JOURNAL OF APPLIED PHYSICS 112, 063912 (2012)
Magnetically doped semiconducting topological insulators
X. F. Kou,1 W. J. Jiang,1 M. R. Lang,1 F. X. Xiu,2 L. He,1,a) Y. Wang,3,4 Y. Wang,4 X. X. Yu,1
A. V. Fedorov,5 P. Zhang,5 and K. L. Wang1,a)
1
Device Research Laboratory, Department of Electrical Engineering, University of California,
Los Angeles, California 90095, USA
2
Department of Electrical and Computer Engineering, Iowa State University, Ames, Iowa 50011, USA
3
Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
4
Materials Engineering & Centre for Microscopy and Microanalysis, The University of Queensland,
Brisbane, QLD 4072, Australia
5
Advanced Light Source Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
(Received 13 March 2012; accepted 24 August 2012; published online 21 September 2012)
The time invariant behaviors of topological insulators are expected to be changed with magnetic
doping, which motivate the present study. Here, we show that for Bi2xCrxSe3 (0.01 x 0.3) thin
films grown on Si, the non-trivial topological surface state is weakened by the Cr dopants. The
band gap of surface is opened and monotonically increased with Cr concentration up to 100 meV
at 10 K. Meanwhile, the semiconducting behavior is well-maintained in the bulk owing to the
reduction of background doping by means of a modified growth strategy and an in situ passivation
method. Besides, we also observe the existence of unconventional ferromagnetic ordering below
35 K, for which the Curie-Weiss Law and conventional/modified Arrott equations do not apply.
These observations may further help us investigate extraordinary magneto-electric effect in
topological insulators, and the result will also pave the way for realizing the quantized anomalous
C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754452]
Hall effect. V
Topological insulators (TIs) are drawn unparalleled
attentions in recent research highlights.1–4 Exciting progress
based on the time-reversal-invariant properties of TIs, such
as high quality materials preparations5–10 and manipulation
of surface states,11–14 has been made. Such efforts have
accelerated the speed towards the demonstration of quantum
spin Hall (QSH).15–19 To this end, the effort to break the
topologically protected surface states by introducing magnetic ordering inside the TIs system would enable us to
observe the quantized anomalous Hall (QAH),20–26 extraordinary magneto-electric (ME) effects, and perhaps other discoveries.27,28 Specifically, QAH is striking in terms of
transport properties, arising from the fact that backscatterings are prohibited even under the perturbation from
magnetic impurities, and thus simultaneously the quantum
Hall conductance of e2/h appears even in the absence of
external magnetic field.22,23
Efforts to dope tetradymite family materials with magnetic impurities were made before the discovery of their topological characteristics.29–32 However, the discussions of
such magnetic doped materials at that time have been limited
to the scope of conventional dilute magnetic semiconductors
(DMS), despite that the doping concentration of magnetic
impurities did obviously go far beyond the “dilute” regime.
Most recently, ferromagnetism was proposed to exist in
Cr/Fe doped TIs through the van-Vleck mechanism in the
absence of itinerant carriers,22 and this proposal is contradictory to the s-d exchange interaction mechanism in standard
DMS systems.33–35 This carrier-independent ferromagnetism
was later observed in BixSb2xTe3 system with different Cr
a)
Authors to whom correspondence should be addressed. Electronic
addresses: heliang@ucla.edu and wang@ee.ucla.edu.
0021-8979/2012/112(6)/063912/6/$30.00
doping concentrations.36 In addition, several groups have
also experimentally prepared Mn/Fe/Cr doped Bi2Se3 by
means of a modified Bridgman method,9 vapor-liquid-solid
(VLS),37 and molecular beam epitaxial (MBE) growth.38
Extensive transport measurements were conducted in these
systems, for instance, the crossover between weak localization (WL) and weak anti-localization (WAL) was found.38
However, these studies were either incomplete due to the
limited Fe doping concentration (less than 2% as shown in
Ref. 37) or due to the presence of heavy background n-type
doping, i.e., metallic behavior in bulk.38 For the purpose of
realizing of QAH in TIs, one should tune the magnetically
doped TIs into bulk insulating states, and the relevant magnetic properties, such as phase transition information and
relation of magnetism, with dopant/carrier concentration in
these systems need to be comprehensively studied.
Following this motivation, we study the Cr doped Bi2Se3
epitaxial thin films grown using a solid source MBE system.
We observe the band opening of the surface states below the
Curie temperature (TC 35 K). We demonstrate a wellestablished ferromagnetic ordering in the semiconducting background by combining both magneto-transport measurements
and magnetic property measurements. Furthermore, we discover two exotic phenomena related to the “unconventional”
ferromagnetism, which clearly contradict to the behaviors of
the conventional s-d exchange mechanism in the DMS systems.
Our findings in the Cr doped TI system within the semiconducting region may facilitate the associated understandings of
intrinsic magnetic interaction mechanisms in the present
systems.
Thin films of Cr doped Bi2Se3 are grown under an ultrahigh vacuum (UHV) system by MBE. High resistivity Si
(111) wafers (q > 105 Xcm) are first cleaned with standard
112, 063912-1
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V
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Kou et al.
Radio Corporation of America (RCA) clean method.39,40
The substrates are then treated by hydrofluoric acid wet etching so that the surface dangling bonds are saturated by a
layer of hydrogen atoms and the (111) surface is 1 1 reconstructed to further enhance the film quality.41,42 The growth
is conducted under the Se-rich environment with a nominal
Se to Bi ratio approximately 10:1, which is expected to
reduce the Se vacancy defects. In addition, the substrate is
remained at a relatively high substrate temperature (300 C)
to optimize both the surface migration rate and Cr solubility
simultaneously.30 To inhibit the degradation introduced from
ambient n-doping after growth, we use in-situ Al passivation
method, which is to deposit 2 nm Al immediately after the TI
thin film growth.43 In situ growth dynamics are monitored by
reflection high energy electron diffraction (RHEED) measurements. Sharp streaky patterns in Figure 1(a) indicate a 2D
pseudomorphic growth. Meanwhile, the intensity of zeroorder pattern is tracked and the oscillations are evident in
Fig. 1(b). The growth rate can thus be estimated as 0.56
quintuple layer (QL)/min.
The surface morphology of the thin film is examined by
atomic force microscope (AFM). Typical triangular terraces
are revealed without visible clusters even with the Cr doping
concentration reaching to as high as 20%. Figure 1(c) illustrates the AFM image of a Cr0.1Bi1.9Se3 sample with a film
thickness of 50 QLs. The average terrace size is estimated to
be 200 nm, which is comparable with the un-doped Bi2Se3
thin films grown on Si (111) substrates following a similar
growth method.6 Further structural characterization is proceeded by using high resolution transmission electron microscopy (HRTEM) shown in Fig. 1(d), the layered
structures of the 7 QL single-crystalline Cr0.1Bi1.9Se3 thin
film can be clearly seen and the lattice spacing between
(0003) planes is measured to be 1 nm, corresponding to
one quintuple layer. It also confirms that there are no clusters
J. Appl. Phys. 112, 063912 (2012)
or second phase developed inside the crystalline structural
matrix, within the resolution of the HRTEM. This result indicates that Cr atoms are most likely uniformly distributed
inside the Bi2Se3 and the tetradymite quintuple layered structure is well maintained.
Energy dispersion relations of the Cr doped Bi2Se3 thin
films are studied by angular resolved photoemission spectroscopy (ARPES). Atomically clean surfaces of the samples
are obtained after mild annealing at 423 K for 2 h, and all
photoemission data are collected at 10 K. To understand the
evolution of surface states with the Cr doping level, we compare the band maps of un-capped Bi2xCrxSe3 grown on Si
(111) with same thickness (50 QL) but different Cr compositions, as given in Figures 2(a)–2(d). While a linear Diraccone-like dispersion relation can be clearly observed on the
surface of the un-doped sample in Fig. 2(a), the gap of the
surface states below the transition temperature is opened at
the C point and the electrons behave like massive Dirac fermions even without applying an external magnetic field in
Figs. 2(b)–2(d). The change of surface state is mainly due to
the factor that ferromagnetic ordering generated by the
Cr dopants inside the material will break the time-reversalsymmetry (TRS) and thus force the surface opens the band
gap. As Cr doping is increased, the magnetic moment gets
enhanced, which further weakens the non-trivial topological
surface states and enlarges the band opening. Furthermore,
we can roughly estimate the amplitude of the surface gap D
by means of projecting the photoemission intensity shown in
Fig. 2 onto the energy spectrum. As indicated by the solidyellow curves depicted in Figs. 2(b)–2(d), D are found to be
around 5 meV, 35 meV, and 100 meV for Bi2xCrxSe3 with
x ¼ 0.02, 0.1, and 0.2 at 10 K, respectively. The relation of
the Berry phase to D in the presence of magnetic ordering
perpendicular to the surface can also be determined as
follows:44
FIG. 1. (a) RHEED pattern along [1120]
direction of an as-grown surface of
Bi2xCrxSe3 with a thickness of 7 QLs. (b)
RHEED oscillations of intensity of the specular beam. The oscillation period is found to
be 108 s, corresponding to a growth rate of
0.56 QL/min. (c) AFM image of the
Bi1.9Cr0.1Se3 thin film with the size of
0.3 lm 0.3 lm. (d) HRTEM of a
Bi1.8Cr0.2Se3 grown on a Si (111) substrate.
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J. Appl. Phys. 112, 063912 (2012)
FIG. 2. ARPES intensity maps of un-capped 50 QL Bi2xCrxSe3 thin films with (a) x ¼ 0, (b) x ¼ 0.02, (c) x ¼ 0.1, and (d) x ¼ 0.2 on Si (111) along the C-K
direction. With the introduction of magnetic Cr doping, the surface will deviate from the original linear massless Dirac fermion state and becomes broaden.
The surface will also open a larger band gap with higher Cr concentration as illustrated by the solid yellow lines. All data are taken using 52 eV photons under
the temperature of 10 K.
D
du ¼ p 1 þ
;
2EF
(1)
where EF is the energy gap between the Fermi level measured from the Dirac cone. For Cr0.1Bi1.9Se3 as one example,
we subsequently obtain a perturbed Berry phase of 7.6%
deviating from the ideal p phase. Moreover, higher Cr doping concentration will also damage the crystalline structure
of Bi2xCrxSe3 films and introduce strong electron scattering
in these samples. This along with the Berry phase deviation
will further degrade the ARPES spectrum, and in our experiments the surface states of Cr doped Bi2Se3 can no longer be
detected by ARPES when the doping composition of Cr
exceeds 0.3. Meanwhile, it should be noted that the Fermi
levels almost remain the same regardless of Cr doping
concentration in the ARPES images. However, this does not
have any direct relation with the intrinsic carrier densities.
Instead, we credit such Fermi level pinning to un-intentional
ambient doping, band bending, and photoemission gating
effects brought during the ARPES measurements.
The material challenges for 3D TIs at the current stage lie
in the effort to sustain the bulk insulating states. However, doping concentrations in Bi2Se3 based materials are usually and
inevitably high because of intrinsic Se vacancy defects. Consequently, the Fermi level is pinned up in the conduction band,
and thus introduces undesirable metallic behaviors in TI materials.38 In our experiment, by modifying the cleaning procedure,
optimizing growth conditions, and with in-situ Al passivation,
we successfully suppress these drawbacks.43 In Fig. 3(a), the
temperature dependence of the longitudinal resistance Rxx are
FIG. 3. (a) The dependence of the longitudinal
resistance Rxx on temperature for a Hall bar device fabricated on the 50 QL Bi1.9Cr0.1Se3 thin
film sample on Si (111). The monotonically
increase in Rxx with temperature decreasing
shows the semiconductor behavior. Inset: modified Arrhenius law of the R-T curve. The polaron formation energy Ea is found to be
35.5 meV and a ¼ 3/2 for non-adiabatic small
polaron hopping. (b) Magnetization versus temperature for the sample under zero-field cooling
(red circles) and field cooling (blue squires)
conditions. The external field is 50 Oe perpendicular to the sample surface. Inset: plot of
(v v0)1 versus temperature T. This relation
does not follow the linear Curie-Weiss law
above Tc.
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J. Appl. Phys. 112, 063912 (2012)
displayed. The monotonic increase in Rxx as the decrease in
temperature (from 300 K) reveals typical semiconductor behavior (dq/dT < 0 in the phonon scattering dominant region) in the
sample.6 Similar to other doped semiconductor systems, the
transport characteristic in a high temperature insulating phase
follows the Emin-Holstein theory:45
qðTÞ ¼ q0 T a expðEa =kB TÞ:
(2)
Here Ea is the activation energy and kB is the Boltzmann
constant. With linear fitting in the high temperature region
(T > 200 K) as shown in the inset of Fig. 3(a), the exponent a
is found to be 3/2 and thus corresponds to the non-adiabatic
small polaron hopping (SPH), with a small polaron bandwidth;46,48 Ea is estimated to be 35 meV.
The magnetic properties of the 50 QL Bi1.9Cr0.1Se3 thin
film sample are investigated by superconducting quantum interference device (SQUID). The phase transition information
and the relation of magnetization as a function of temperature
can be obtained by performing the zero-field cooling (ZFC)
and field cooling (FC) measurements. An external magnetic
field of 50 Oe is applied perpendicular to the sample plane
during these measurements. The bifurcation of ZFC and FC
curves at 8 K in Figure 3(b) corresponds to a blocking temperature, which may be associated with the formation of coherent
nanostructures formed during growth as also observed in Mn
doped DMS.49–51 The Curie temperature (TC) is found to be
35 K in Fig. 3(a), where the magnetic momentum reduced to
approximately zero, and above this temperature the material
becomes paramagnetic (PM). However, the evolution of the
DC magnetic susceptibility (v ¼ M/H) on temperature above
TC does not follow the linear relationship manifested by the
well-known Curie-Weiss Law
v/
C
;
ðT TC Þa
(3)
where a is the critical exponent which modifies the susceptibility in the immediate vicinity of the Curie point and the
Curie constant C gives the information of the Lande g-factor
and magnetic impurity density in the material.52,53 Instead of
a linear dependence, a curvature existing between two linear
regions can be clearly seen in the inset of Fig. 3(b).
To understand the above unconventional ferromagnetism, detailed field dependent characterizations are carried
out. The field dependent hysteresis loops (M-H) in various
temperatures as displayed in Fig. 4(a) clearly indicate the
presence of FM ordering in the low temperature range
(T < 35 K) with the coercivity field HC 150 Oe (inset of
Fig. 4(a)) and a saturation field around 2000 Oe. The large
volume susceptibility with the value of 7.3 (SI) at 5 K inside
the system is established via the van-Vleck model22 and is
originated from the unique topological property of band
inversion due to the strong spin-orbital coupling (SOC) of
the Bi2Se3 matrix.22 As temperature increases towards
TC ¼ 35 K, ferromagnetic ordering is gradually suppressed
and finally the system becomes paramagnetic above 35 K.
To comprehensively investigate the underlying interaction in the present system, for example, long range or nearest
neighbor interactions, we study the FM-PM phase transition.
Here, we adopt modified Arrott-Noakes equation of state54
1=c
1=b
H
T TC
H
¼
þ
:
T1
M
M
(4)
Provided that the linearized parallel straight lines are
observed, one can thus experimentally determine the underlying dominant interaction by replotting M-H curves;54,55 for
example, in the long range mean field model, these exponents
are c ¼ 0.5, b ¼ 1, while in the nearest neighbor 3-D Heisenberg model, the corresponding values change to c ¼ 0.37,
b ¼ 1.39. However, as depicted in Figs. 4(b) and 4(c), rather
than displaying the parallel straight lines, both plots display
some continuous curvatures, even in the saturation region up
to 8000 Oe, and these effects turn to exclude the dominant
long range interactions, as well as preclude us from giving an
accurate estimation of the transition temperature.44,47,56 In
FIG. 4. (a) M-H loops of the 50 QL Bi1.9Cr0.1Se3 thin film at 5 K, 10 K, 15 K, 20 K, 30 K, and 35 K. Inset: zoom-in hysteresis loop at 5 K, the coercivity field is
started to be around 150 Oe. (b) Arrott plots of H/M versus M2 for magnetic isotherms from 14 K to 26 K. (c) Modified Arrott-Noakes plots of (H/M)1/1.39 versus M1/0.37 for data in (b). The applied magnetic field is always perpendicular to the sample surface, and the field range which covers from 8000 Oe to
8000 Oe is high enough to saturate the magnetic moment.
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J. Appl. Phys. 112, 063912 (2012)
FIG. 5. Magneto-transport measurements of
50 QL Bi2xCrxSe3 thin films on Si (111)
substrate. (a) The dependence of 2D carrier
density (red-open circle) and mobility
(blue-solid square) on the Cr doping concentration at 1.9 K. (b) B-field dependent
anomalous Hall effect (RAM) with Cr doping concentration (x ¼ 0.02, 0.1, 0.2, and
0.3). Linear ordinary Hall component of
RoH has been subtracted from the Hall resistance. Inset: the evolution of coercivity
field HC under different Cr compositions at
1.9 K.
addition, the absence of “S” shape in the Arrott plot suggests
the underlying phase transition is of second order. Given the
above observed abnormal inverse susceptibility shown in
Fig. 3(b), as well as applicability of the modified ArrottNoakes equation of the state, we suggest that these behaviors
should result from the intrinsic magnetism in Cr doped Bi2Se3
systems where the major contribution of spin susceptibility is
brought by a strong coupling between the magnetic impurities
and local valence electrons.22 Clearly, this needs to be further
studied.
Finally, the FM phase and its relation with Cr doping can
also be confirmed by the magneto-transport measurements.
Standard Hall bars structures on different Bi2xCrxSe3 samples with 0.01 x 0.3, with the same thickness of 50 QL
and device size of 10 lm (L) 40 lm (W), are fabricated
using photolithography. As we can observe in Figure 5(a), the
overall two-dimensional (2D) Hall carrier density decreases
modestly when more Cr atoms are increasingly introduced.
Given the intrinsic n-type behavior caused by Se-vacancies in
un-doped Bi2Se3 thin films, the suppression of electron concentration in Bi2xCrxSe3 suggests that a majority of Cr atoms
are incorporated within the crystal lattice with the form of
Cr3þ state, and therefore substitute on the Bi sublattice in the
TI matrix.57,58 On the other hand, the degradation of conduction mobility reveals the factor that extra impurity scattering
centers will form in the bulk due to Cr doping and thus hamper the electron transport under low temperature.
Provided there is close correlation between magnetism
and transport in magnetic materials, anomalous Hall effect
(AHE) is utilized to confirm the prevailing ferromagnetism.59 Other than a linear slope of ordinary Hall resistance
Rxy in non-magnetic semiconductors, the magnetization
induced by the exchange field modifies Rxy, leading to the
following empirical relation:59
existence of remnant magnetization within the FM phase. By
extracting the linear ordinary Hall component RoH, we plot
the dual-loop anomalous Hall data RAM as a function of
applied field at 1.9 K in Fig. 5(b). With the increase in Cr
composition, more distinct hysteresis behavior can be found,
and both the saturation magnitude of anomalous Hall component and coercivity field HC as shown in the inset will
become enhanced.
In conclusion, we have demonstrated the presence of
FM ordering in the epitaxial Bi2xCrxSe3 thin films on Si
substrate using MBE growth. The Cr can be fully incorporated into the Bi2Se3 matrix without altering the quintuple
layer structure. The ARPES result shows the magnetic doping can also drive the topologically protected surface states
into the massive Dirac fermions region. Furthermore, magnetization measurements confirm that the ferromagnetic
ordering forms below TC 35 K. In addition, the semiconductor behavior and the presence of Anomalous Hall Effect
are all revealed by transport measurements. It is important to
approach the bulk insulating state by decreasing the carrier
concentration. The Fermi level also needs to be engineered
in the surface states band gap with the fabrication of gated
devices. By combining them together, we can verify the
intrinsic magnetic mechanisms inside the Cr doped TI systems and forward a crucial step towards the realization of
critical QAH effect and magneto-electric coupling based
applications.
This work was in part supported by the Focus Center
Research Program-Center on Functional Engineered Nano
Architectonics (FENA), the DARPA-MESO program, and
the Australia Research Council.
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