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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