sign of the contamination of ferromagnetic Bi2-xMnxTe3, which
has been occasionally observed when measuring the magnetic susceptibility of
flux-grown MnBi2Te4 crystalsYan  _et al._ (2019b).

We also measured the field dependence of magnetization at 2 K in magnetic
fields up to 120 kOe in order to obtain the critical fields for the spin flop
transition and the first magnetization plateau(Lai  _et al._ , 2021). The
correlation between TN and the critical field for spin flop transition is
presented later. It is worth mentioning that the magnetization at 2 K and 120
kOe is around 3.8$\mu_{B}$/Mn for all the batches we measured. This suggests
that all crystals we checked have similar amount of Mn/Bi site mixing, which
is supported by the STM measurements presented later.

The temperature and field dependence of electrical resistivity was measured in
the temperature range 2 K$\leq$T$\leq$300 K and in magnetic fields up to 120
kOe. Figure 3 shows the temperature dependence of the in-plane electrical
resistivity of some vapor-transported crystals. The electrical resistivity
data of two batches of flux grown crystals are also plotted for comparison.
The temperature and field dependence agrees with previous reports.Lee  _et
al._ (2018); Zeugner  _et al._ (2018); Otrokov  _et al._ (2018) From the Hall
measurements, the electron density is in the range 1-8$\times$1019cm-3. The
charge carrier concentration of some selected batches is listed in Table I.

###  III.2 STM

Figure 4(a) shows the topographic image of the surface of sample #1164 after
room-temperature cleavage. Unlike the atomically flat surfaces seen in
previous STM reports on our flux grown crystalsYan  _et al._ (2019b); Liu  _et
al._ (2021); Huang  _et al._ (2020), the surface here is covered with adatoms
of height 60-80 pm as inferred from Fig. 4(b). Interestingly, the adatoms tend
to align along the three crystallographic directions of the underlying
triangular lattice, forming adatom chains. As shown in Fig. 4(c), the room-
temperature cleaved sample #1198B show a similar surface. However, the
atomically flat surface can be obtained after low temperature cleavage, as
shown in Fig. 4(d) for sample #1198B. Measurements on other cold cleaved
samples #1174B and #1178 shown in Fig. 4(f) and (h) further confirm that cold
cleavage exposes atomically flat and clean surface. To understand the origin
of the adatoms appearing after room-temperature cleaving, we warmed up the
cold cleaved samples to about 220 K and inserted them back in the STM head. As
shown in Fig. 4(e) and (g), adatoms appear on the surface and arrange in the
similar pattern as that after room-temperature cleavage. It should be noted
that different transport agents are used in the above batches mentioned. We
also carefully monitored the $c$-lattice of these crystals and found no
noticeable difference within experimental uncertainty. We thus speculate that
these adatoms are the decomposition of transport agents (I or Cl ions) trapped
on surfaces or grain boundaries during crystal growth. Immediately after cold
cleavage, there is not enough thermal energy for them to diffuse so that we
can observe clean surfaces. At elevated temperature these atoms could diffuse
on the cleaved surface, forming the pattern that we see in the STM images.
This might need to be considered in ARPES measurements and crystal exfoliation
for flakes.

From the atomically flat surface obtained after cold cleaving, the densities
of the dominant defect MnBi antisites are (3.1$\pm$0.1)% and (3.3$\pm$0.2)% in
sample #1198B and #1174B, respectively. The density of MnBi in #1178 is
slightly higher at (4.0$\pm$0.2)%. This amount of MnBi defects is comparable
to that in our flux grown crystalsLai  _et al._ (2021); Huang  _et al._
(2020); Yan  _et al._ (2019b).

###  III.3 Vapor transport growth of MnSb2Te4

The same procedure can be employed to grow MnSb2Te4 crystals. Figure 5 shows
the magnetic properties of MnSb2Te4 crystals grown at 590∘C using I2 as the
transport agent. The temperature dependence of magnetization suggests a
ferromagnetic inter-septuple-layer coupling and the magnetic ordering
temperature, Tc, is about 44 K. According to our previous work on MnSb2Te4Liu
_et al._ (2021), Mn/Sb site mixing favors a ferromagnetic interlayer coupling
and Tc can be tuned from 24 K to about 50 K. The magnetic behavior shown in
Figure 5 signals a large amount of Mn/Sb antisite defects and few amount of Mn
deficiency. The elemental analysis suggests a composition of
Mn1.15(2)Sb1.95(1)Te3.90(1) which is Mn rich. The field dependence of
magnetization at 2 K (see Fig. 5(b)) can be employed to get a good estimate of
the Mn/Sb antisite defects. The saturation moment is about 1.40$\mu_{B}$/Mn
around 60 kOe, which suggests about 72% Mn site is taken by Mn assuming a
local magnetic moment of 5$\mu_{B}$/Mn and a ferrimagnetic arrangement in each
septuple layerLiu  _et al._ (2021); Lai  _et al._ (2021).

The electrical transport properties were also characterized by measuring the
temperature dependence of electrical resistivity. A room temperature value of
1.6$\times$10${}^{-3}\ohm.cm$ is similar to that of our flux grown crystalsYan
_et al._ (2019a); Liu  _et al._ (2021). Upon cooling, a metallic conducting
behavior is observed and a quick drop of electrical resistivity was observed
upon cooling through Tc. This temperature dependence is similar to that of
ferromagnetic MnSb2Te4 grown out of Sb2Te3 fluxLiu  _et al._ (2021). The Hall
resistivity was measured at multiple temperatures in the temperature range 50
K - 300 K. The Hall coefficient shows little temperature dependence below room
temperature. With the assumption that a single band dominates the Hall signal,
the coefficient at 250 K gives a carrier density of 1.1$\times$1021cm-3. Just
like the flux grown crystals, the vapor transported MnSb2Te4 crystals are also
heavily hole doped.

Figure 6: (color online) Temperature and field dependence of magnetization for
(a,b) $x$ = 0.74, (c, d) $x$ = 1.0, and (e, f) $x$ = 1.53 of
MnBi2-xSbxTe4crystals grown using I2 as the transport agent.

Obviously, vapor transport growth can tune the chemistry of MnSb2Te4 crystals
in a wide range and the millimeter sized vapor transported crystals makes
possible a careful investigation of the anisotropic properties. Compared to
MnSb2Te4 crystals grown out of Sb2Te3 flux at different temperatures, the I2
transported crystals have more Mn ions residing on the Sb site which leads to
a smaller saturation magnetization at low temperatures. We further tested the
vapor transport growths at temperatures above 630∘C with the motivation of
further increasing the concentration of MnSb. However, only Mn-doped Sb2Te3
was obtained above 630∘C. Once the growth temperature is above the melting
temperature of Sb2Te3, liquid Sb2Te3 droplets can be found at the cold end and
no MnSb2Te4 crystals could be obtained. We did not perform growths using other
transport agents. However, it would be interesting to investigate whether
other transport agents can affect the concentration and distribution of Mn
defects and thus the magnetic and topological properties of MnSb2Te4. In
addition to the growth temperature and transport agent, the effect of the
composition of the starting materials on the final nonstoichiometry of
MnSb2Te4 crystals also deserves a systematic investigation.

###  III.4 Vapor transport growth of MnBi2-xSbxTe4

We further tested the growth of Sb-doped MnBi2Te4 crystals using I2 as the
transport agent. The focus of the current work is to explore routes to defect
engineering of the magnetic and topological properties by controlling the
growth parameters rather than to perform a systematic study of the physical
properties of MnBi2-xSbxTe4. Figure 6 shows the magnetic properties of $x$ =
0.74, 1.0, and 1.53. The temperature dependence of magnetic susceptibility
suggests an antiferromagnetic order for $x$ = 0.74 and 1.0. TN, which is
defined as the temperature where a cusp is observed in the temperature
dependence of $\chi_{c}$, is 24.2 K and 23.5 K for $x$ = 0.74 and 1.0,
respectively. TN for these two compositions agrees with that reported
previously for flux grown crystals of similar compositionsYan  _et al._
(2019a). The antiferromagnetic ground state is further confirmed by the field
dependence of magnetization results shown in Fig. 6 (b,d) where a spin flop
transition is observed. For $x$ = 1.53, the temperature and field dependence
of magnetization suggests a ferromagnetic order below Tc=26 K, similar to that
observed in $x$=0.20 crystal grown by flux methodChen  _et al._ (2020).

Figs. 6 (b,d,f) show the field dependent magnetization at 2 K. The absence of
the metamagnetic transition further confirms the ferromagnetic order in
$x$=1.53. With increasing Sb content, the magnetization at 65 kOe decreases.
This indicates that the amount of antisite Mn ions sitting at Bi/Sb site
increases with increasing Sb content, which explains the ferromagnetism
observed for $x$=1.53. Compared to the flux-grown crystals of similar
compositions, the vapor transported MnBi2-xSbxTe4 crystals have a smaller
magnetization at 2 K and 65 kOe, suggesting that vapor transport growth using
I2 as transport agent leads to more site mixing between Mn and Bi/Sb. This has
important consequences for $x$=0.74 and 1.0 on their critical magnetic fields,
Hc1 for the spin flop transition and Hc2 for the magnetization plateau when
the magnetic field is applied along the crystallographic$c$-axis. For $x$ =
0.74, Hc1 is 19 kOe and Hc2 is 60 kOe. For $x$ = 1.0, Hc1 is 14 kOe and Hc2 is
46 kOe. For both compositions, both Hc1 and Hc2 are about 5-6 kOe smaller than
those in flux grown crystals with the same Sb content. When the magnetic field
is applied perpendicular to the $c$-axis, the magnetization increases with
field and saturates at Hab which is larger than Hc2. Hab decreases from above
70 kOe for $x$ = 0.74 to 58 kOe for $x$ = 1.0 with increasing Sb content. Hab
is also smaller than that of flux grown crystals for these two compositions.
All these observations support that vapor transported MnBi2-xSbxTe4 crystals
have more antisite defects than flux-grown crystals. This indicates that the
detailed chemistry and physical properties of MnBi2-xSbxTe4 crystals can be
finely adjusted by using different growth techniques with different growth
mechanism and kinetics.

It is worth mentioning that our EDS results suggest that Mn is near
stoichiometric while Te tends to be deficient for all the MnBi2-xSbxTe4
crystals we checked. As discussed later, this seems to be one difference
between the vapor transport growth and the flux growth out of Bi2Te3.

Figure 7 shows the relation between the Sb concentration inside of the
crystals and the nominal one in the starting materials. The amount of Sb
inside of the crystals is close to that in the starting materials. This is in
sharp contrast to that in growths out of Bi2Te3 flux where the Bi/Sb ratio can
be quite off from the starting compositions due to the distribution
coefficient of (Bi) and (Sb) in the fluxYan  _et al._ (2019a). The consistency
between the composition of the starting materials and single crystals enables
an easier control of the composition and easier targeted growths in future
vapor transport growths of MnBi2-xSbxTe4 crystals.

Figure 7: (color online) Distribution of Bi/Sb in crystals and starting
materials.

###  III.5 Vapor transport growth of MnBi4-xSbxTe7

In one test growth (batch #1193C) of MnBi2-xSbxTe4 using I2 as the transport
agent, MnBi4-xSbxTe7 crystals were obtained instead. The growth details are
listed in Table 1. Elemental analysis suggests a composition of
Mn0.88(2)Bi1.76(1)Sb2.39(1)Te6.96(2). Figure 8 presents the $(00l)$
reflections collected using x-ray diffraction on the surface of the plate-like
single crystals. These $(00l)$ reflections can be indexed with the structure
of MnBi4Te7 and the $c$ lattice is 23.794(3)$\AA$, close to that of MnBi4Te7
reported previouslySouchay  _et al._ (2019); Hu  _et al._ (2020); Yan  _et
al._ (2020). Figure 9 shows the temperature dependence of the magnetic
susceptibility measured in magnetic fields applied perpendicular (labelled as
H//$ab$) and parallel (H//$c$) to the crystallographic c-axis. All
measurements were carried out in a field cooled mode. The anisotropic magnetic
susceptibility data collected in an applied magnetic field of 1 kOe suggest a
ferromagnetic interlayer coupling with the moments aligned along the
crystallographic $c$-axis. The magnetic ordering temperature is about 14 K,
which is close to that reported for Sb-doped MnBi4Te7Hu  _et al._ (2021); Chen
_et al._ (2021). When a magnetic field of 100 Oe is applied along $c$-axis
during the measurements, a sharp drop of magnetization is observed upon
cooling below about 6 K. A much weaker anomaly was observed at 6 K when this
small field is applied perpendicular to the $c$-axis. This suggests the
appearance of antiferromagnetic alignment of magnetic moments. The difference
between the magnetization data collected in 100 Oe and 1 kOe suggests that a
small field near 1 kOe is enough to polarize the antialigned spins. It should
be noted that the mexican-hat-like temperature dependence of magnetization is
not observed in flux grown MnBi4-xSbxTe7 crystalsHu  _et al._ (2021); Chen
_et al._ (2021). The magnetic susceptibility curves (not shown) measured with
H//ab and H//c in the temperature range 50$\leq$T$\leq$300 K can be described
by the Curie-Weiss law, $\chi=C/(T-\theta$), where C is the Curie constant and
$\theta$ is the Weiss temperature. The Curie-Weiss fitting of the high
temperature susceptibility data obtains a Weiss temperature of 6 K and an
effective moment of 4.95 $\mu_{B}$/Mn.

The mexican-hat-like temperature dependence of magnetization shown in Fig.
9(a) suggests a ferromagnetic order around 14 K and then a transition upon
cooling to an antiferromagnetic order around 6 K. The sharp drop of
magnetization around 6 K is more likely due to the change of the inter-
septuple-layer coupling from ferromagnetic to antiferromagnetic other than a
sudden alignment of MnBi moments antiparallel to MnMn. First, MnBi in the
septuple layers are strongly antiferromagnetically coupled to MnMn and a large
magnetic field is needed to change their alignment(Lai  _et al._ , 2021).
Second, it is not clear whether and how the MnBi ions in the quintuple layers
of MnBi4Te7 order magnetically. A recent study(Hu  _et al._ , 2021) on Sb-
doped MnBi4Te7 proposed the absence of any long range magnetic order of MnBi
ions in the quintuple layers but it is yet to be confirmed experimentally. It
is reasonable to speculate that the state of MnBi ions in the quintuple layers
depends on the concentration and distribution of magnetic defects. However,
considering the small population of MnBi ions in the quintuple layers, one
would not expect such a large drop of temperature dependence of magnetization
around 6 K. This is supported by the large magnetization change at the spin
flip transition presented in Fig. 9(b). Finally, previous studies show that
the energy difference between antiferromagnetic and ferromagnetic inter-
septuple-layer coupling is small in MnBi2Te4 and related compounds and the
delicate magnetic ground state is fragile and sensitive to the inter-septuple-
layer spacing or lattice defects. The mexican-hat-like temperature dependence
of magnetization shown in Fig. 9 (a) should result from a temperature driven
change of the magnetic ground state.

Figure 8: (color online) ($00l$) reflections of MnBi4-xSbxTe7 suggesting the
c-axis is perpendicular to the plane of the plate. Figure 9: (color online)
(a) The temperature dependence of magnetization. (b) The field dependence of
magnetization at 2 K. Inset shows the spin flip transition around 300 Oe when
H//$c$.

With an antiferromagnetic inter-septuple-layer coupling below 6 K, one would
expect a metamagnetic transition in applied magnetic fields. Figure 9(b) shows
the field dependence of magnetization at 2 K in fields up to 70 kOe applied
along or perpendicular to the crystallographic c axis. The inset highlights
the spin flip transition at a critical field about 300 Oe, which disappears
when measured above 6 K. This confirms that our sample shows a thermal induced
change of magnetic order. The magnetization measured at 2 K and 65 kOe is
about 2.6$\mu_{B}$/Mn, which is much smaller than the expected value and
signals that there are significant amount of antisite Mn ions antiparalllel to
those Mn ions in the main Mn layer. In MnBi2Te4 and MnSb2Te4, the
antiferromagnetic coupling between MnMn and MnBi/Sb in the same septuple layer
is strong and a large magnetic field near 50 T is needed to polarize all Mn
moments. This strong coupling is also expected in the septuple layers in
MnBi4Te7. With the assumption that Mn ions at Bi site in the quintuple layers
are already polarized in a magnetic field of 70 kOe, the magnetization of
about 2.6$\mu_{B}$/Mn suggests that 20% of the Mn ions stay at the Bi sites of
the setuple layers. Similar to that observed in the MnBi4Te7, both H//$ab$ and
H//$c$ magnetization curves show an increase of about 10% in the field range
10-40 kOe. Previously, we speculated that this 10% increases comes from the
polarization of the moment on those Mn ions sitting at Bi site in the
quintuple layersYan  _et al._ (2020). If these Mn ions do not exhibit a
spontaneous magnetic order, the field required for this 10% magnetization
change should signal the exchange field from the neighbouring septuple layers.

Figure 10 shows the temperature dependence of the in-plane electrical
resistivity with the electrical current flowing in the $ab$-plane. As shown in
the inset, a metallic conducting behavior was observed and there are two cusps
at low temperatures where the mexican hat like magnetic susceptibility was
observed. When a small magnetic field is applied along the $c$-axis, the cusp
centering around 14 K shifts to higher temperatures, while the one around 6 K
is suppressed to lower temperatures and disappears above 400 Oe. This
interesting field dependence signals that the transition around 6 K is fragile
and is consistent with the spin flip transition shown in inset of Fig. 9(b).

We would like to mention that this is the only batch of MnBi4-xSbxTe7 single
crystals that we obtained in over 10 similar growths. It is likely that the
temperature gradient along the growth ampoule happens to be in the appropriate
range for the crystallization of MnBi4-xSbxTe7. This is similar to the flux
growth of MnBi4Te7 crystals out of Bi2Te3 flux and it is understandable
considering all MnTe.$m$Bi2Te3 phases exist in a narrow temperature range in
the pseudobinary MnTe-Bi2Te3 systemAliev  _et al._ (2019). Although it is
unfortunate that we failed to identify the exact growth conditions and to
understand the growth mechanism, this only successful growth demonstrates that
more complex MnTe.$m$Bi2Te3 compounds can be obtained by the chemical vapor
transport growth. Compared to MnBi4Te7 crystals grown out of Bi2Te3 flux, our
MnBi4-xSbxTe7 crystals is less Mn deficient. The Mn deficiency in
MnTe.$m$Bi2Te3 increasing with $m$ driven by the increasing lattice mismatch
between the MnTe and the Bi2Te3 in the nature heterostructure(Du  _et al._ ,
2021). The large Mn deficiency might prevent the experimental observation of
the theoretically predicted quantum phenomena in MnTe.$m$Bi2Te3 with $m>$1\.
Chemical vapor transport growth reported in this work provides a different
approach for the materials synthesis and a careful control of the growth
process might eventually lead to a good control of magnetic defects (MnBi and
magnetic vacancy at Mn site) thus for the intrinsic properties and maybe the
theoretically predicted topological phenomena.

Figure 10: (color online) Temperature dependence of in-plane electrical
resistivity of MnBi4-xSbxTe7 in small magnetic fields applied along the
$c$-axis. The inset shows the data in the temperature range 2-300 K in zero
magnetic field.

###  III.6 Other variants

$n$MnTe.Bi2Te3, with more than one MnTe sheet inserted into Bi2Te3, might show
complex magnetism and host novel topological propertiesZhang  _et al._ (2020);
Li  _et al._ (2020b); Lei  _et al._ (2020). A recent study reports the
successful growth of $n$=2 member, Mn2Bi2Te5, by flux methodCao  _et al._
(2021). It is interesting to note that we found only MnTe.mBi2Te3 crystals
even though the starting materials are $n$MnTe.Bi2Te3 with $n$ up to 5. This
indicates the current growth parameters are not ideal for the growth of
$n$MnTe.Bi2Te3 single crystals. As presented earlier, once the growth
temperature is below 500∘C or above 600∘C, only Bi2Te3 doped with 1-4% Mn was
obtained. The growth below 500∘C is limited by the effective transport of Mn.
Thus, growths using other transport agents which can transport Mn more
effectively should be investigated which might help obtain $n$MnTe.Bi2Te3
compounds.

It is noteworthy that our elemental analysis did observe regions with the
elemental ratio consistent with Mn2Bi2Te5 in one MnBi2Te4 crystal. Figure 11
shows the SEM image of one cleaved surface of one piece of MnBi2Te4 crystal
from #1198B. While we observed Mn:Bi:Te=1:2:4 in most positions on this
surface, the top flake was found to have Mn:Bi:Te=1.96:2.14:4.90. We carefully
looked at the regions nearby but failed to find any sign of MnTe, therefor,
the observed elemental ratio of Mn:Bi:Te=1.96:2.14:4.90 doesn’t seem to be
from a mixture of MnBi2Te4 and MnTe. It is unfortunate that we failed to
isolate enough pieces with that elemental ratio for further characterization.
More growths are in progress to identify the appropriate growth parameters for
the crystallization of Mn2Bi2Te5. However, the presence of that Mn2Bi2Te5-like
flake indicates that (1) vapor transport growth might be employed to grow
Mn2Bi2Te5, (2) some strain field or nonequilibrium conditions might help the
crystallization of Mn2Bi2Te5, and (3) the intergrowth of Mn2Bi2Te5 and
MnBi2Te4 can occur and should be considered in future growths and
characterization of Mn2Bi2Te5.

Figure 11: (color online) SEM image of the cleaved surface of one crystal from
batch #1198B and the elemental analysis of different regions.

Introducing Cr or V into Mn or Bi site might be able to tune the magnetism of
MnBi2Te4. For example, Mn1-xVxBi2Te4 is proposed to show a ferromagnetic
inter-septuple-layer coupling which is preferred for the observation of
QAHEHou and Wu (2021). Partial substitution of Bi by Cr or V might be another
way toward a ferromagnetic interlayer coupling since these magnetic defects
are expected to favor a ferromagnetic inter-septuple-layer coupling. We thus
performed vapor transport growth starting with premelted MnBi1.9M0.1Te4
($M$=Cr, V) using I2 as transport agent at 585∘C in a box furnace. In all test
growths, the obtained single crystals show a TN of 25 K. Elemental analysis
does not suggest any successful substitution. One weak anomaly was observed
around 200 K in the temperature dependence of magnetic susceptibility for the
crystals grown out of MnBi1.9Cr0.1Te4 premelt. This suggests the presence of
Cr2Te3. We further increased the amount of $M$Te in the starting materials and
tried growths starting with equal mass of Mn2Bi2Te5 and $M$Te. Elemental
analysis and magnetic measurements do not suggest any incorporation of Cr or V
in MnBi2Te4 crystals. Vapor transport growths using $MX_{3}$ ($M$=Cr, V,
$X$=Cl, Br, I) as transport agent might deserve some effort as all $MX_{3}$
have a reasonably high vapor pressure around 600∘C.

###  III.7 Vapor transport vs flux growth

Both chemical vapor transport and flux growths can grow single crystals of
MnBi2Te4 and related compounds of similar quality. They both can be employed
to grow crystals for various measurements. The vapor transport growth
developed in this work expands our capability of fine tuning of the
nonstoichiometry, concentration and distribution of lattice defects, and hence
the magnetic and topological properties of these fascinating compounds.
Understanding the difference between vapor transported and flux grown crystals
and also that between these two growth techniques will help us select the
appropriate crystals or growth technique that could best address the physics
questions or meet the scientific needs.

(1) Vapor transported crystals tend to be more Mn stoichiometric. As listed in
Table I, once the temperature gradient is small enough, all MnBi2Te4 and
MnBi2-xSbxTe4 crystals are Mn stoichiometric. In our vapor transported
MnBi2Te4 crystals, our STM results shown in Fig. 4 suggest that there are
about 3-4% MnBi, comparable to what we observed in flux grown MnBi2Te4
crystalsYan  _et al._ (2019b); Huang  _et al._ (2020). This is also supported
by magnetic measurements which show the vapor transported and flux-grown
crystals have similar magnetic ordering temperature, saturation moment,
critical magnetic fields for spin flop transition and moment saturation at low
temperatures. The difference in Mn nonstoichiometry in vapor transported and
flux-grown MnBi2Te4 crystals results from the different growth mechanisms. In
crystal growth using Bi2Te3 as flux, Mn content in MnBi2Te4 crystals depends
on the distribution coefficient of (Mn) between the flux and the crystal,
which normally depends on both temperature and composition. Considering the
growth temperature is close to the melting temperature of Bi2Te3, the
diffusivity of (Mn) in Bi2Te3 flux is expected to be small, which can further
lead to Mn deficiency even though a rather slow cooling rate has been
employed. The Mn content in flux-grown crystals can be purposely controlled by
using carefully selected growth parameters such as the composition of starting
materials and temperature profiles. For vapor transported growths, the
effective transportation of Mn seems to control the nonstoichiometry. As shown
in Table I, Mn-deficient MnBi2Te4 crystals were obtained in several early
batches for which a slightly larger temperature gradient has been used. We
also tried to add more MnTe in the starting materials and this does not seem
to change the total Mn content in the resulting crystals. A careful monitoring
of the correlation between crystal chemistry and growth parameters suggests
the temperature gradient plays a key role in determining the Mn
nonstoichiometry when we fix the growth temperature around 580∘C. If this
understanding is right, an even smaller temperature gradient may facilitate
the growth of Mn2Bi2Te5.

(2) Vapor transported Sb-bearing crystals tend to have more antisite Mn ions.
The vapor transported MnSb2Te4 crystals are Mn-rich (Table I) and have a
ferromagnetic ordering temperature of about 44 K, consistent with previous
studies that MnSb favors a ferromagentic interlayer coupling and the magnetic
ordering temperature can be fine tuned in a wide temperature range 20-50 KLiu
_et al._ (2021). The field dependence of magnetization curves shown in Fig. 6
also suggest that Sb-doped MnBi2Te4 crystals grown by vapor transport have
more antisite magnetic defects. This can have important implications for the
fine tuning of the magnetic and topological properties of Bi-rich
MnBi2-xSbxTe4. Previous studies(Yan  _et al._ , 2019a; Chen  _et al._ , 2019)
have demonstrated that Sb-doping can effectively tune the physical properties
of MnBi2Te4. Vapor transport growth makes possible further tuning of the
properties in a sample with a fixed Sb content via controlling the
distribution of Mn at different crystallographic sites.

(3) Vapor transported crystals are smaller in dimension than flux grown
crystals. This is especially true when chlorides are used as the transport
agent. Most crystals are in sub-millimeter size and less than 2 mg/piece,
which are at least one order of magnitude smaller than the flux-grown
crystals. Thus flux growth is more appropriate when large crystals or a large
amount of crystals are needed for some special measurements such as inelastic
neutron scattering. This doesn’t mean any sacrifice of the crystal quality
because large stoichiometric MnBi2Te4 crystals can be grown out of Bi2Te3 flux
with carefully controlled growth parameters.

(4) Vapor transported MnBi2Te4 crystals are free of contamination by magnetic
Mn-doped Bi2Te3. This is well illustrated by the magnetic susceptibility
results shown in Fig.2. While for flux grown crystals, a careful cleaning is
normally needed to remove residual flux on the surfaceYan  _et al._ (2019b).
However, as shown in Fig. 4, the residual transport agent can contaminate the
cleaved surface of vapor transported crystals.

(5) Vapor transport technique can have an easier control of the Sb content in
MnBi2-xSbxTe4 crystals than the flux growth. This is demonstrated by the
correspondence of Bi/Sb in crystals and starting materials shown in Fig. 7. As
we have not been able to identify the right growth conditions for
MnBi4-xSbxTe7, it is not clear whether Bi/Sb ratio in crystals would be the
same as that in the starting materials for MnBi4-xSbxTe7. The only data point
(#1193C) that we have signals a more complex relation.

(6) Vapor transport growths of MnBi2Te4 crystals were performed in a wider
temperature range 500∘C-590∘C. The highest possible growth temperature of our
vapor transport growths is limited by the melting temperature of Bi2Te3, and
the lowest temperature by the effective transport of all constituents. While
for flux growths, the highest and lowest growth temperature is determined by
the peritectic decomposition temperature of MnBi2Te4 and the melting
temperature of Bi2Te3, respectively.

Figure 12: (color online) (a) Dependence of the magnetic ordering temperature,
TN, on the Mn content. The upper circle shows $x_{Mn}$ range that are likely
good for high temperature device performance. mK temperature is normally
needed for devices using more Mn-deficient crystals (lower circle). (b) The
relation between TN and the critical magnetic field, Hc, for spin flop
transition. The Mn content was determined from EDS. TN was determined from
temperature dependence of magnetization measured in an applied magnetic field
of 1 kOe. Hc was determined from field dependence of magnetization data
collected at 2 K.

###  III.8 Crystal screening before exfoliation

MnBi2Te4 has been proved to be an ideal materials playground for investigating
the intimate correlation between magnetism and electronic topology. There are
ample experimental evidence that the device performance depends on the quality
of starting bulk MnBi2Te4 single crystals. Considering the time consuming
process of device fabrication and low temperature measurements, it is
important to know what crystals could yield high quality flakes that would
exhibit desired physical properties at the atomically thin limit. Ideally, one
would be able to tell the crystal quality before exfoliation by routine bulk
crystal characterization. Motivated by this, we have been trying to correlate
the performance of thin flake devices from our collaboratorsOvchinnikov  _et
al._ (2021); Cai  _et al._ (2021) with the magnetic or transport properties of
bulk crystals since these measurements can be easily performed in most advance
laboratories. Figure 12(a) shows the relation between TN and the Mn content,
$x_{Mn}$, determined from elemental analysis. Here we consider the total Mn
content only because it is too time consuming to determine the population and
distribution of magnetic defects (Mn deficiency in the main Mn layer, and MnBi
antisite defects) of every batch. Crystals with more Mn tend to have a higher
TN, but they don’t exhibit a simple linear relation. The fact that TN varies
even for crystals with the same $x_{Mn}$ signals the importance of magnetic
defects. Our collabors showed that quantized transport properties can be
always observed above 2 K for flakes exfoliated from high quality crystals
with $x_{Mn}>$0.94. In contrast, mK temperature is normally needed if more Mn
deficient crystals are used. Figure 12(b) shows the linear relation between TN
and the critical field for spin flop transition, Hc1. This linear relation
indicates the importance of the interlayer exchange interaction on the
magnetic properties and TN and Hc1 are equivalent in crystal screening. All
MnBi2Te4 crystals that we synthesized order antiferromagentically and have
about 3% MnBi which is not enough to change the sign of interlayer magnetic
interactions. Therefore, TN and Hc1 can be employed to screen crystals before
exfoliation and device fabrication.

##  IV Summary

In summary, we report the chemical vapor transport growth of MnBi2Te4,
MnSb2Te4, MnBi2-xSbxTe4, and MnBi4-xSbxTe7 using I2, MnI2, MnCl2, MoCl5, and
TeCl4 as the transport agent. A small temperature gradient $<$20∘C is found to
be critical for the crystallization of MnBi2Te4 and related compounds at the
cold end of the growth ampoule. The vapor transported crystals grown with a
small temperature gradient tend to have a stoichiometric Mn concentration.
MnBi2Te4 crystals grown by both vapor transport and flux technique have
similar amount of MnBi. However, the chemical vapor transport technique leads
to more antisite Mn ions in Sb-bearing compositions, as evidenced by the
characterization of MnSb2Te4, MnBi2-xSbxTe4 and MnBi4-xSbxTe7 crystals. Both
vapor transport and flux growth techniques can be employed to grow high
quality crystals of MnBi2Te4 and related compounds. They can be complimentary
to each other to meet the different scientific needs. The difference between
these two growth techniques provides us more options to fine tune the magnetic
and topological properties via defect engineering.

This careful work is far from a thorough investigation of the vapor transport
growth of MnBi2Te4 and related compounds. Instead, we hope this work would
initiate more systematic studies on the vapor transport growths to further
optimize the growth parameters for each member of the large family, a mission
impossible for a single group. We would also hope that this work can motivate
more studies on the fine tuning of the magnetic and topological properties of
these fascinating compounds via materials synthesis. In addition to further
optimizing the parameters of vapor transport growths, the following work
deserves some special attention from crystal growth point of view.

(1) To identify the vapor transport conditions and develop the growth protocol
for other $n$MnTe.$m$Bi2Te3 members. The presence of regions with a
composition of Mn2Bi2Te5 in a MnBi2Te4 crystal is encouraging and indicates
that vapor transport growth might be a valid route to sizable crystals of
$n$MnTe.Bi2Te3 ($n>$1). The successful growth of MnBi4-xSbxTe7 crystals in
this work occurs by serendipity instead of by design. Considering that vapor
transported crystals tend to be less Mn deficient, a carefully optimized vapor
transport growth might lead to high quality MnTe.$m$Bi2Te3 ($m>$1) crystals
for the study of their intrinsic properties and the theoretically predicted
exotic properties.

(2) To use the combination of two or more transport agents or to identify new
transport agents. Our work shows that iodides and chlorides are good transport
agents for the growth of MnBi2Te4 and related compounds. We would expect that
bromides or Br2 are also valid transport agents and the appropriate growth
temperature should also be in the range 500-590∘C which is not that far away
from that used for flux growth. It is reasonable to expect that MnBi2Te4
crystals grown using bromides as transport agent might have similar amount of
MnBi. To further increase or reduce the amount of magnetic defects, using the
combination of two or more transport agents might be a valid approach. It
should be noted that a large number of halides, rather than only those studied
in this work, can be effective transport agents. In addition to mixing halogen
or halides, adding some C, S, Se, H2 might be helpful. Identifying new
transport agents or combinations might help expand the growth temperature
window of MnBi2Te4 and facilitate the growth of other $n$MnTe.$m$Bi2Te3
members.

(3) Possible low temperature growth in halide flux. The mechanism of growing
MnBi2Te4 crystals good for QAHE out of MnCl2 flux is still not clear. The
vapor pressure of chlorides might play a role during the mass transport.
Mixing MnCl2 and other chloride salts can significantly lower the melting
temperature and allow crystal growths at lower temperatures. Crystal growths
of MnBi2Te4 and related compounds out of a mixture of halide salts can be
performed in the conventional vertical configuration or in the horizontal
configurationYan  _et al._ (2017); the latter is ideal for a precise control
of the precipitates in a system such as MnTe-Bi2Te3 with multi-phases in a
narrow temperature range. Once the appropriate salt mixture is identified, the
horizontal flux growth can be more effective in identifying the right growth
temperature of each phase taking advantage of the temperature gradient along
the ampoule.

##  V Acknowledgment

The authors would thank Michael McGuire, Brian Sales, and Xiaodong Xu for
helpful discussions. Work at ORNL was supported by the U.S. Department of
Energy, Office of Science, Basic Energy Sciences, Materials Sciences and
Engineering Division.

This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-
AC0500OR22725 with the U.S. Department of Energy. The United States Government
retains and the publisher, by accepting the article for publication,
acknowledges that the United States Government retains a non-exclusive, paid-
up, irrevocable, world-wide license to publish or reproduce the published form
of this manuscript, or allow others to do so, for the United States Government
purposes. The Department of Energy will provide public access to these results
of federally sponsored research in accordance with the DOE Public Access Plan
(http://energy.gov/ downloads/doe-public-access-plan).

##  VI references

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