Manipulating Magnetism at Organic/Ferromagnetic Interfaces by. Molecule-Induced Surface Reconstruction

Transcription

1 Supporting Information of Manipulating Magnetism at Organic/Ferromagnetic Interfaces by Molecule-Induced Surface Reconstruction Rui Pang, 1,2 Xingqiang Shi 1, and Michel A. Van Hove 3 1Department of physics, South University of Science and Technology of China, Shenzhen , China 2School of Physics and Engineering, Zhengzhou University, Henan , China 3Institute of Computational and Theoretical Studies and Department of Physics, Hong Kong Baptist University, Hong Kong, China * shixq@sustc.edu.cn Contents: 1. Geometric and Magnetic Structure Determination 2. Calculating Surface Vacancy Formation Energies: Placing the Atom at Surface Kinked-Step Sites 3. Details of Magnetocrystalline Anisotropic Energy (MAE) partition 4. Comparing of PDOS of C 60 on 5-layer-slab and 9-layer-slab 5. Validity of PBE 6. Error estimation of charge transfer 7. Discussion about the thermal stability 8. Discussion about the spin polarization 9. Structural Data of Unreconstructed and Reconstructed surfaces S1

2 1. Geometric and Magnetic Structure Determination Geometric Structure Determination. As shown in Fig. S1, the Ni (111) surface has four kinds of symmetrical adsorption sites and C 60 can show three different symmetrical bonding arrangements on this surface depending on its orientation. Our strategy is to try to calculate all these combinations. However, some of the previously published investigations can be used as references to simplify our structural search. As is reported in Ref [S1] C 60 is oriented on Cu (111) with a hexagonal face upward (and thus also the opposite hexagonal face downward). As fcc Ni (111) and fcc Cu(111) have similar lattice constants and structures, we can thus limit our search to case (b) in Fig. S1. In fact, various studies also suggest that hexagonal face binding is the most stable for C 60 on fcc(111) surfaces; for details, see Ref. 32 in the main text and references therein. Figure S1. (a) High-symmetry adsorption sites on the fcc Ni(111) surface with 3- and 2-fold rotational symmetries; (b), (c) and (d) high-symmetry sites on the C 60 adsorbate of 3-, 5- and 2-fold symmetry, corresponding to bonding to the surface with the hexagonal face, the pentagonal face and the 6-6 edge, respectively. For the unreconstructed substrate configuration, different adsorption sites are considered, including C 60 on atop, hollow (hcp and fcc), and bridge sites. At each site, different orientations of the molecule were considered, and geometries with a hexagonal face pointing down are found to be energetically better than other orientations, which agrees with the observed three-fold symmetry in experiments for C 60 on different fcc(111) surfaces[s2]. For the reconstructed configuration due to C 60 adsorption on fcc(111) metal surfaces, only reconstructions with one-atom holes and seven-atom holes were reported[s2]. Three-atom-hole reconstruction was excluded in Ref [S3]. A two-atom-hole is ineffective to form more C-Ni bonds to S2

3 compensate for the energy cost of a larger vacancy. Most other kinds of reconstructions do not fit the symmetry of the Ni (111) surface. Thus only one-atom-hole and seven-atom-hole reconstructions are considered. The results are list in Table S1. Table S1. Adsorption energies corrected for vacancy formation energies Eads + Evac (in ev). For Evac, numbers without (with) parentheses are calculated for missing atoms placed in surface kinked-step sites (placed in bulk sites) Unreconstructed Reconstructed 1-hole 7-hole Eads Evac (0.98) 3.45 (3.04) Eads + Evac (-2.07) (-3.82) Magnetic Structure Determination. We also considered different magnetic configurations. We considered ferromagnetic and antiferromagnetic coupling between C 60 and the substrate with combinations of different starting magnetization. The results listed in the main text are the most favored energetically. 2. Calculating surface vacancy formation energies: putting the missing atom at the surface kinked-step sites Figure S2. (a), (b) and (c) structures of the clean unreconstructed surface, 1-hole and 7-hole reconstruction configurations, resp.; (d) initial structure of the kinked-step model; (e) kinked-step model with one nickel atom added. S3

4 The vacancy formation energy is calculated in the following way. First we calculate the energies of structures shown in Fig. S2: E Ni(unrec) for the clean unreconstructed surface (a) and E Ni(rec) for the reconstruction (b) or (c), with 1-or 7-atom holes, respectively. Then we calculate the energies of (d) and (e), corresponding to taking an atom removed from the surface and placing it at a kinked-step site, the absolute value of the difference is called E Ni(atom). The vacancy formation energy is now calculated as E vac = E Ni(unrec) - E Ni(rec) +n E Ni(atom). Note: The vacancy formation energies calculated from different models, i.e. placing missing Ni atoms at kinked-step sites vs placing them at bulk sites, give the same preference for the adsorption geometry (see Table S1). 3. Details of MAE partition Second order perturbation theory is used to partition the MAE of a supercell onto each atom. Only the contribution from d orbitals is considered, which is also adopted in Ref. [S4]. H SO In second-order perturbation, E SO = =λl S o, u u λl S o ε o o ε λl u S u The labels o and u denote occupied and unoccupied states, resp. indices, these states can be expressed as: o ( u ) = ak (3) where a is the band index, k the wave vector and the spin index. (1) (2) Explicitly writing out the Approximating the atomic orbitals as complete orthogonal sets and using them by expanding the Kohn-Sham states, one gets in which φ ak ak ( r ) C = φ ( r ) Rnlm Rnlm Rnlmk ik T φ r ) = A e φ ( r R T ) (5) Rnlmk ( Rnlm Rnlm T where φ (r ) is the local atomic orbital centered on the atom at position R in the unit cell with Rnlm orbital index n,l,m. R is the inner cell position vector corresponding to R and T is the translation vector between different unit cells. A is the renormalization factor. Rnlm (4) Applying the operator L S to equation (4), the operator will act on the atomic orbital φ (r ). Rnlm S4

5 Here we only focus on 3d electrons, thus the indices can be simplified as φ = φ φ L (6) Rnlm RL = R Here L and φ R are the angular and radial parts of an atomic orbital, respectively, is the spin-dependent part of the Kohn Sham orbital to be expanded. Using the orthogonality hypothesis, the spin orbital energy can be rewritten as E SO = D = 2 λ R, R R LL L L e RR ) unocc occ ( ( C ka RL * ) C ε ka R L R a a k L, L, L, L, ka ( C ε ka R L ka * ) C ka RL (7) with D = L L S L L L S L (8) L L L L Thus, the MAE can be decomposed as the sum of a series of pair interactions e RR. The contribution of each atom to the total MAE can be calculated as 1 R R e RR + ( err + e 2 R R R ). C can be obtained from an ab initio code such as Quantum Espresso. DLL L L can be kn RL calculated by using the ladder operator. Thus the onsite spin-orbit interaction energy can be expressed as being proportional to λ 2 with a known coefficient. If one has the total MAE of the system, λ 2 can be determined by equation (7). With this parameter one can calculate the onsite MAE. In our calculation, λ=0.07ev, consistent with values in Ref [S4] of 0.09 and 0.08 ev. 4. Comparing the PDOS of C 60 on 5- vs. 9-layer slabs S5

6 Figure S3. PDOS of C 60 on reconstructed Ni layers of different thicknesses. The 9-layer-slab calculation contains a dipole correction. These curves show that thickness and dipole correction do not change the final result significantly in the energy range we are interested in. 5. Validity of PBE We have several reasons to trust PBE. First, in our PBE calculation, the magnetic moment of the middle layer (the 5th layer in the 9 layer model) is about 0.62 µb, which is quite close to the experimental value of µb (For experiment, see Table 12.5 in Ref [S5].) As DFT+U usually enlarge the magnetic moment, the PBE+U will not probably improve this datum. Therefore, DFT+U for pure metallic Ni is unnecessary. What about the surface nickel atoms which couple to the fullerene? There is no direct experiment evidence about this system. However, in one of our previous paper on C 60 /Fe (100), we found that even a quite small U (Ueff = 2eV) will lead to overestimation of the magnetic moment of Fe that coupled to C. In contrary, PBE without U coincides with the XMCD experiment (for detailed discussions, see Ref [S6]). And in another paper about Co surface coupled to C 60, PBE also satisfyingly explained the experiment results on magnetocrystalline anisotropy (Ref [S7]). Considering the high similarity between Fe, Co, and Ni, we think comparing to PBE+U, PBE is more capable in describing C 60 /Ni (111). Besides, for 3d-metal substrates interacting with aromatic molecules, the validity of PBE is checked by a serial works of PBE combined with STM (Ref [S8]). The reason why DFT+U does not improve the results should be due to that the molecule/metal interface system is metallic. There is no band gap problem to be fixed so that GGA is enough. Because DFT+U does not improve the result, for the similar reason, we think hybrid functional could improve the result quite little, too. And the computational cost of hybrid functional is too high for our large C 60 /ferromagnetic metal systems. In conclusion, based on the published data and our experiences, PBE can well describe our S6

7 system, and DFT+U and hybrid functional should not give better results for our system. 6. Error estimation of charge transfer There seems no objective ways to assign the charge in a chemical bond into the individual atoms involved. According to some benchmark investigations (Ref [S9], for example), the Bader charge yields successful correlations to some quantities observable (pka, in that paper), demonstrating its rationality. The only error in Bader charge comes from the real-space grid densityfor the Bader charge integration. As was showed in a recent paper (Ref [S10]), in the grid spacing of about 0.06 Å (which is used in our calculation, corresponding 10 million grids in Ref [S10]), the error is about electron for NaCl within one unit cell. Considering the charge transfer occurs in a 16-atom surface in our system, our error should be less than *16=0.06 electrons for the total charge transfer. 7. Discussion about the thermal stability The spin splitting in organic/ferromagnetic metal interfaces is more robust against temperature than that in single-molecule magnets. There are three characteristic temperatures above which the magnetism on C 60 may be destroyed. The first is the phase transition temperature of the substrate, which is about 600K for Nickel. The second is the binding energy of C 60 to the substrate, which is 3.41 ev corresponding to 105 K. The last is the magnetic coupling between the molecule and the substrate. From the coupling, a flipping energy of 8 mev corresponding 80 K is estimated. Thus, 80K could be the temperature that the spin filtering phenomenon can persist. The other properties such as exchange coupling and MAE are usually believed to be stable in the range of zero to room temperature. 8. Discussion about the spin polarization Some investigations found that in some 3d magnetic metal surface, the spin polarization cannot be directly interpreted by the band structure calculations; the reason is due to the scattering provided by the localized d bands around the Fermi level (Ref [S11]). First, we want to emphasize that the polarization of C dominates the transport properties in our system. Because with the adsorption of C 60, the molecular orbital localized at the C 60 equator is about three Angstrom higher than the surface, so in an STM experiment the signal on C 60 should be detected. And for C, there is no localized d state, so the polarization shall be consistent directly with the first-principles calculation. As an illustration, paper (Ref [S12]] finds that the experimental spin polarization is consistent with the DOS of graphene. We believe that the same condition happens in C 60 /Ni (111), also. The reconstruction reduces the positive spin polarization of the outermost Ni atoms; and the hybridization of s and p electrons in Ni with d electrons competes with the hybridization of p electrons in C with d electrons. First, as can be seen in Figure 3 in our main text, the PDOS of minority spin d bands are significantly reduced at the Fermi level in the reconstructed structure. Thus S7

8 the scattering from minority spin d electrons is weakened compared to the clean one; and the hybridization of s and p electrons in Ni with d electrons will be reduced, also. Thus the conductance of the minority spin will get enhanced. Second, if we plot the PDOS of s and p in Ni, we find that with the adsorption and reconstruction, the s and p electronic PDOS in Ni move away from the Fermi level (see Figure S4). This is because that the more p electrons in C hybridize with d electrons, the less s and p electrons in Ni do. And the dominating effect that results in the spin-polarized molecular orbitals comes from the hybridization of carbon p and nickel d electrons. The evidence can be seen from Figures 2(a) and 3(a) in our main text. Because the reconstruction only increase the number of C-Ni bonds and this enhance the p-d hybridization at the C 60 /Ni (111) interface. The hybridization between Ni electrons has no other factor that can influent. So, around Fermi level, the difference between Rec and Unrec can be viewed as a net effect of p-d hybridization. (a) (b) Figure S4. (a) PDOS of p electrons in Ni of reconstructed and clean surfaces; (b) PDOS of s electrons in Ni of reconstructed and clean surfaces. References: [S1] W. W. Pai, C. L. Hsu, M. C. Lin, K. C. Lin, and T. B. Tang, Phys. Rev. B 69, (2004) [S2] X.-Q. Shi, M. A. Van Hove, and R.-Q. Zhang, J. Mater. Sci. 47, 7341 (2012) [S3] L. Tang, X. Zhang, Q. Guo, Y.-N. Wu, L.-L. Wang, and H.-P. Cheng, Phys. Rev. B (2010) [S4] Electronic Structure and Physical Properties of Solids, Hugues Dreyssé (Ed.), 2000, Springer [S5] Magnetism: From Fundamentals to Nanoscale Dynamics, Joachim Stöhr, Hans Christoph Siegmann, 2006, Springer [S6] Yang, Zhen-Hua, Rui Pang, and Xing-Qiang Shi., J. Phys. Chem. C , 119 (2015) [S7] Bairagi, K., et al. Phys. Rev. Lett. 114, (2015) [S8] Atodiresei, Nicolae, et al., Phys. Rev. Lett. 105, (2010); Brede, Jens, et al., Phys. Rev. Lett.105, (2010); Lennartz, M. C., et al., Phys. Rev. Lett.105, (2010) [S9] Gross K C, Seybold P G, Hadad C M, Int. J. Quantum. Chem. 90, (2002) [S10] Tang, W., E. Sanville, and G. Henkelman. J. Phys.: Condens. Matter (2009) [S11] Kim, T. H., & Moodera, J. S., Phys. Rev. B 69, (2004); Hertz, J. A., & Aoi, K., Phys. Rev. B S8

9 8, 3252(1973) [S12] Sun, X., Entani, S., Yamauchi, Y., Pratt, A., & Kurahashi, M. J. Appl. Phys., 114, (2013) 9. Structure data (all in Å) 2D Ni(111)-4x4 cell vectors: Optimized atomic coordinates in XYZ format (Z perpendicular to the surface) 1) Reconstructed structure: C C C C C C C C C C C C C C C C C C C C C C C C C C S9

10 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni S10

11 Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni S11

12 Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni ) Unreconstructed structure: C C C C C C C C C C C C C C C C C C C C C S12

13 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C Ni Ni Ni Ni Ni S13

14 Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni S14

15 Ni Ni Ni Ni Ni Ni Ni Ni E Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni S15