Strong Facet-Induced and Light-Controlled Room-Temperature. Ferromagnetism in Semiconducting β-fesi 2 Nanocubes

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1 Supporting Information for Manuscript Strong Facet-Induced and Light-Controlled Room-Temperature Ferromagnetism in Semiconducting β-fesi 2 Nanocubes Zhiqiang He, Shijie Xiong, Shuyi Wu, Xiaobin Zhu, Ming Meng, and Xinglong Wu * Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Collaborative Innovation Center of Advanced Microstructures, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing , P. R. China Figure S1. Diagrammatic illustration of the chemical vapor deposition apparatus showing that a shorter and smaller diameter quartz tube with a diameter of 2.5 cm (tube 1) is placed in the 6 cm diameter quartz tube (tube 2). S1

2 Figure S2. EDX spectrum obtained from a β-fesi 2 nanocube. The C and Cu elements are from the Cu grid substrate which is used for measuring the EDX spectrum. Details pertaining to the growth process and mechanism of β-fesi 2 nanocubes. To investigate the growth process of the β-fesi 2 nanocubes, the FE-SEM images acquired from the samples at different time during the reaction are shown in Figure S3. Figure S3a shows the beginning of nucleation in the first 30 min. After 45 min, a three-dimensional structure with six protuberances is formed as shown in Figure S3b. The six protuberances may evolve into two {100} top facets and four {011} lateral facets. After 1 h, a three-dimensional octahedral structure begins to take shape (Figure S3c). The eight crystal facets are the {101} facets and {110} facets and have higher growth rate than others, resulting in formation of nanocubes after 90 min (Figure S3d). The crystal surface becomes smoother and the nanocube grows bigger afterwards as shown in Figure S3e. In the case when the carrier gas flow rate is constant at 100 SCCM, the reaction temperature is found to be crucial (Figures S4 and S5). The optimal synthesis S2

3 conditions for the β-fesi 2 nanocubes are attained at a downstream heating temperature of 800 o C (Hung, S. W. et al., J. Mater. Chem. 2011, 21, 5704). Figure S4a shows the products at 750 o C. The sheet structures and small cubic particles coexist on the Si substrate. including ε-fesi and β-fesi 2. The XRD pattern in Figure S4c shows two phases The small particles possess the shape of a cube corresponding to β-fesi 2 and it is reasonable that the sheet structures are ε-fesi. Figure S4b shows the nanowires and cubic particles on the Si substrate at 850 o C and the XRD pattern in Figure S4d also reveals the two phases of ε-fesi and β-fesi 2. The cubic particles are clearly observed and almost the same as those obtained under the optimal conditions corresponding to β-fesi 2. So the nanowires should be ε-fesi. As shown in Figure S5 in Supporting Information, when the temperature of the downstream heating zone is set at 725 and 900 o C, pure phase ε-fesi microsheets and nanowires are obtained (Hung, S. W. et al., J. Phys. Chem. C 2011, 115, 15592). It is noted that Fe 3 Si nanooctahedrons form directly at 650 o C, as shown in Figure S5a. Figure S3. Schematic illustration and SEM images of the β-fesi 2 nanocube at different times during the reaction: (a) 30, (b) 45, (c) 60, (d) 90, and (e) 120 min. S3

4 Figure S4. (a) and (b) SEM images of the synthesized products found at the downstream zone at 750 and 850 o C, respectively. Insets: higher magnification image of the regions shown in boxes in (a) and (b). (c) and (d) XRD patterns corresponding to (a) and (b). Black and red (hkl) indices belong to the diffraction peaks of β-fesi 2 and ε-fesi phases, respectively. S4

5 Figure S5. Morphology of the products formed at different temperature: (a) 675 o C, Fe 3 Si nanooctahedrons with inset showing the magnified image of a single nanooctahedron. (b) XRD pattern confirming that the nanooctahedrons have the Fe 3 Si phase. (c) 725 o C, ε-fesi microsheets with the inset showing the magnified image of several microsheets. (d) XRD pattern confirming that the sheets have the ε-fesi phase. (e) 900 o C, ε-fesi nanowires with the inset showing the high-resolution image revealing that the growth direction is along [110]. (f) XRD pattern showing that the nanowires have the ε-fesi phase. S5

6 Figure S6. (a,b) Topography and MFM images of the oxidized β-fesi 2 nanocubes. (c,d) Topography and MFM images of the as-made (pristine) β-fesi 2 nanocubes deposited with a 10 nm thin layer of Au, taken after exposure to dry air for weeks. First-principles calculation: First-principles calculation is performed using the generalized gradient approximation (GGA) of the Perdew, Burke, and Ernzerholf (PBE) form (Perdew, J. P. et al., Phys. Rev. Lett. 1996, 77, 3865) under package CASTEP (Clark, S. J. et al., Zeitschrift fuer Kristallographie 2005, 220, 567) in which a plane-wave norm-conserving pseudopotential method (Hamann, D. R. et al., Phys. Rev. Lett. 1979, 43, 1494) is adopted. A kinetic energy cutoff of 600 ev is used to represent the single-particle wave functions. The calculation is conducted on two slabs with Fe atoms exposed on the surfaces normal to the {011} and {100} directions and having thicknesses 1.42 and 0.95 nm, respectively. S6 To form a periodic structure for the band

7 calculation, the same slabs are repeated along the normal direction and separated with vacuum slabs of thickness 1.0 nm. The geometry of the configurations is optimized using the BFGS minimizer in the CASTEP package with default convergence tolerances: 2 x 10-5 ev for the energy change, 0.05 ev/å for the maximum force, and Å for the maximum displacement (Pfrommer, B. G. et al., J. Comput. Phys. 1997, 131, 233). In the self-consistent (SC) calculation of the electronic properties, the spin configurations are optimized in every 6 SC steps. To take into account the strong correlation effects on the Fe atoms, the GGA+U scheme (Dudarev, S. L. et al., Phys. Rev. B 1998, 57, 1505) is adopted with U = 2.5 ev for the Fe 3d states. Figures S7a and S7b show the structure of the {011} and {100} slabs, respectively, with the non-zero Mulliken spins of atoms in units of µ B marked on the atoms. The Fe atoms on the surfaces have large magnetic moments which are in the ferromagnetic phase. To investigate the energy distribution of the spin states of the surface Fe atoms, Figure S8 plots the local density of spin states of the surface Fe atoms in the {100} slab. The occupied itinerant band at the Fermi level has a down spin, but the majority of the electrons in the occupied bands contributing to the local moments have an up spin. S7

8 Figure S7. Structure of (a) {011} and (b) {100} β-fesi 2 slabs with the non-zero Mulliken spins of atoms in units of µ B marked on the atoms. The intersections of the purple and yellow bonds represent Fe and Si atoms, respectively. The Fe atoms on the surfaces of the slabs have large magnetic moments which are in ferromagnetic phase. Calculated temperature and size dependence of magnetization: In the Hamiltonian expressed in Eq. (3) of the main text, the sum of k is over the states in the itinerant continuum, including the Fe dangling bonds created by the S8

9 surfaces and by vacancies near the surfaces. An electron with a spin σ experiences a repulsive interaction I on a site occupied by another electron with opposite spin σ. In the mean-field treatment, this repulsion is described by an effective potential λi n σ in the Hamiltonian. Spin σ of the electron feels an effective magnetic field h, expressed with the Zeeman term µ σ. The effective B h field includes the external field h 0 and the internal field produced by the local moments. With the classical treatment, the internal field is proportional to the average projection of local moments to the direction of external field as expressed by JS cosθ. The average number of electrons of spin σ per site at temperature T is nσ = f ( E σµ Bh + λi n σ, T ) ρ( E) de ( S1) where ρ(e) is the density of states of the itinerant electrons per site, and 1 f ( E, T ) = exp[( E E ) / k T ] + 1. is the Fermi-Dirac distribution factor with E F being the Fermi energy. The edge effect of facets with a size d influences the area of width w, and can be estimated as F B 4 w( d w) λ 1. (S2) 2 d The average direction cosine <cosθ> of local moments can be approximately calculated as cos θ = dxx exp{ Sx[ h J µ ( n n )] / k T} 0 0 B dx exp{ Sx[ h J µ ( n n )] / k T} B B B. (S3) From Eqs. (S1) and (S3), one can solve n σ and cosθ. The average magnetization per atom is S9

10 M 0 = S cos θ + µ B ( n n ). (S4) One can convert the magnetization per atom in Eq. (S3) to the magnetization per unit mass as M = νm o /m o, where m o is the total mass of a cell containing one Fe atom and ν is the fraction of volume influenced by the magnetization. In vacancy-rich layers beneath the surfaces, the vacancy-induced dangling bonds of Fe ions are merged into the itinerant continuum of the surfaces. So the continuum should have a finite thickness η, rather than a single layer at the surface. Thus the fraction ν can be estimated as 3 d 2η ν = 1 d. (S5) The parameters are fitted from the experiment. By comparing the calculated curves in Figure 8 with the experimental data, we can fit out that J = 0.45 ev/µ 2 B, I = 2.5 ev, w = 50 nm and ν = 0.2. According to the first-principles calculation shown in Figure S7, we determine the density of states ρ ( E) and the magnetic moment on a Fe atom as S = 3 µ B. S10

11 Figure S8. Local density of spin states of the surface Fe atoms in the (100) slab. The green circle indicates the area of the gap where the detailed density of spin states is given in Figure 7. The occupied itinerant band at the Fermi level has a down spin but the majority of the electrons in the occupied bands contributing to the local moments have an up spin. S11

12 Figure S9. Main panel: Plot of transformed Kubelka-Munk function versus the photo energy of the β-fesi 2 nanocubes on Si substrate. The dotted line is used to determine the direct band gap. Inset: UV-visible diffusive reflectance curves of the β-fesi 2 nanocubes on Si substrate. To estimate the band gap E gap, (αhν) 2 is plotted as a function of the photon energy in Fig. S9. The linear behavior of the absorption spectrum suggests a direct optical gap. Extrapolating the linear fit to α = 0, we can find that E gap = 0.79 ev, which is consistent with the band gap determined for β-fesi 2 (He, J. Y. et al., RSC Adv. 2012, 2, S12