Download Supplementary Information (doc 3822K)

Supplementary Information on the manuscript:
Unexpected orbital magnetism in Bi-rich Bi2Se3 nanoplatelets
by
Hae Jin Kim1, Marios S. Katsiotis2, Saeed Alhassan2, Irene Zafiropoulou3,
Michael Pissas3, Yannis Sanakis3, Georgios Mitrikas3, Nikolaos Panopoulos3,
Nikolaos Boukos3, Vasileios Tzitzios3, Michael Fardis3, Jin-Gyu Kim1, SangGil Lee1, Young-Min Kim1, Seung Jo Yoo1, Ji-Hyun Lee1, Antonios
Kouloumpis4, Dimitrios Gournis4, Michael Karakassides4 and Georgios
Papavassiliou3
1 Nano-Bio Electron Microscopy Research Group, Korea Basic Science
Institute, 169-148 Gwahak-ro, Yuseong-go, Daejeon 305-806, Republic of
Korea.
2
Department of Chemical Engineering, The Petroleum Institute, PO Box
2533, Abu Dhabi, United Arab Emirates.
3
Institute of Nanoscience and Nanotechnology, National Centre for Scientific
Research “Demokritos”, 153 10 Aghia Paraskevi, Attiki, Greece.
4
Department of Materials Science & Engineering, University of Ioannina,
45110 Ioannina, Greece.
The supplementary information is organized into two parts. Additional
experimental information are provided in Part I, while a theoretical model to
simulate the DC magnetization and AC magnetic susceptibility vs. magnetic
field B measurements is presented in Part II.
1
PART I. ADDITIONAL EXPERIMENTAL INFORMATION
A. Magnetic & ESR Measurements
A.1 Comparison of Magnetic and ESR measurements between raw materials
and synthesized Bi2Se3
Figure S.1 | AC-magnetic susceptibility at 5 kHz and DC-magnetization (inset) vs.
magnetic field H of Bi2Se3 and raw materials at RT
In order to exclude that DC-magnetization, AC-susceptibility and electron spin
resonance
(ESR)
signals
are
produced
by
ferromagnetic
(FM)
or
superparamagnetic (SPM) impurities, the magnetic properties of all raw
materials have been carefully examined and compared with those of
synthesizes Bi2Se3 specimens. Figure S.1 presents the magnetic ACsusceptibility and DC-magnetization measurements (inset) of Se and
Bi(OOCH3)3 in comparison with Bi2Se3. It is clearly observed that the magnetic
response of Bi2Se3 is orders of magnitude higher than the response of the raw
materials. Similar behaviour is observed in the ESR spectra of Figure S.2.
2
Figure S.2 | Electron Spin Resonance spectra of Bi2Se3 and raw materials at RT.
In addition, magnetization vs. magnetic field H loops were performed on a
SQUID magnetometer at selective temperatures between 5K and 300K. No
hysteresis effect was observed at all temperatures.
In conclusion, magnetic and ESR measurements exclude FM or SPM impurity
effects as origin of the observed magnetic response of Bi2Se3.
A.2 Magnetic Measurements at different magnetic field sweep rates and ACfrequencies
The possibility of slow magnetic relaxation was examined by performing χ vs.
H and M vs. H measurements, at different magnetic field sweep rates and ACfrequencies. Figure S.3 shows representative χ vs. H curves of sample BS2 in
the temperature range 50K-300K, at magnetic field sweep rate dHdc/dt=100
Oe/sec.
3
Figure S.3 | AC magnetic susceptibility at 5 kHz vs. magnetic field for sample BS2 at
the temperature range 5 – 300 K at dHdc/dt= 100 Oe/sec.
Results are similar with those of sample BS1 in Figure 2.c, differing only by a
factor of three in the signal intensity. Figure S.4 shows the relevant χ vs. H
and M vs. H curves in magnetic field sweep rates 10 Oe/sec and 50 Oe/sec.
(the corresponding M vs. H curves at 100 Oe/sec are shown in Figure 2.b of
the article).
No change was observed at all temperatures, in both the AC susceptibility
and DC magnetization by varying the magnetic field sweep rate. For
presentation reasons, Figure S.5a compares the AC susceptibility curves at
100K, in field sweep rates 10 Oe/sec, 50 Oe/sec and 100 Oe/sec.
Similarly, AC susceptibility measurements were insensitive to the AC
frequency, as seen in Figure S.5b. Results in Figures S3, S4, and S5 provide
strong evidence about the absence of slow magnetic relaxation in the Bi 2Se3
nanoplatelets.
4
Figure S.4 | AC (at 5 kHz) & DC magnetic susceptibility vs. magnetic field for sample
BS2 at the temperature range 5 – 300 K. DC spectra shown in (b) are collected at
dHdc/dt=10 Oe/sec, while spectra shown in (d) are collected at 50 Oe/sec.
b
a
Figure S.5 | AC magnetic susceptibility vs. magnetic field for sample BS2 at
temperature of 100 K: (a) at varying magnetic field sweep rates and frequency 5 kHz,
(b) at varying frequencies and magnetic field sweep rate 100 Oe/sec.
5
B. Nuclear Magnetic Resonance (NMR) supplementary material
Figure S.6 |
shows
209
Bi NMR magnetization recovery for sample BS2 at T=20 K. The inset
data for the two
components at selected temperatures; the dashed
line indicates metallic behaviour according to the Korringa relation.
209Bi
NMR (I = 9/2) in all measured polycrystalline samples consist of
inhomogeneously broadened lines, corresponding to the central transition
of the quadrupolarly shifted Zeeman energy levels. The ability of
209Bi
NMR to provide information on the local crystal environment becomes
evident in Figure 1.e, where spectra for two Bi2Se3 samples (BS2 and BS3) at
5 K are demonstrated.
In both cases, spectra are resolved in two peaks separated by ≈0.9 MHz,
which dictates the presence of two non-equivalent Bi-sites, in agreement with
the findings of the XRD and TEM measurements (Figure 1).
6
The opinion that the two peaks originate from two non-equivalent Bi sites is
further confirmed by the
209Bi
NMR spin-lattice relaxation time (T1)
measurements.
The
209Bi
NMR saturation recovery curve at 20K of sample BS2 is presented
in Figure S.6. Data verify the presence of two well-separated signal
components relaxing with different T1 values, in accordance with the spectra
in Figure 1.e. The saturation-recovery curve has been fitted as the sum of two
exponential terms: a single exponential and a Kohlraush (stretched
exponential) function with stretched exponent n=0.5, indicating a broad
distribution of T1 values for this signal component, in agreement with previous
measurements1.
The inset in Figure S.6 contains the values for
of the two signal
components at various temperatures. It is observed that the long
component agrees relatively well with the Korringa relation
as
indicated by the dashed line, which is characteristic for NMR of metallic
states2, 3. Most probably, the other component exhibits metallic behaviour as
well, however it is difficult to observe due to the broad
distribution.
C. Morphological and Elemental Characterization of Bi2Se3 nanoplatelets
a. Scanning Electron Microscopy (SEM)
a
b
7
Figure S.7 | a & b, SEM images of Bi2Se3 nanoplatelets (BS1); scale bars represent
100nm.
Typical SEM images of Bi2Se3 nanoplatelets are shown in Supplementary
Figure S.7. The nanoplatelets appear as hexagonal particles with lateral
dimension ranging between 200 and 600nm, while their thickness was
estimated to range between 20 and 50 nm.
b. Energy Dispersion Spectroscopy (EDS) with Transmission Electron
Microscope (TEM) and High Resolution Transmission Electron Microscopy
(HRTEM) Study
TEM EDS analysis of the Bi2Se3 nanoplatelets was performed with a FEI
Tecnai G20 and a FEI CM20, both equipped with EDAX EDS units; a Bi2Se3
bulk powder sample was analysed as reference (not shown here). Concerning
the calculation of stoichiometry, two options of quantification exist: using the
Se L peak and the Bi L peak, or using the Se K peak and the Bi L peak.
Usually, the first option is more accurate as the X-ray scattering cross-section
is similar for the same type of orbitals (L type). However, it was observed that
due to high uncertainty of background determination and subsequent
subtraction in the region of Se L peak, the corresponding error was higher
than in the case of using the Se K peak and the Bi L peak. Accordingly, the
second option was selected. Cliff and Lorimer4 observed that matrix
corrections are not required when analysing thin specimens, as in the case of
EDS-TEM and introduced “kAB” factors to relate the peak intensity ratio IA/IB to
concentration ratio CA/CB of elements A and B, according to the formula:
(S. Eq. 1)
8
a
c
b
d
Bi:
47.6
Se:
52.4
Bi:
41.3
Se:
58.7
Figure S.8 | a & c, Representative TEM bright field images of Bi2Se3 nanoplatelets
(BS1 and BS3); scale bars represent 100nm. b & d, Respective EDS spectra
collected at the areas marked with yellow rectangles; the calculated atomic ratios (%)
of Bi : Se are shown for each spectrum. Cu and C peaks originate from the TEM grid.
Different theoretical models can be applied for the determination of k AB
factors; in the present case and in order to improve accuracy, the k AB factor
for Se K and Bi L peak were experimentally derived from the spectrum of the
bulk Bi2Se3 powder as standard for an atomic ratio between Bi and Se equal
to 2 : 3 (Bi 40at% - Se 60at%). Utilizing the above kAB factor the spectra of the
synthesized specimen were subsequently quantified.
9
Table S.1 | TEM EDS Quantification Results for Bi2Se3 specimens. Values
correspond to the mean atomic ratios (%) of Bi and Se.
Bi L
40.1
Bi L
42.4
Bi L
45.7
Bi L
46.9
Bulk Bi2Se3
Se K
Bi
59.9
2
BS3
Se K
Bi
57.6
2.21
BS2
Se K
Bi
54.3
2.52
BS1
Se K
Bi
53.1
2.65
Se
3
Se
3
Se
3
Se
3
More than 20 particles from each of samples BS1, BS2, and BS3 were
analysed to obtain sound statistical representation of the synthesized
specimen; the standard error in the quantification was found to be 0.5%.
The results are presented in Table 1. It is observed that there is significant
increasing of the Bi : Se ratio following the series BS3<BS2<BS1.
A cross section TEM specimen of Bi2Se3 nanoplatelet was prepared by using
a focused ion beam (FIB) method with Quanta 3D (FEI Co., USA). To avoid
the sample damages by the Ga+ ion, 5 times carbon coating were performed
on the glass substrate. After 30 minutes sonication, second C-coating, Pt Edeposition with 0.12nA at 2kV, and Pt deposition with 0.3nA at 30kV were
carried out on Bi2Se3 nanoplatelet, respectively. The first rough milling was
performed using a 30kV Ga ion beam with a current of 7 nA and 3 nA. Fine
milling for TEM observation were carried out with a range from 0.5nA to 50pA
at 30kV. Finally, sample cleaning was performed with a current of 50pA at
5kV.
10
Figure S.9 | a, Representative HRTEM cross sectional images from specimen BS1.
b, simulated TEM images and atomic modelling of Bi2Se2. c, simulated TEM images
and atomic modelling of Bi2Se3. Green spheres correspond to Bi and red to Se,
respectively.
Several instrumental parameters were optimized to achieve HRTEM
simulation of the mixed phase of two crystal structures. These include
acceleration voltage (200 kV), spherical aberration coefficient (Cs, -0.03700
mm), convergence angle (1.00 mrad) and spread of defocus (80Å). Final
11
simulated images were optimized with experimental ones at defocus (120Å)
condition.
c. Atomic Force Microscopy (AFM) Measurements
a
c
b
d
Figure S.10 | a, AFM topography images of typical Bi2Se3 hexagonal particle (BS1);
b, corresponding 3D image. c, Section analysis of thick hexagonal particle. d,
Section analysis of thin hexagonal particle.
AFM topography images and cross section analysis of the prepared Bi2Se3
particles are shown in Figure S.10. Isolated thick and thin hexagonal particles
with well-defined edges are clearly visible in the images. The two morphology
types of Bi2Se3 platelets were examined by cross section analysis. Moreover,
the average height of the platelets ranges between 20-30 nm for thin particles
(Figure S.10d) and between 50 to 90 nm for thick particles (Figure S.10c).
12
PART II. PHENOMENOLOGICAL MODEL
Figure S.11 | Electron Energy vs. Magnetic Field Flux of the toy model Hamiltonian.
Green, respectively blue lines correspond to spin up, respectively spin down.
Quantum number n corresponds to angular momentum eigenvalues. By sweeping
the magnetic field through zero, spin up electrons (left handed circulating) flip to spin
down (right handed circulation). The Fermi level is set at EF=0.
DC and AC susceptibility experiments have been simulated on the basis of a
toy model Hamiltonian,
5.
, and
Here,
Rashba coefficient, and
is the magnetic flux quantum,
is the
the standard diagonal Pauli matrix. This
Hamiltonian is used to simulate electrons under the Rashba interaction, which
13
are moving in a circular trajectory of size L, enclosing a time dependent
magnetic flux
with
being a constant magnetic flux, and
a small oscillating flux5. For simplicity, (i) the magnetic
field is assumed to be oriented in the z-axis, representing the vertical direction
to the surface of the nanoplatelets, (ii) electron spins are considered to be
oriented in the z-axis, i.e.
instead of
as in the Rashba Hamiltonian. The
Fermi level EF has been set to EF=0.
In the absence of the time-dependent drive
, the circular motion is
described by the static part of the Hamiltonian
persistent electron current
, which provides a robust
, characterized by a maximal amplitude
at zero temperature5, 6. The flux-dependent energy levels are given by
, where
. The energy levels are discrete
and identified by angular momentum n and spin σ quantum numbers, with
for the two spin states, as shown in Figure S.8. This model
demonstrates
strong
spin-momentum-locking
property;
clockwise
(anticlockwise) states being polarized totally spin-up (respectively spin-down).
By sweeping the magnetic field (the magnetic flux) through zero, spin down
(right handed circulating) electrons acquire lower energy than spin up
electrons (left handed circulation) and spin flip takes place, accompanied with
current reversal. By further increasing field,
On the basis of this model the static susceptibility is given by formula
is calculated by the expression5:
, where the persistent current
(S. Eq. 2),
with
, and
the chemical potential.
Despite the simplicity of the model, a remarkable similarity between the
experimental data and the theoretical simulation is observed, as shown in
Figure 2.b. AC-susceptibility in the presence of a sinusoidal flux with
14
frequency ω can be calculated in terms of the static susceptibility, as the real
part of
.
15
REFERENCES
1.
Nisson DM, Dioguardi AP, Klavins P, Lin CH, Shirer K, Shockley AC, et al.
Nuclear magnetic resonance as a probe of electronic states of Bi2Se3. Phys.
Rev. B. 87, 195202 (2013).
2.
Abragam A. The Principles of Nuclear Magnetism. (Oxford University Press,
New York, USA, 1961).
3.
Young B-L, Lai Z-Y, Xu Z, Yang A, Gu GD, Pan ZH, et al. Probing the bulk
electronic states of Bi2Se3 using nuclear magnetic resonance. Phys. Rev. B.
86, 075137 (2012).
4.
Cliff G, Lorimer GW. The quantitative analysis of thin specimens. J. Microsc.
103, 203-207 (1975).
5.
Sticlet D, Dóra B, Cayssol J. Persistent currents in Dirac fermion rings. Phys.
Rev. B, 88, 205401 (2013).
6.
Sticlet D, Cayssol J. Dynamical response of dissipative helical edge states.
Phys. Rev. B. 90, 201303 (2014).
16