# Effect on the Electronic and Magnetic Properties of Antiferromagnetic
Topological Insulator MnBi2Te4 with Sn Doping

Susmita Changdar  Condensed Matter Physics and Material Sciences Department,
S. N. Bose National Centre for Basic Sciences, Kolkata, West Bengal-700106,
India.  Susanta Ghosh  Condensed Matter Physics and Material Sciences
Department, S. N. Bose National Centre for Basic Sciences, Kolkata, West
Bengal-700106, India.  Kritika Vijay  Synchrotrons Utilization Section, Raja
Ramanna Centre for Advanced Technology, Indore 452013, India.  Homi Bhabha
National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094,
India.  Indrani Kar  Condensed Matter Physics and Material Sciences
Department, S. N. Bose National Centre for Basic Sciences, Kolkata, West
Bengal-700106, India.  Sayan Routh  Condensed Matter Physics and Material
Sciences Department, S. N. Bose National Centre for Basic Sciences, Kolkata,
West Bengal-700106, India.  P. K. Maheswari  Condensed Matter Physics and
Material Sciences Department, S. N. Bose National Centre for Basic Sciences,
Kolkata, West Bengal-700106, India.  Soumya Ghorai  Condensed Matter Physics
and Material Sciences Department, S. N. Bose National Centre for Basic
Sciences, Kolkata, West Bengal-700106, India.  Soma Banik  Synchrotrons
Utilization Section, Raja Ramanna Centre for Advanced Technology, Indore
452013, India.  Homi Bhabha National Institute, Training School Complex,
Anushakti Nagar, Mumbai, 400094, India.  S. Thirupathaiah<EMAIL_ADDRESS>Condensed Matter Physics and Material Sciences Department, S. N. Bose National
Centre for Basic Sciences, Kolkata, West Bengal-700106, India.

###### Abstract

We thoroughly investigate the effect of nonmagnetic Sn doping on the
electronic and magnetic properties of antiferromagnetic topological insulator
MnBi2Te4. We observe that Sn doping reduces the out-of-plane antiferromagnetic
(AFM) interactions in MnBi2Te4 up to 68% of Sn concentration, and above the
system is found to be a paramagnetic. In this way, the anomalous Hall effect
observed at a very high field of 7.8 T in MnBi2Te4 is reduced to 2 T with 68%
of Sn doping. Electrical transport measurements suggest that all compositions
are metallic in nature, while the low temperature resistivity is sensitive to
the AFM ordering and to the doping induced disorder. Hall effect study
demonstrates that Sn actually dopes electrons into the system, thus, enhancing
the electron carrier density almost by two orders at 68% of Sn. In contrast,
SnBi2Te4 is found to be a p-type system. Angle-resolved photoemission
spectroscopy (ARPES) studies show that the topological properties are intact
at least up to 55% of Sn as the Dirac surface states are present in the
valance band, but in SnBi2Te4 we are unable to detect the topological states
due to heavy hole doping. Overall, Sn doping significantly affects the
electronic and magnetic properties of MnBi2Te4.

##  I Introduction

Introduction of magnetism into a topological insulator has been known to give
rise to various exotic quantum phenomena such as Axion [1, 2, 3] and Chern
insulating states, [4, 5, 6], Majorana zero modes [7], and Weyl semimetallic
phase [8, 9, 10]. However experimental realization of such peculiar systems
has been quite challenging due to the lack of intrinsic magnetism in
topological insulators. Earlier, magnetic ordering in the topological
insulators, (Bi/Sb)2Te3, was achieved by doping with the magnetic ions like
Cr/V [5, 11, 4, 12] in order to induce quantum anomalous Hall insulating
(QAHI) phase. In this way, a ferromagnetic (FM) order is induced to break the
time reversal symmetry (TRS) in the system. When TRS breaks, the degeneracy of
surface Dirac point is lifted and the gap opening is followed by the chiral
edge states, responsible for the QAH effect as observed in these systems.
However, so far this method showed QAHI states at very low temperatures ($<$ 1
K) [5, 13].

Interestingly, MnBi2Te4 was recently discovered to be one of such intrinsic
topological insulator with spontaneous AFM order [14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25], in which the layers of ferromagnetically ordered Mn ions
are coupled antiferromagnetically along the $c$-axis. Here, the long range
magnetic ordering breaks TRS but the combination of TRS ($\Theta$) and half-
lattice translational operator ($T_{1/2}$) connecting the two nearest Mn
layers, i.e. $S=\Theta T_{1/2}$ remains protected [19]. As a result, MnBi2Te4
becomes a potential candidate for hosting intriguing topological properties.
It was also found that MnBi2Te4 thin flakes exhibit Axion insulating state for
even number of layers [26]. Chern insulating state is noticed for odd number
of layers at zero magnetic field [17]. But at much higher magnetic fields even
number of layers also show Chern insulating phase [26]. Similar to even number
layered thin flakes, bulk MnBi2Te4 shows magnetization, thus requiring a very
high magnetic fields (7.8 T) to obtain the QAH effect [27]. One approach to
see QAH effect in MnBi2Te4 at lower fields is by weakening the interlayer AFM
exchange coupling by doping with nonmagnetic ion like Sn at the Mn site.

Figure 1: (a) Rhombohedral crystal structure of MnBi2Te4. Red arrows indicate
the Mn2+ ion spins in AFM state. (b) Single crystal XRD patterns showing
$(00l)$ reflections from all the compositions. Insets in (b) show single-
crystal photographic images of each doping concentration on which the
measurements were done. (c) and (d) Show XPS spectra exhibiting the Bi 4f, Sn
3d, Te 3d, and Mn 2p core levels for x=0.55 and Bi 4f, Te 3d, and Sn 3d core
levels for x=1, respectively. (e) Shows LEED data taken with 70 eV photon
energy revealing hexagonal pattern for both x=0.55 and x=1 single crystals.

In this work, we report comprehensively on the effect of Sn doping on the
electronic and magnetic properties of the magnetic topological insulator
MnBi2Te4. For this, we studied various single crystals of Mn1-xSnxBi2Te4 with
x=0, 0.2, 0.55, 0.68, 0.86, and 1. We realized that Sn doping has a
significant effect on the antiferromagnetic (AFM) ordering. That is, we
observe a decrease in Néel temperature (TN) from 24 K for MnBi2Te4 to 6 K for
68% of Sn doping, while x=0.86 and 1 are found to be paramagnetic in nature.
Further, we observe that the out-of-plane magnetic ordering is intact up to
x=0.68, while for in-plane there is a change from linear M(H) behaviour to a
very weak ferromagnetic type M(H) curve with a saturated magnetization of 0.8
$\mu_{B}$/f.u with increasing Sn. We find a cusp on the resistivity data at
the Néel temperature, which decreases with increasing Sn up to x=0.2,
consistent with magnetic studies. However, as the Sn doping increased beyond
x=0.2, we do not observe cusp at respective Néel temperatures but rather we
observe low temperature resistivity upturn due to Sn doping induced disorder.
On the other hand, SnBi2Te4 show Fermi-liquid type resistivity as the
disordered is significantly reduced by fully replacing Mn with Sn. We further
notice that Sn induces electron carriers into MnBi2Te4. As a result, the
electron carrier concentration increase by two orders at a Sn concentration of
68% compared to MnBi2Te4. In contrast to MnBi2Te4, SnBi2Te4 is found to be a
p-type system. The Fermi level shift in the electronic band dispersions
observed from ARPES studies on x=0.55 and x=1 single crystals is consistent
with carrier concentrations estimated from the Hall measurements. We further
notice that the topological properties are intact up to 55% of Sn doping as
the surface Dirac states are present in the valance band, while in SnBi2Te4 we
are unable to detect them due to heavy hole doping.

##  II Experimental details

Figure 2: (a) Temperature dependent magnetic susceptibility ($\chi$) measured
in field-cooled and zero field-cooled modes with H$\parallel$c and
H$\parallel$ab. (b) Inverse magnetic susceptibility plotted as a function of
temperature with H$\parallel$c and H$\parallel$ab. Doping dependent (c) Néel
temperature (TN), (d) Curie temperature ($\theta_{W}$) for H$\parallel$c and
H$\parallel$ab, and (e) JAF/JF for H$\parallel$c.

We synthesized high quality single crystals of Mn1-xSnxBi2Te4 with x=0, 0.2,
0.55, 0.68, 0.86, and 1 using the solid state reaction route [27]. Constituent
elements of Mn (99.9%), Sn (99.99%), Bi (99.99%), and Te (99.99%) were taken
in stoichiometric ratio, mixed thoroughly in argon atmosphere, and kept in an
alumina crucible before sealing it in a quartz ampoule under a vacuum of
$10^{-4}$ mbar. The sealed quartz ampoule was then heated in a chamber furnace
up to $900^{o}$C at a rate of $150^{o}$C/hr, and kept at that temperature for
24 hours. The ampoule was then cooled at a rate of $2^{o}$C/hr. The growth
temperature of MnBi2Te4 is $590^{o}$C and for SnBi2Te4 it is $600^{o}$C [28].
After the controlled cooling, we performed prolonged annealing within the
temperature range of $590^{o}$C to $600^{o}$C for a maximum of seven days
depending on the amount of Sn doping concentration. Finally, the ampoule was
quenched in cold water. In this way, we got shiny and plate-like single
crystals with a maximum size of 3$\times$3 mm2.

As grown single crystals were structurally analyzed using the high-resolution
X-ray diffractometer (Rigaku smartLab 9 kW) having Cu-Kα radiation. The
chemical composition of the crystals were thoroughly examined using energy
dispersive X-ray spectroscopy (EDS) on cleaved sample surfaces [see Fig. S1 in
supplemental information]. For convenience, herein, we will use respective
nominal composition to represent each sample. Transport and magnetic
properties were measured using Quantum Design Physical Property Measurement
System (PPMS) with magnetic field up to 9 Tesla by varying the temperature
between 2 and 300 K during the measurements. XPS and ARPES measurements were
performed at the undulator based Angle Resolved Photoelectron Spectroscopy
beamline (ARPES BL-10), Indus-2, India. All samples were cleaved in-situ in
the vacuum better than 5×10–11 mbar and performed low energy electron
diffraction (LEED) measurements using SPECS ErLEED 1000A to examine the sample
surface quality. Both the XPS and ARPES measurements were carried out at a
sample temperature of 20 K using SPECS Phoibos150 electron analyser. ARPES
measurements were performed with a photon energy of h$\nu$ = 70 eV. The energy
and angular resolutions were set at 40 meV and 0.1∘, respectively, for the
ARPES studies. XPS measurements were performed with a photon energy of h$\nu$=
800 eV and at an energy resolution of 0.4 eV.

##  III Results and discussion

MnBi2Te4 crystallizes in the rhombohedral structure with a space group of
$R\bar{3}m$, consists Te-Bi-Te-Mn-Te-Bi-Te septuple layers as shown in Fig.
1(a). Fig. 1(b) shows the XRD data of Mn1-xSnxBi2Te4 single crystals for x=0,
0.2, 0.55, 0.68, 0.86, and 1. XRD data of all crystals show clear reflections
from $(00l)$ plane without any impurity peaks, confirming phase purity for all
the crystals. Low energy electron diffraction (LEED) images taken on the
freshly cleaved surfaces of x=0.55 and x=1 single crystals are shown in Fig.
1(e). The LEED pattern of both samples are in hexagonal symmetry with clear
first order diffraction spots coming from $(001)$ crystal planes. This is in
good agreement with the XRD data, again confirming the high quality of single
crystals. XPS data collected on x=0.55 and x=1 samples are shown in Figs. 1(c)
and 1(d), respectively. Both crystals exhibit major core level peaks at 157.35
eV of Bi 4f5/2 and 162.75 eV of Bi 4f7/2, which can be assigned to the Bi3+
ions from the Bi-Te bond [29, 30]. Additionally, we noticed two major peaks of
Sn 3d3/2 and Sn 3d5/2 at 484.85 eV and 493.3 eV, respectively, from Sn2+ ions
associated to the Sn-Te bond [31]. Te $3d$ core levels at 582.2 eV (Te 3d3/2)
and 571.85 eV (Te 3d5/2) corresponding to the Te2- ions from Sn-Te, Mn-Te, and
Bi-Te bonds of Mn0.45Sn0.55Bi2Te4 [32] and also from Sn-Te, and Bi-Te bonds in
SnBi2Te4. The peaks corresponding to Mn2+ from Mn-Te bonds appear at 641.1 eV
of Mn 2p1/2 and 652.8 eV of Mn 2p3/2 [27, 33]. We further noticed a few low
intensity peaks related to Mn2+ at 639.9 eV and 651.45 eV of the Mn-O bond as
observed in a previous report on this system [27].

Figure 3: Magnetization isotherms taken from (a) x=0, (b) x=0.2, (c) x=0.55,
(d) x=0.68, and (e) x=0.86 for the field applied parallel to $c$-axis
(H$\parallel$c) (top figure) and parallel to $ab$-plane (H$\parallel$ab)
(bottom figure) measured up to 7 T. The insets are schematics representing the
Mn spins in their respective color regions for two nearest Mn inter-layers
(SLs).

To elucidate the effect of Sn doping on the magnetic properties of MnBi2Te4,
we performed thorough magnetic measurements on various Sn doping
concentrations. Fig. 2(a) depicts field-cooled (FC) and zero-field-cooled
(ZFC) magnetic susceptibility ($\chi$) plotted as a function of temperature up
to 40 K with magnetic field applied in-plane ($H\parallel ab$) and out-of-
plane ($H\parallel c$) orientations. The FC and ZFC curves overlap for all
samples, suggesting negligible magnetic hysteresis. In agreement with the
previous reports [27, 18], MnBi2Te4 shows AFM ordering at a Néel temperature
(TN) of 24 K, thereby causing a sharp decrease in the magnetic susceptibility
below $T_{N}$ for $H\parallel c$, whereas the magnetic susceptibility for
$H\parallel ab$ remains almost constant below $T_{N}$. Next with increasing Sn
substitution in Mn1-xSnxBi2Te4, the 2D ferromagnetic sublattice gets diluted,
causing the decrease in $T_{N}$ linearly from 24 K for x=0 to 6 K for x=0.68
as shown in Fig.2(c). The large decrease in $T_{N}$ implies a significant
weakening of interlayer AFM coupling, while the overall AFM ordering is intact
up to 68% of Sn concentration. An earlier magnetic study suggested for a
magnetic transition from AFM to paramagnetic for the 66% of Sn doped
Mn1-xSnxBi2Te4 [34]. The discrepancy between our study and that of Ref. 34
could be that the low temperature AFM ordering is dominated by the applied
magnetic field when measured with 1 T [see Fig. S2 in supplemental
information]. Thus, we measured the magnetic data with a field of 0.4 T to see
the AFM ordering at 6 K for x=0.68.

Fig. 2(b) shows the inverse magnetic susceptibility plotted as a function of
temperature with $H\parallel c$ and $H\parallel ab$. From the Curie-Weiss law
fitting to the data, we obtained Curie-Weiss temperature ($\theta_{W}$) for
each composition and is plotted in Fig. 2(d) as a function of Sn
concentration. Earlier reports on MnBi2Te4 showed positive Curie-Weiss
temperature for $H\parallel ab$ due to the in-plane FM exchange interaction
and a negative Curie-Weiss temperature for $H\parallel c$ due to the out-of-
plane AFM interactions [27]. In agreement to that, we obtained
$\theta^{ab}_{W}$ = 3 K and $\theta^{c}_{W}$ = -0.08 K with an effective
magnetic moment $\mu_{eff}=5.3\mu_{B}/Mn$ for MnBi2Te4 [16]. The estimated
$\mu_{eff}$ value matches very well with that of Mn2+ ions with spin $J=5/2$
[27]. As shown in Fig. 2(d), we found different Curie-Weiss temperatures for
in-plane ($\theta^{ab}_{W}$) and out-of-plane ($\theta^{c}_{W}$) field
directions for the samples x=0 and 0.2, but at higher Sn concentrations both
Curie-Weiss temperatures become almost equal due to decreasing magnetic
anisotropy with increasing Sn concentration.

Moreover, both $\theta^{ab}_{W}$ and $\theta^{c}_{W}$ are found to be positive
for x=0.2 and for other higher Sn concentrations, suggesting for dominating FM
interactions with increasing Sn. The strength of FM exchange interaction with
respect to AFM can be determined from the ratio of $\theta_{W}/T_{N}$, which
equals to $(J_{F}+J_{AF})/(J_{F}-J_{AF})$ [35]. Here $J_{F}$ is intralayer FM
exchange coupling and $J_{AF}$ represents interlayer AFM exchange coupling.
The calculated $J_{AF}/J_{F}$ ratio is plotted in Fig. 2(e) as a function of
doping concentration. For MnBi2Te4, $J_{AF}/J_{F}$ is found to be -1, which
indicates stronger AFM exchange coupling between two Mn-layers. Increase in Sn
concentration weakens the AFM coupling, thereby, decreases the $J_{AF}/J_{F}$
ratio as shown in Fig. 2(e). Although the $J_{AF}/J_{F}$ ratio is relatively
low for doped systems ($J_{AF}/J_{F}$=-0.43 for x=0.68) compared to the parent
MnBi2Te4 ($J_{AF}/J_{F}$=-1 ), it is much higher than MnBi4Te7
[$J_{AF}/J_{F}\approx-0.04$] [36].

Figure 4:  Field dependent magnetoresistance ($\rho_{xx}$) from (a) x=0, (b)
x=0.2, (c) x=0.55, (d) x=0.68, (e) x=0.86, and (f) x=1 measured at 3 K, 5 K.
15 K, and 40 K. (g) Shows doping dependent critical fields of spin-flop
transition (H${}^{SF}_{c}$) and ferromagnetic ordering magnetic moment
saturation (H${}^{FM}_{c}$). Figure 5: (a) Stacked in-plane resistivity
($\rho_{xx}$) plotted as a function of temperature from all the samples. Inset
shows normalised in-plane resistivity (R(T)/R(2K)) vs. temperature curve at
low temperature. (b) $\rho_{xx}$ vs. temperature data for x=0.68, measured
with 0 T, 4 T, and 9 T applied magnetic field along crystallographic $c$-axis
of the single crystal. (c) and (d) Field dependent Hall resistivity
($\rho_{xy}$) measured at 3 K. (red, yellow, green, and white colored regions
in (d) signifies AFM, canted-AFM, FM, and PM states of the system,
respectively.) (e) Charge carrier density (n) plotted as a function of Sn
doping concentration.

Figs. 3(a)-(e) show field dependent magnetization M(H) isotherms measured with
$H\parallel c$ and $H\parallel ab$. The crystallographic $c$-axis is known to
be spin-easy axis for MnBi2Te4. In agreement to this, Fig. 3(a) shows a spin-
flop (SF) transition at a critical field of $H^{SF}_{c}$=3.3 T for $H\parallel
c$ at 3 K, which gradually decreases to lower fields with increasing
temperature up to the Néel temperature. Beyond the Néel temperature, the
system transforms to paramagnetic (PM) in nature. During the spin-flop
transition, the spin-structure of the system switches from an AFM state to a
canted-AFM (CAFM) state, which upon further increase in magnetic field reaches
to FM state due to complete polarization of the spins at a critical field of
$H^{FM}_{c}$=7.8 T for MnBi2Te4 [27]. With increasing Sn concentration, the
spin-flop transition critical field decreases for $H\parallel c$. That means,
for x=0.2 the critical field of spin-flop transition $H^{SF}_{c}$=2.5 T [see
Fig. 3(b)], which gradually goes down to $H^{SF}_{c}$=0.7 T for x=0.68 [see
Fig. 3(d)]. These observations further support our earlier argument that the
AFM transition in x=0.68 sample can be detected only with the magnetic fields
below 0.7 T. Further increase in Sn concentration to x=0.86, the spin-flop
transition is completely disappeared and the system turns to be a very weak
ferromagnet as it shows a sigmoid-like M(H) isotherm at 3 K for $H\parallel c$
[see Fig. 3(e)].

Increase in Sn concentration not only decreases the spin-flop critical fields
[$H^{SF}_{c}$], but also the saturation magnetization ($M_{S}$). MnBi2Te4 is
known to show a saturation magnetization of 3.56 $\mu_{B}/f.u.$ at 8 T for
$H\parallel c$ [37], it goes down to a negligible saturation magnetization of
0.32$\mu_{B}/f.u$ for x=0.86. In fact at 3 K, we notice magnetization
saturation at 4 T for x=0.55 and at 2.2 T for x=0.68 due to weak FM ordering
induced with Sn doping. On the other hand, for $H\parallel ab$, the
magnetization M(H) isotherms of x=0, 0.2, and 0.55 show linear dependents on H
due to gradual polarization of spins towards the applied field direction.
However, the magnetic saturation is noticed for x=0.55 at around 5 T.
Interestingly, for x=0.68 and 0.86 the nature of the M(H) curves at lower
fields resembles to a weak ferromagnet with sigmoid-like shape and magnetic
saturation is around 2 T. These observations suggest that Sn doping into
MnBi2Te4 transforms the system to a weak ferromagnet.

Next, field dependent magnetoresistance (MR) up to 9 T measured at various
temperatures for all compositions are plotted in Figs. 4(a)-(f). During the
measurements, the magnetic field was applied along the $c$-axis with current
applied parallel to $ab$-plane. From Fig. 4(a), we can see that $\rho_{xx}(H)$
of MnBi2Te4 jumps suddenly at a critical field of 3.2 T when measured below
TN, and again slope changes at a critical field of $7.8$ T. The critical
fields found from MR data are matching very well with that of $H^{SF}_{c}$ and
$H^{FM}_{c}$ from the M(H) data. We notice that the field dependent MR
behaviour is consistent with M(H) data up to Néel temperature, and above TN we
observe a parabolic field dependent MR, in agreement with an earlier report
[36]. Also, the critical fields decrease monotonically with increasing Sn as
demonstrated in Fig. 4(g). Next, x=0.86 and x=1 (SnBi2Te4) show parabolic
field dependent MR at all the measured sample temperatures due to their
paramagnetic nature [see Figs. 4(e) and 4(f)].

Temperature dependent in-plane resistivity ($\rho_{xx}$) data are plotted in
Fig. 5(a). $\rho_{xx}$ of all samples suggest an overall metallic behavior. We
notice a cusp on the resistivity at 24 K for at x=0 and 21 K for x=0.2, due to
the spin-fluctuations triggered at respective Néel temperatures. On the other
hand, the compositions with higher Sn such as x=0.55 and x=0.68 we find no
effect of AFM ordering on $\rho_{xx}$ data at their respective $T_{N}$’s. But
both these compositions show upturn resistivity with minima at 15 K for x=0.55
and at 28 K for x=0.68. Note here that these temperature minima are higher
than their respective Néel temperatures, suggesting rather a different
mechanism for increasing resistivity at low temperatures such as the disorder
induced electron-electron ($e-e$) interactions [38], weak localization (WL)
[39], or the Kondo effect [40]. In order to explore further on the origin of
resistivity upturn, we performed field dependent resistivity on x=0.68 and
plotted the data as shown in Fig. 5(b). From Fig. 5(b) we can see that up to 9
T the resistivity upturn does not suppress, contradicting to the possibility
of Kondo effect or weak localization in which case the resistivity upturn
suppresses [40, 41]. Thus, low temperature resistivity upturn found could be
originated from the induced disorder with Sn doping [42, 43, 38].
Nevertheless, the resistivity upturn is absent from SnBi2Te4 compound and
rather we find a clean Fermi-liquid type resistivity curve that is satisfying
the T2 law.

Figure 6: (a) and (b) Energy distribution maps (EDMs) of x=0.55 and x=1,
respectively, taken along $\overline{\Gamma}-\overline{M}$ direction with 70
eV photon energy using linearly polarized light. (c) and (d) are the zoomed-in
EDMs of x=0.55 and x=1 near $E_{F}$. The red curve in x=0.55 is the energy
distribution curve taken by integrating around the $\overline{\Gamma}$ point.

Field dependent Hall resistivity ($\rho_{xy}$) measurements at 3 K for all
compositions are shown in Fig. 5(c). As can be seen from Fig. 5(c), the
$\rho_{xy}$(H) decreases with increasing Sn concentration up to x=0.68 and
then slope reverses the sign for SnBi2Te4. The change in slope of
$\rho_{xy}$(H) clearly hints at increase in electron carrier concentration up
to x=0.68 and then the system SnBi2Te4 becomes a p-type when Mn is totally
replaced by Sn. To explore the Hall resistivity in details, we plotted
$\rho_{xy}$(H) individually for every composition as shown Fig. 5(d). From a
closer look on the Hall data of MnBi2Te4 we can notice a change in slope at
the spin-flop critical field H${}^{SF}_{c}$=3.2 T and the ferromagnetic
ordering critical field H${}^{FM}_{c}$= 7.8 T. The change in slope at the
critical fields is due to the anomalous Hall effect. With increasing Sn
concentration, the slope change in Hall resistivity appears at much lower
fields of H${}^{SF}_{c}$=0.8 T and H${}^{FM}_{c}$= 2 T when measured on x=0.68
sample. These observations clearly demonstrate the tuning of anomalous Hall
effect from higher fields to lower fields in going from parent to 68% of Sn
doping. However, we do not observe AHE from x=0.86 and x=1 samples as they are
the paramagnetic in nature.

Next, the charge carrier concentration has been estimated from the Hall data
and plotted in Fig. 6 (e) for all the compositions. We calculated an electron
carrier density of $5.4\times 10^{19}$ cm-3 for x=0, $8.18\times 10^{19}$ cm-3
for x=0.2, $4.59\times 10^{20}$ cm-3 for x=0.55, $1.2\times 10^{21}$ cm-3 for
x=0.68, and $1.04\times 10^{21}$ cm-3 for x=0.86. Thus, in going from x=0 to
x=0.68 the electron carrier density increased by an order of 2 and then starts
decreasing. On the other hand, for x=1 (SnBi2Te4) we estimated a hole carrier
density of $1.39\times 10^{21}$cm-3, which is in good agreement with previous
reports on hole carrier concentration of SnBi2Te4 [44, 45, 46]. Further, our
observation of increase in electron density with Sn doping is in good
agreement with a previous report [34].

In order to understand the effect of Sn doping on the electronic band
dispersions near the Fermi level, we performed ARPES measurements on x=0.55
and x=1 single crystals as shown in Fig. 6 measured with 70 eV photon energy
of linearly polarized light. Figs. 6(a) and 6(b) depict energy distribution
maps (EDMs) plotted for x=0.55 and x=1, respectively, along
$\overline{\Gamma}-\overline{M}$ orientation as schematically shown in the
inset. Figs. 6(c) and 6(d) depict zoomed-in images of 6(a) and (b),
respectively, showing band dispersions near the Fermi level. From Fig. 6(c),
we can notice surface Dirac state with a band crossing point at a binding
energy of 0.23 eV as usually observed in MnBi2Te4 [47, 22, 48]. The band
crossing point is estimated with the help of energy dispersive curve (EDC)
extracted by integrating the EDM around $k_{\parallel}$=0, overlapped on the
EDM. However, the surface Dirac state completely shifted above the Fermi level
when Mn is totally replaced by Sn [see Fig. 6(d)] due to Fermi level shifting
towards higher binding energy. This is in good agreement with the dominant
hole carrier density estimated from the Hall measurements in the case of
SnBi2Te4. Overall, the band dispersions of MnBi2Te4 along
$\overline{\Gamma}-\overline{M}$ orientation are in good agreement with
previous reports [49]. Though we are unable to resolve surface and bulk bands
more clearly near the Fermi level within our experimental energy resolution
(40 meV), the main message is clear that the topological Dirac surface states
are intact at least up to 55% of Sn doping in MnBi2Te4. On the other hand, the
bulk band dispersions look almost identical between x=0.55 and x=1, except
that the bulk bands shifted towards the Fermi level in x=1 compared to x=0.55.

Despite MnBi2Te4 being topological insulator with intrinsic magnetic ordering,
there are mainly two obstacles on the path of realizing Chern insulating state
in this system. One of them is the high magnetic fields needed to obtain FM
order [47] and the other one is the dominant bulk electron carriers induced by
the excess Bi and the antisite defects in single crystals [50], shifting the
Fermi level into the bulk conduction band. Doping Sn at the Mn site appeared
to be a promising technique for suppressing the $n$-type bulk carriers as
SnBi2Te4 is isostructural to MnBi2Te4 and has high $p-$type carrier
concentration [45]. But the magnetism, an important ingredient to realize the
Chern insulating state [51], seems to be disappearing beyond 68% of Sn doping
while still the electron carriers dominating the transport. On the other hand,
when the electron density decreased at higher Sn doping (x=0.86) the system
turns into nonmagnetic [see Fig. 5].

##  IV Conclusions

In conclusion, we have successfully grown high quality single crystals of
Mn1-xSnxBi2Te4 (x=0, 0.2, 0.55, 0.68, 0.86 and 1). We noticed that Sn doping
in MnBi2Te4 is an effective way of acquiring quantum Hall state at lower
magnetic fields as the critical field of FM ordering goes from 7.8 T to 2 T in
going from x=0 to x=0.68. Electrical resistivity is found to be sensitive to
the AFM ordering temperature (TN), but with Sn doping the low temperature
resistivity shows upturn due to the doping induced disorder. However, low
temperature upturn is absent in SnBi2Te4 as the disorder is reduced. Hall
effect study shows electron doping into the system with Sn, and thus,
enhancing the electron carrier density almost by two orders with 68% of Sn
concentration. In contrast, SnBi2Te4 is found to be a $p$-type system. ARPES
studies show that topological properties are intact up to 55% of Sn doping,
but the Dirac surface states disappeared in SnBi2Te4 as they moved to
conduction band due to heavy hole doping. Thus, our studies clearly
demonstrate the effect of Sn doping on the electronic and magnetic properties
of MnBi2Te4.

##  V Acknowledgement

S.C. acknowledges University Grants Commission (UGC), India for the Ph.D.
fellowship. S.T. acknowledges financial support by the Department of Science
and Technology (DST) through the grant no. SRG/2020/000393. Dr. Tapas Ganguli
from RRCAT is thanked for all the support and encouragement.

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