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Supplementary Information
High-precision realization of robust quantum anomalous Hall state in
a hard ferromagnetic topological insulator
Cui-Zu Chang, 1 Weiwei Zhao,2 Duk Y. Kim,2 Haijun Zhang,3 Badih A. Assaf,4 Don Heiman,4
Shou-Cheng Zhang,3 Chaoxing Liu,2 Moses H. W. Chan,2 and Jagadeesh S. Moodera1,5
1Francis Bitter Magnet Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2The Center for Nanoscale Science and Department of Physics, The Pennsylvania State University, University Park, PA16802-6300, USA
3Department of Physics, McCullough Building, Stanford University, Stanford, CA 94305-4045, USA
4Department of Physics, Northeastern University, Boston, MA 02115, USA
5Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Corresponding author: [email protected](C. Z. C.); [email protected] (W. Z.) and [email protected] (J. S. M.)
Content
Ⅰ. Sample characterization
Ⅱ. Hall bar structure for transport measurements
Ⅲ. Ferromagnetic response in V- and Cr-doped Sb2Te3
Ⅳ. Curie temperatures of V- and Cr-doped Sb2Te3 films
Ⅴ. Tuning the Bi dopant level in V-doped Sb2Te3 to search for the QAH insulating state
Ⅵ. Ferromagnetic properties of QAH samples
Ⅶ. The QAH signature up to 3K (sample S2)
Ⅷ.The gate electric-field dependence of QAH effect measured at 120mK (sample S2)
Ⅸ.The QAH state at 130mK (sample S1)
High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
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Ⅰ. Sample characterization
Figure S1 | RHEED patterns of the substrate, film and protection layer. a, Heat-treated insulating
SrTiO3(111); b, 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on SrTiO3(111); c, 10nm Te epitaxial protection layer
on 4QLs (Bi0.29Sb0.71)1.89V0.11Te3 film.
Figure S1 displays the reflective high energy electron diffraction (RHEED) patterns of heat-
treated bare substrate SrTiO3(111), the molecular beam epitaxy (MBE)-grown four quintuple-
layers (QL) (Bi0.29Sb0.71)1.89V0.11Te3 film on this substrate, and 10nm epitaxial Te protection
layer on a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film. They all show highly-ordered flat crystalline
surfaces. The clear reconstruction of heat-treated SrTiO3(111) (Fig. S1a) indicates an atomic flat
surface suitable for high-quality film growth. The sharp and streaky 1×1 diffraction spots of
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4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (Fig. S1b) and Te protection layer (Fig. S1c) indicate a highly-
ordered and smooth surface of the ferromagnetic topological insulator (FMTI) film and
protection layer, respectively.
Figure S2 | AFM images (5m×5m) showing the smooth surface morphology of the substrates and
films. a, Heat-treated SrTiO3(111). b, 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on heat-treated SrTiO3(111).
Figure S2a shows an atomic force microscopy (AFM) image (5m×5m) of a heat-treated
SrTiO3(111) substrate. The substrate shows an almost atomically flat surface with roughness less
than 0.2nm, which indicates that the heat-treated SrTiO3(111) substrate is excellent for film
growth. Figure S2b shows an AFM image (5m×5m) of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on
the heat-treated SrTiO3(111) substrate. The surface of 4QL (Bi0.29Sb0.71)1.89V0.11Te3 films
exhibits one single terrace over this area, with a few voids, 1QL (~1nm) deep. Thus, the whole
FMTI film appears to be essentially a uniform film of 4QL thickness.
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Ⅰ. Sample characterization
Figure S1 | RHEED patterns of the substrate, film and protection layer. a, Heat-treated insulating
SrTiO3(111); b, 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on SrTiO3(111); c, 10nm Te epitaxial protection layer
on 4QLs (Bi0.29Sb0.71)1.89V0.11Te3 film.
Figure S1 displays the reflective high energy electron diffraction (RHEED) patterns of heat-
treated bare substrate SrTiO3(111), the molecular beam epitaxy (MBE)-grown four quintuple-
layers (QL) (Bi0.29Sb0.71)1.89V0.11Te3 film on this substrate, and 10nm epitaxial Te protection
layer on a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film. They all show highly-ordered flat crystalline
surfaces. The clear reconstruction of heat-treated SrTiO3(111) (Fig. S1a) indicates an atomic flat
surface suitable for high-quality film growth. The sharp and streaky 1×1 diffraction spots of
3
4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (Fig. S1b) and Te protection layer (Fig. S1c) indicate a highly-
ordered and smooth surface of the ferromagnetic topological insulator (FMTI) film and
protection layer, respectively.
Figure S2 | AFM images (5m×5m) showing the smooth surface morphology of the substrates and
films. a, Heat-treated SrTiO3(111). b, 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on heat-treated SrTiO3(111).
Figure S2a shows an atomic force microscopy (AFM) image (5m×5m) of a heat-treated
SrTiO3(111) substrate. The substrate shows an almost atomically flat surface with roughness less
than 0.2nm, which indicates that the heat-treated SrTiO3(111) substrate is excellent for film
growth. Figure S2b shows an AFM image (5m×5m) of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film on
the heat-treated SrTiO3(111) substrate. The surface of 4QL (Bi0.29Sb0.71)1.89V0.11Te3 films
exhibits one single terrace over this area, with a few voids, 1QL (~1nm) deep. Thus, the whole
FMTI film appears to be essentially a uniform film of 4QL thickness.
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Figure S3 | X-ray diffraction data for pristine and doped Sb2Te3 films on sapphire(0001). a-c, X-ray
diffraction patterns for: a, 20QL Sb2Te3; b, 20QL Sb1.84Cr0.16Te3; c, 20QL Sb1.85V0.15Te3 thin films,
respectively. All films had 10nm epitaxial Te protection layer. d, Zoomed-in view of (0015) peak in
above three films. The arrow indicates the Laue fringes of (0015) peak.
Figure S3a shows the X-ray diffraction (XRD) pattern for pristine 20QL Sb2Te3 film. All
peaks are identified with (00n) diffraction of Sb2Te3, while the protection layer Te shows (100)
peak and sapphire show (006) diffraction peak. Fig. S3b and S3c display the XRD pattern for the
20QL Sb1.84Cr0.16Te3 and Sb1.85V0.15Te3 films, respectively, capped with 10nm epitaxial Te layer.
The positions of all peaks are similar to that of pristine Sb2Te3 films, indicating that the Cr- and
V-doped Sb2Te3 films have the same crystalline quality as that of the pristine film (Fig. S3a).
Presence of no other phase could be identified in the doped Sb2Te3 films from these XRD data.
The Te(100) peak in these protective layers indicates that it forms epitaxially, that is consistent
with the RHEED data (Fig. S1c). Fig. S3d shows a zoomed- in view of the (0015) peak exhibiting
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Laue fringes (noted by an arrow), indicating the high crystalline quality of the films. The (0015)
peak in Cr-doped Sb2Te3 is shifted to a larger angle; while that for V-doped Sb2Te3 is shifted to a
smaller angle. The corresponding c-axis lattice parameters for pristine, Cr- and V-doped Sb2Te3
films are 30.34Å, 30.15Å and 30.39Å, respectively. Slight shrinking and expansion of the lattice
for Cr and V doping is apparent, as a result of substitution for Sb in the lattice. This can be
expected from the different ionic radii of Cr and V.1
Ⅱ. Hall bar structure for transport measurements
Figure S4 | Hall bar structure of FMTI films for transport measurements. a, Schematics of the Hall
bar (not to scale). The chemical potential of the FMTI film can be tuned by a bottom gate voltage applied
on the back side of the dielectric substrate. Here, ρxx and ρyx represent the longitudinal resistance and the
Hall resistance, respectively. b, Photograph of a Hall bar device made from a FMTI film on the substrate.
The red arrow indicates the current flow direction during the measurements. The black area is the film,
whereas the dark gray area is the bare substrate. The light-colored spots are the indium contacts to the
film, which connect to 50m diameter gold wires.
Figure S4a shows the schematic structure of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film for transport
measurements. The film is patterned by mechanically removing material into a Hall bar
configuration for transport measurements, as shown in Fig. S4b. 50m diameter gold wires were
attached with six indium contacts on the Hall bar geometry for electrical measurements, and
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Figure S3 | X-ray diffraction data for pristine and doped Sb2Te3 films on sapphire(0001). a-c, X-ray
diffraction patterns for: a, 20QL Sb2Te3; b, 20QL Sb1.84Cr0.16Te3; c, 20QL Sb1.85V0.15Te3 thin films,
respectively. All films had 10nm epitaxial Te protection layer. d, Zoomed-in view of (0015) peak in
above three films. The arrow indicates the Laue fringes of (0015) peak.
Figure S3a shows the X-ray diffraction (XRD) pattern for pristine 20QL Sb2Te3 film. All
peaks are identified with (00n) diffraction of Sb2Te3, while the protection layer Te shows (100)
peak and sapphire show (006) diffraction peak. Fig. S3b and S3c display the XRD pattern for the
20QL Sb1.84Cr0.16Te3 and Sb1.85V0.15Te3 films, respectively, capped with 10nm epitaxial Te layer.
The positions of all peaks are similar to that of pristine Sb2Te3 films, indicating that the Cr- and
V-doped Sb2Te3 films have the same crystalline quality as that of the pristine film (Fig. S3a).
Presence of no other phase could be identified in the doped Sb2Te3 films from these XRD data.
The Te(100) peak in these protective layers indicates that it forms epitaxially, that is consistent
with the RHEED data (Fig. S1c). Fig. S3d shows a zoomed- in view of the (0015) peak exhibiting
5
Laue fringes (noted by an arrow), indicating the high crystalline quality of the films. The (0015)
peak in Cr-doped Sb2Te3 is shifted to a larger angle; while that for V-doped Sb2Te3 is shifted to a
smaller angle. The corresponding c-axis lattice parameters for pristine, Cr- and V-doped Sb2Te3
films are 30.34Å, 30.15Å and 30.39Å, respectively. Slight shrinking and expansion of the lattice
for Cr and V doping is apparent, as a result of substitution for Sb in the lattice. This can be
expected from the different ionic radii of Cr and V.1
Ⅱ. Hall bar structure for transport measurements
Figure S4 | Hall bar structure of FMTI films for transport measurements. a, Schematics of the Hall
bar (not to scale). The chemical potential of the FMTI film can be tuned by a bottom gate voltage applied
on the back side of the dielectric substrate. Here, ρxx and ρyx represent the longitudinal resistance and the
Hall resistance, respectively. b, Photograph of a Hall bar device made from a FMTI film on the substrate.
The red arrow indicates the current flow direction during the measurements. The black area is the film,
whereas the dark gray area is the bare substrate. The light-colored spots are the indium contacts to the
film, which connect to 50m diameter gold wires.
Figure S4a shows the schematic structure of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film for transport
measurements. The film is patterned by mechanically removing material into a Hall bar
configuration for transport measurements, as shown in Fig. S4b. 50m diameter gold wires were
attached with six indium contacts on the Hall bar geometry for electrical measurements, and
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another indium pad is attached on the back side of SrTiO3(111) substrate for back-gate electrode.
The Hall bar geometries we employed did not affect the measurements.
Ⅲ. Ferromagnetic response in V- and Cr-doped Sb2Te3
Figure S5 | ρyx and ρxx hysteresis loops of V- or Cr-doped Sb2Te3 films. a, c, Field dependence of ρyx
and ρxx of a 6QL Sb1.85V0.15Te3 thin film. b, d, ρyx and ρxx of a 6QL Sb1.84Cr0.16Te3 thin film at 2K. The red
curves in a to d are the ‘virgin’ magnetized curves, where the samples were not exposed to external field.
The ρyx of Cr-doped Sb2Te3 shows nearly non-ferromagnetic behavior under initial zero-field
and it is driven into the ferromagnetic state by an external field showing a hysteresis loop. In
contrast, the ρyx of V-doped Sb2Te3 shows self-driven ferromagnetic behavior in the ‘virgin’
condition of zero initial magnetic field. The red curves in panels Figs. S5a and S5c, the ‘virgin’
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magnetized curves nearly overlap with the ρyx–0H hysteresis and the ρxx–0H butterfly structure
(blue curve). This is not the case for the Cr-doped sample. The ρyx–0H curve in Fig. S5a shows
a nearly square-shaped hysteresis loop with the coercive field Hc~1.3T, suggesting a good long-
range ferromagnetic order with the easy magnetization axis perpendicular to the sample plane.
Figure S6 | Magnetic properties of V- or Cr-doped Sb2Te3 films. Temperature dependence of
magnetization M without field during cooling (blue squares) and with a perpendicular magnetic field of
100Oe (red circles) during cooling. a, a 6QL Sb1.85V0.15Te3 film, and b, a 6QL Sb1.84Cr0.16Te3 thin film.
This contrasting behavior of the two materials is also confirmed by the superconductivity
quantum interference device (SQUID) measurements. The magnetization for the V-doped
samples under zero field cooling (ZFC) condition is about 70% of that for field cooling (FC), as
shown in Fig. S6a. In the Cr- doped sample, ZFC value is only ~12% of the FC value, indicating
the presence of many non-aligned magnetic domains.
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another indium pad is attached on the back side of SrTiO3(111) substrate for back-gate electrode.
The Hall bar geometries we employed did not affect the measurements.
Ⅲ. Ferromagnetic response in V- and Cr-doped Sb2Te3
Figure S5 | ρyx and ρxx hysteresis loops of V- or Cr-doped Sb2Te3 films. a, c, Field dependence of ρyx
and ρxx of a 6QL Sb1.85V0.15Te3 thin film. b, d, ρyx and ρxx of a 6QL Sb1.84Cr0.16Te3 thin film at 2K. The red
curves in a to d are the ‘virgin’ magnetized curves, where the samples were not exposed to external field.
The ρyx of Cr-doped Sb2Te3 shows nearly non-ferromagnetic behavior under initial zero-field
and it is driven into the ferromagnetic state by an external field showing a hysteresis loop. In
contrast, the ρyx of V-doped Sb2Te3 shows self-driven ferromagnetic behavior in the ‘virgin’
condition of zero initial magnetic field. The red curves in panels Figs. S5a and S5c, the ‘virgin’
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magnetized curves nearly overlap with the ρyx–0H hysteresis and the ρxx–0H butterfly structure
(blue curve). This is not the case for the Cr-doped sample. The ρyx–0H curve in Fig. S5a shows
a nearly square-shaped hysteresis loop with the coercive field Hc~1.3T, suggesting a good long-
range ferromagnetic order with the easy magnetization axis perpendicular to the sample plane.
Figure S6 | Magnetic properties of V- or Cr-doped Sb2Te3 films. Temperature dependence of
magnetization M without field during cooling (blue squares) and with a perpendicular magnetic field of
100Oe (red circles) during cooling. a, a 6QL Sb1.85V0.15Te3 film, and b, a 6QL Sb1.84Cr0.16Te3 thin film.
This contrasting behavior of the two materials is also confirmed by the superconductivity
quantum interference device (SQUID) measurements. The magnetization for the V-doped
samples under zero field cooling (ZFC) condition is about 70% of that for field cooling (FC), as
shown in Fig. S6a. In the Cr- doped sample, ZFC value is only ~12% of the FC value, indicating
the presence of many non-aligned magnetic domains.
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Ⅳ. Curie temperatures of V- and Cr-doped Sb2Te3 films
Figure S7 | Estimation of Curie temperatures of 6QL V- or Cr-doped Sb2Te3 films . Arrott plots in
6QL Sb2-xVxTe3 films for: a, x=0.08; b, x=0.15; c, x=0.20; and d, x=0.25. Arrott plots in 6QL Sb2-xCrxTe3
films for: e , x=0.10; f, x=0.16; g, x=0.23; and h, x=0.29.
The Curie temperature (TC) of a magnetic material can be determined from Arrott plots.2 The
relation between ρyx2 and 0H/ρyx is given by ρyx
2 = a + bH/ρyx, where a and b are constants.
When the FM state is approached from above TC, the slope b of H/ρyx increases and the intercept
a changes sign from negative to positive, as shown in Fig. S7. Therefore, the temperature where
the relation is linear and goes through the origin corresponds to TC. Figure S7 shows Arrott plots
for some V- and Cr-doped Sb2Te3 samples in Fig. 2a of the main text.
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Ⅴ. Tuning the Bi dopant level in V-doped Sb2Te3 to search for the QAH insulating state
Figure S8 | Transport properties of the 6QL (BixSb1-x)1.85V0.15Te3 films as a function of x, the Bi
dopant level. a-g, Magnetic field dependent Hall resistance yx of 6QL (BixSb1-x)1.85V0.15Te3 films at
T=2K with: a, x = 0; b, x = 0.09; c, x = 0.18; d, x = 0.21; e , x = 0.27; f, x = 0.36; and g, x=0.46. h-n,
Temperature-dependent longitudinal resistivity xx of films with: h, x = 0; i, x = 0.09; j, x = 0.18; k, x =
0.21; l, x = 0.27; m, x = 0.36; and n, x=0.46.
The anomalous Hall resistance exhibits dramatic and systematic change with Bi-dopant level
in a 6QL V-doped Sb2Te3. yx at zero magnetic field (labeled as yx(0)) is only 108at T= 2K
for the sample with x = 0whereas increasing to 221in the x = 0.09 film. The value is further
enhanced to 498at x = 0.18, 685at x = 0.21, and 1.9k at x=0.27However, when x reaches
0.36, yx(0) rapidly reduced to 1.1k, and then lowered to only 682 at x = 0.46as shown in the
top panel of Fig. S8. The evolution of yx(0) with Bi-content is summarized in Fig. S9a. A
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Ⅳ. Curie temperatures of V- and Cr-doped Sb2Te3 films
Figure S7 | Estimation of Curie temperatures of 6QL V- or Cr-doped Sb2Te3 films . Arrott plots in
6QL Sb2-xVxTe3 films for: a, x=0.08; b, x=0.15; c, x=0.20; and d, x=0.25. Arrott plots in 6QL Sb2-xCrxTe3
films for: e , x=0.10; f, x=0.16; g, x=0.23; and h, x=0.29.
The Curie temperature (TC) of a magnetic material can be determined from Arrott plots.2 The
relation between ρyx2 and 0H/ρyx is given by ρyx
2 = a + bH/ρyx, where a and b are constants.
When the FM state is approached from above TC, the slope b of H/ρyx increases and the intercept
a changes sign from negative to positive, as shown in Fig. S7. Therefore, the temperature where
the relation is linear and goes through the origin corresponds to TC. Figure S7 shows Arrott plots
for some V- and Cr-doped Sb2Te3 samples in Fig. 2a of the main text.
9
Ⅴ. Tuning the Bi dopant level in V-doped Sb2Te3 to search for the QAH insulating state
Figure S8 | Transport properties of the 6QL (BixSb1-x)1.85V0.15Te3 films as a function of x, the Bi
dopant level. a-g, Magnetic field dependent Hall resistance yx of 6QL (BixSb1-x)1.85V0.15Te3 films at
T=2K with: a, x = 0; b, x = 0.09; c, x = 0.18; d, x = 0.21; e , x = 0.27; f, x = 0.36; and g, x=0.46. h-n,
Temperature-dependent longitudinal resistivity xx of films with: h, x = 0; i, x = 0.09; j, x = 0.18; k, x =
0.21; l, x = 0.27; m, x = 0.36; and n, x=0.46.
The anomalous Hall resistance exhibits dramatic and systematic change with Bi-dopant level
in a 6QL V-doped Sb2Te3. yx at zero magnetic field (labeled as yx(0)) is only 108at T= 2K
for the sample with x = 0whereas increasing to 221in the x = 0.09 film. The value is further
enhanced to 498at x = 0.18, 685at x = 0.21, and 1.9k at x=0.27However, when x reaches
0.36, yx(0) rapidly reduced to 1.1k, and then lowered to only 682 at x = 0.46as shown in the
top panel of Fig. S8. The evolution of yx(0) with Bi-content is summarized in Fig. S9a. A
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maximum can be clearly seen near the crossover region between p- and n-type (light green area)
conduction, where yx(0) is about 20 times larger than the minimum value. The enhancement of
yx(0) indicates carrier-independent ferromagnetism in this system, which is the bas is for
observing the QAH state.3,4
Figure S9 | Ferromagnetic properties of 6QL (BixSb1-x)1.85V0.15Te3 films at various carrier density
and type. a, Dependence of anomalous Hall resistance in zero magnetic field yx(0) (blue squares) and
longitudinal resistance in zero magnetic field xx(0) (red circles) at T=2K, and b, Dependence of
yx(0)/xx(0) for different Bi content x (varying carrier density) The charge carriers change from p-type to
n-type with increasing Bi content x.
The xx of all 6QL (BixSb1-x)1.85V0.15Te3 films increases with decreasing temperature (Figs.
S8h-n), exhibiting an insulating behavior. Evolution of xx at 2K (same as xx(0)) with Bi content
exhibits similar behavior as yx(0), also showing a peak near the p-n crossover region (i.e. with
x~0.27) (Fig. S9a). Figure S9b displays yx(0)/xx(0) ratios, the arctangent of yx(0)/xx(0), called
anomalous Hall angle , at different Bi concentration x. The ratio is only 0.032 for the x=0 (high
carrier density) sample, but is enhanced to more than 0.2 near the crossover region of x~0.27,
11
which also indicates the carrier- independent ferromagnetism in this system, signifying the
achievement of the QAH state in V-doped TI system.3,4
Ⅵ. Ferromagnetic properties of QAH samples
Figure S10 | Ferromagnetic properties of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2). a, Magnetic
field dependence of yx measured at various temperatures (from 0.3 to 80K). b, Temperature dependence
of yx(0). c, Arrott plots for a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film, which shows a TC of ~23K.
Figure S10a displays a series of yx–0H measurements for a 4QL (Bi0.29Sb0.71)1.89V0.11Te3
film (sample S2) taken at different temperatures. At low temperature, yx shows a square-shaped
hysteresis loop, indicating a long-range ferromagnetic order with out-of-plane magnetic
anisotropy. At high temperatures, yx exhibits linear magnetic field dependence due to the
ordinary Hall effect. The film mobility is only ~130cm2/Vs, as estimated from xx and the
carrier density determined from the Hall trace at T=80K. Other measured 4QL samples that show
QAH state also had similar mobilities. A TC of ~23K is determined from both the temperature
dependence of yx(0) (Fig. S10b) and the Arrot plots (Fig. S10c).2
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maximum can be clearly seen near the crossover region between p- and n-type (light green area)
conduction, where yx(0) is about 20 times larger than the minimum value. The enhancement of
yx(0) indicates carrier-independent ferromagnetism in this system, which is the bas is for
observing the QAH state.3,4
Figure S9 | Ferromagnetic properties of 6QL (BixSb1-x)1.85V0.15Te3 films at various carrier density
and type. a, Dependence of anomalous Hall resistance in zero magnetic field yx(0) (blue squares) and
longitudinal resistance in zero magnetic field xx(0) (red circles) at T=2K, and b, Dependence of
yx(0)/xx(0) for different Bi content x (varying carrier density) The charge carriers change from p-type to
n-type with increasing Bi content x.
The xx of all 6QL (BixSb1-x)1.85V0.15Te3 films increases with decreasing temperature (Figs.
S8h-n), exhibiting an insulating behavior. Evolution of xx at 2K (same as xx(0)) with Bi content
exhibits similar behavior as yx(0), also showing a peak near the p-n crossover region (i.e. with
x~0.27) (Fig. S9a). Figure S9b displays yx(0)/xx(0) ratios, the arctangent of yx(0)/xx(0), called
anomalous Hall angle , at different Bi concentration x. The ratio is only 0.032 for the x=0 (high
carrier density) sample, but is enhanced to more than 0.2 near the crossover region of x~0.27,
11
which also indicates the carrier- independent ferromagnetism in this system, signifying the
achievement of the QAH state in V-doped TI system.3,4
Ⅵ. Ferromagnetic properties of QAH samples
Figure S10 | Ferromagnetic properties of a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2). a, Magnetic
field dependence of yx measured at various temperatures (from 0.3 to 80K). b, Temperature dependence
of yx(0). c, Arrott plots for a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film, which shows a TC of ~23K.
Figure S10a displays a series of yx–0H measurements for a 4QL (Bi0.29Sb0.71)1.89V0.11Te3
film (sample S2) taken at different temperatures. At low temperature, yx shows a square-shaped
hysteresis loop, indicating a long-range ferromagnetic order with out-of-plane magnetic
anisotropy. At high temperatures, yx exhibits linear magnetic field dependence due to the
ordinary Hall effect. The film mobility is only ~130cm2/Vs, as estimated from xx and the
carrier density determined from the Hall trace at T=80K. Other measured 4QL samples that show
QAH state also had similar mobilities. A TC of ~23K is determined from both the temperature
dependence of yx(0) (Fig. S10b) and the Arrot plots (Fig. S10c).2
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Ⅶ. QAH signature up to 3K (sample S2)
Figure S11 | Temperature evolution of Vg-dependent yx(0) (blue) and xx(0) (red) of a 4QL
(Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2). a, Measured at 100mK without magnetic field training. b-j,
Measured after magnetic training. b, 100mK; c, 300mK; d, 500mK; e , 1K; f, 1.5K; g, 2K; h, 2.5K; i, 3K;
and j, 4K, respectively. Note that yx(0) always exhibits a single maximum, with a peak value
considerably suppressed at increasing temperatures, accompanied by the disappearance of the dip in xx(0).
13
The QAH state dies away at T=3K. The vertical purple dashed-dotted line indicates the charge neutral
point Vg0. The variation in position and width of the yx(0) and xx(0) peaks with temperature results from
the change in substrate dielectric properties induced by charging and temperature effect.
The observation of a self-driven QAH state in this hard FMTI is further supported by the
temperature-dependent behavior of the resistivity, as shown in Fig. S11. We show continuous Vg
dependences of yx(0) and xx(0) measured at various temperatures on sample S2 in Fig. 3 of the
main text. At the lowest T=100mK, there is not much difference in the Vg-dependent yx(0) and
xx(0), either with or without magnetic training (Figs. S11a and S11b), also indicating the self-
driven QAH state.
Ⅷ.The gate electric-field dependence of QAH effect measured at 120mK (sample S2)
Figure S12 | The QAH effect in a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2) measured at 120mK.
a, b, Magnetic field dependence of the Hall resistance yx (a) and the longitudinal resistance xx (b) at
different applied gate voltage Vg = -200, -50, -12, +25 and +200V. c, Dependence of yx(0) (blue squares)
and xx (0) (red circles) plotted as a function of Vg. Note the 0.9985 h/e2 quantization near charge neutral
point Vg0=-12V.
The 0H-dependence of yx and xx at T=120mK at different bottom-gate voltages Vg are
shown in Figs. S12a and S12b. Overall, the shape of the yx hysteresis loops (Fig. S12a) varies
only slightly with Vg, demonstrating the robust nature of the ferromagnetism. It does point out
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Ⅶ. QAH signature up to 3K (sample S2)
Figure S11 | Temperature evolution of Vg-dependent yx(0) (blue) and xx(0) (red) of a 4QL
(Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2). a, Measured at 100mK without magnetic field training. b-j,
Measured after magnetic training. b, 100mK; c, 300mK; d, 500mK; e , 1K; f, 1.5K; g, 2K; h, 2.5K; i, 3K;
and j, 4K, respectively. Note that yx(0) always exhibits a single maximum, with a peak value
considerably suppressed at increasing temperatures, accompanied by the disappearance of the dip in xx(0).
13
The QAH state dies away at T=3K. The vertical purple dashed-dotted line indicates the charge neutral
point Vg0. The variation in position and width of the yx(0) and xx(0) peaks with temperature results from
the change in substrate dielectric properties induced by charging and temperature effect.
The observation of a self-driven QAH state in this hard FMTI is further supported by the
temperature-dependent behavior of the resistivity, as shown in Fig. S11. We show continuous Vg
dependences of yx(0) and xx(0) measured at various temperatures on sample S2 in Fig. 3 of the
main text. At the lowest T=100mK, there is not much difference in the Vg-dependent yx(0) and
xx(0), either with or without magnetic training (Figs. S11a and S11b), also indicating the self-
driven QAH state.
Ⅷ.The gate electric-field dependence of QAH effect measured at 120mK (sample S2)
Figure S12 | The QAH effect in a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S2) measured at 120mK.
a, b, Magnetic field dependence of the Hall resistance yx (a) and the longitudinal resistance xx (b) at
different applied gate voltage Vg = -200, -50, -12, +25 and +200V. c, Dependence of yx(0) (blue squares)
and xx (0) (red circles) plotted as a function of Vg. Note the 0.9985 h/e2 quantization near charge neutral
point Vg0=-12V.
The 0H-dependence of yx and xx at T=120mK at different bottom-gate voltages Vg are
shown in Figs. S12a and S12b. Overall, the shape of the yx hysteresis loops (Fig. S12a) varies
only slightly with Vg, demonstrating the robust nature of the ferromagnetism. It does point out
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that the magnetism appears to be weakly dependent on the location of Fermi energy, which is a
characteristic of the van Vleck mechanism.4 However, both Hc and yx(0) can be seen to vary
somewhat with Vg in Fig. S12a, where Hc=1.15T reaches a maximum at Vg=-200V, 30% larger
than at Vg=+200V. This variation in Hc with Vg is much larger than for Cr-doped TI films,3
indicating some carrier-dependent ferromagnetism in V-doped TIs, probably mediated by
impurity bands.4 On the other hand, yx(0), changes less with Vg , reaching a maximum value of
the 0.9985h/e2 around charge natural point Vg0=-12V. Note that in Fig. S12b the longitudinal
resistance xx-0H curve exhibits the typical behavior as that for a ferromagnetic material: two
very sharp symmetric peaks at Hc. Also, xx(0) changes with Vg, with a minimum value of 0.31
h/e2 around Vg=-12V. The Vg dependence of yx(0) and xx(0) are plotted in Fig. S12c. The QAH
state is thus on a firm ground by the occurrence of maximum in yx(0), accompanied by a
minimum in xx(0), and also that the QAH effect can be attained by the gate-tuning chemical
potential.
15
Ⅸ.The QAH state at 130mK (sample S1)
Figure S13 | The QAH effect in a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S1) measured at 130mK.
The magnetic field dependence of yx (blue) and xx (red) at T=130mK. Note the is about 84.40º in
sample S1 at T=130mK.
For comparison with Cr-doped system, to the best of our knowledge, the largest Hall angle
in Cr-doped system is 84.40º at T=30mK,5 whereas in V-doped TI system (sample S1) the QAH
behavior with the same ~84.40º could be reached by ~130mK, as shown in Fig S13.
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that the magnetism appears to be weakly dependent on the location of Fermi energy, which is a
characteristic of the van Vleck mechanism.4 However, both Hc and yx(0) can be seen to vary
somewhat with Vg in Fig. S12a, where Hc=1.15T reaches a maximum at Vg=-200V, 30% larger
than at Vg=+200V. This variation in Hc with Vg is much larger than for Cr-doped TI films,3
indicating some carrier-dependent ferromagnetism in V-doped TIs, probably mediated by
impurity bands.4 On the other hand, yx(0), changes less with Vg , reaching a maximum value of
the 0.9985h/e2 around charge natural point Vg0=-12V. Note that in Fig. S12b the longitudinal
resistance xx-0H curve exhibits the typical behavior as that for a ferromagnetic material: two
very sharp symmetric peaks at Hc. Also, xx(0) changes with Vg, with a minimum value of 0.31
h/e2 around Vg=-12V. The Vg dependence of yx(0) and xx(0) are plotted in Fig. S12c. The QAH
state is thus on a firm ground by the occurrence of maximum in yx(0), accompanied by a
minimum in xx(0), and also that the QAH effect can be attained by the gate-tuning chemical
potential.
15
Ⅸ.The QAH state at 130mK (sample S1)
Figure S13 | The QAH effect in a 4QL (Bi0.29Sb0.71)1.89V0.11Te3 film (sample S1) measured at 130mK.
The magnetic field dependence of yx (blue) and xx (red) at T=130mK. Note the is about 84.40º in
sample S1 at T=130mK.
For comparison with Cr-doped system, to the best of our knowledge, the largest Hall angle
in Cr-doped system is 84.40º at T=30mK,5 whereas in V-doped TI system (sample S1) the QAH
behavior with the same ~84.40º could be reached by ~130mK, as shown in Fig S13.
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References
1. Chien Y. J. Transition metal-doped Sb2Te3 and Bi2Te3 Diluted Magnetic Semiconductors. Ph.D.
Dissertation. The University of Michigan (2007).
2. Arrott A. Criterion for Ferromagnetism from Observations of Magnetic Isotherms. Phys. Rev. B
108, 1394 (1957).
3. Chang C. Z. et al. Thin films of magnetically doped topological insulator with carrier-
independent long-range ferromagnetic order. Adv. Mater. 25, 1065-1070 (2013).
4. Yu, R., et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329,
61-64 (2010).
5. Chang, C. Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic
topological insulator. Science 340, 167-170 (2010).
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