Magnetic Moment Enhancement for Mn7 Cluster on Graphene - The

Article pubs.acs.org/JPCC

Magnetic Moment Enhancement for Mn7 Cluster on Graphene Xiaojie Liu,†,‡ Cai-Zhuang Wang,*,‡ Hai-Qing Lin,*,† and Kai-Ming Ho‡ †

Beijing Computational Science Research Center, Beijing, 100084, P. R. China Ames LaboratoryU.S. Department of Energy, and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States

‡

ABSTRACT: Mn7 cluster on graphene with different structural motifs and magnetic orders are investigated systematically by first-principles calculations. The calculations show that Mn7 on graphene prefers a two-layer motif and exhibits a ferrimagnetic coupling. The magnetic moment of the Mn7 cluster increases from 5.0 μB at its freestanding state to about 6.0 μB upon adsorption on graphene. Mn7 cluster also induces about 0.3 μB of magnetic moment in the graphene layer, leading to an overall enhancement of 1.3 μB magnetic moment for Mn7 on graphene. Detail electron transfer and bonding analysis have been carried out to investigate the origin of the magnetic enhancement.

■

INTRODUCTION Among the transition metal elements, manganese (Mn) exhibits very interesting magnetic properties. While individual Mn atom has very high magnetic moment of 5.0 μB, there is no giant magnetic moment in bulk Mn because of the antiferromagnetic coupling in the crystalline phase. On the other hand, it has been shown that small Mn clusters exhibit giant magnetic moments depending on the size of the cluster.1−5 For example, the magic cluster of the pentagonal bipyramid Mn7 has a giant magnetic moment of 5.0 μB 1−5 due to the surface effects. Recently, there have been a lot of interest in growth of magnetic nanostructures on graphene for spintronics applications and growth of high density magnetic islands on graphene for magnetic nanomemories.6−13 For a better design of such graphene-based magnetic nanostructed device, it is highly desirable to understand how the structure and magnetic properties of the clusters will be affected by the graphene substrate. In this paper, using first-principle calculations, we systematically studied the structures and magnetic properties of Mn7 cluster on graphene. Various structural motifs and magnetic orders were investigated. The results show that Mn7 cluster on graphene prefers a two-layer motif and exhibits ferrimagnetic coupling with opposite magnetic moments in the two layers. The overall giant magnetic moment of the Mn7/graphene system is higher than that of a free-standing Mn7 cluster by about 26%.

calculation is 2.46 Å and agrees well with the experimental value. The 6 × 6 supercell ensures a large distance of about 15 Å for the separation between neighboring adatoms in the xy plane. The dimension of the supercell in the z direction is 15 Å which allows a vacuum region of about 12 Å. The firstprinciples calculations were performed based on the density functional theory (DFT) with generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE)14 and implemented in the Vienna ab initio simulation package (VASP)15−17 code, including spin polarization and dipole moment corrections.18 Valence electrons are treated explicitly, and their interactions with ionic cores are described by projector augmented wave (PAW)19,20 pseudopotentials. The wave functions are expanded in a plane wave basis set with an energy cutoff of 600 eV. A k-point sampling of 4 × 4 × 1 Monkhorst−Pack grids in the first Brillouin zone of the supercell and a Gaussian smearing with a width of σ = 0.05 eV are used in the calculations. All atoms in the supercell are allowed to relax until the forces on each atom are smaller than 0.01 eV/Å. The supercell dimensions are kept fixed during the relaxation.

■

■

CALCULATIONS METHODS The calculations were carried out using a 6 × 6 graphene supercell which contains 72 carbon atoms and 7 Mn atoms. The primitive cell of graphene lattice is a parallelogram with two carbon atoms. The lattice constant obtained from our © 2014 American Chemical Society

RESULTS AND DISCUSSION

The geometries of free-standing Mn7 cluster have been extensively studied.1−5 Among various isomers of Mn7 cluster, the decahedron structure with 1−5−1 stacking has been shown to be energetically much more favorable. This pentagonal bipyramid structure is also confirmed by the present DFT calculations to be the ground-state structure for a free-standing Received: May 2, 2014 Revised: July 15, 2014 Published: July 29, 2014 19123

dx.doi.org/10.1021/jp504329c | J. Phys. Chem. C 2014, 118, 19123−19128

The Journal of Physical Chemistry C

Article

Mn7. The magnetic moment of the decahedron Mn7 cluster is 5.0 μB from our present calculation, in agreement with previous studies.1−5 For Mn7 cluster on graphene, we optimized various structure motifs by DFT calculations including the effects of magnetic order in order to locate the lowest-energy configuration with correct magnetic structure. We found that the low-energy structures are those with the Mn7 decahedron cluster adsorbs on graphene. However, the energy and magnetic properties of the Mn7 decahedron cluster on graphene are sensitive to the orientation and contact position of the cluster relative to graphene. Figure 1 shows five typical

Figure 2. Optimal geometries of Mn7 clusters with different magnetic order on graphene. Relative energies (in unit of eV) with respect to the most stable structure and total net magnetic moments (in unit of μB) in parentheses are listed below each structure. Red color stands for spin-up state (positive magnetic moment), and blue color represents spin-down state (negative magnetic moment).

Figure 1. Five typical structural motifs of Mn7 clusters on graphene are presented. Relative energies (in unit of eV) with respect to the most stable structure and total net magnetic moments (in unit of μB) in parentheses are listed below each structure.

energy difference between the ferrimagnetic and ferromagnetic spin state is about 1.09 eV, as one can see from Figure 2f. The energies of other magnetic orders with respect to that of the lowest-energy one lay between 0.5 and 1.09 eV. It is interesting to note that Mn7 cluster on graphene exhibits a magnetic moment of 6.3 μB which is larger than 5.0 μB in an isolated Mn7 cluster by 26%. We examine the spin-polarized electron density distribution in Mn7 on graphene. Figure 3

structural motifs for Mn7 on graphene obtained from our calculations. Relative energies with respective to the most stable isomer and total net magnetic moment of the system are also presented below the structures. As one can see from Figure 1, a Mn7 decahedron with one of its triangular face laid on graphene as shown in Figure 1a is the most stable structure. Other isomers with one edge (Figure 1b) or one vertex (Figure 1c) of the decahedron cluster in contact with graphene are less stable by 0.61 and 0.71 eV, respectively, in energy. The lowest-energy structure has lower magnetic moment (6.3 μB) as compared to other structures. From Figure 1 one can also see that a twodimensional flake motif (Figure 1e) has the highest magnetic moment of 27.9 μB, but it is the least stable structure with energy higher than the ground-state structures (Figure 1a) by 2.62 eV. A two-layer A−B stacking motif in which four Mn atoms are in the first layer and three Mn atoms in the second layer as shown in Figure 1d also has energy higher by 1.04 eV in comparison with the ground-state structure, although this twolayer structure has relatively high magnetic moment of 17.1 μB. It has been shown that a free-standing Mn7 decahedron cluster exhibits a ferrimagnetic spin coupling, in which three Mn atoms exhibit spin-down state and other four Mn atoms have spin-up state, leading to a total magnetic moment of 5.0 μB.1−5 In order to see how graphene substrate affects the magnetic order of Mn7 on graphene, we take the lowest-energy structure of Mn7 on graphene shown in Figure 1a as an example to examine the energy differences between different magnetic structures in the cluster. The relative energy of the cluster with different magnetic orders from our calculations is shown in Figure 2. We found that when the Mn7 decahedron cluster adsorbs on graphene, the energetic favorable magnetic structure also exhibits ferrimagnetic coupling where three atoms in the layer close to graphene have the spin opposite to that of the other four atoms on the top layer as shown in Figure 2a. The

Figure 3. Spin-polarized electron density difference (i.e., Δρ(r) = ρup(r) − ρdown(r)). Red color indicates spin-up electron density, and blue color indicates spin-down electron density. (a) The most stable geometry of Mn7 cluster on graphene with Mn atom number labeled. (b) 3D spin-polarized Δρ(r) of Mn7 cluster on graphene. (c) 2D contour plot of spin-polarized Δρ(r) on the graphene layer. Dash triangle represents the position of the first three Mn atoms.

shows the three-dimensional (3D) isosurface and two-dimensional (2D) contour plots of the spin-polarized charge density distribution in the most stable isomers of Mn7 on graphene. From Figure 3, we can see that the magnetic moment is mainly from the Mn7 cluster. This result is consistent with the quasiatomic minimal basis orbitals (QUAMBO)21−23 analysis results as shown in Table 1 which will be discussed shortly. The total net magnetic moment from the Mn7 cluster is about 6.0 μB. In addition, Mn7 adsorption induces a magnet moment of 0.3 μB 19124



Article

Table 1. Charge Redistribution of Mn7 Cluster on Graphene (Value in Bold) in Comparison with Free-Standing Mn7 Cluster (Values in Parentheses)a Δq Mn-s Mn-1 Mn-2 Mn-3 Mn-4 Mn-5 Mn-6 Mn-7 Gra

↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓

0.34 0.47 0.26 0.48 0.26 0.48 0.64 0.44 0.66 0.45 0.64 0.44 0.66 0.47

μ

Mn-s

Mn-d

Gra-pz

−2.94 (−2.92)

−1.20 (−0.85)

1.01 (1.08)

0.19

−3.76 (−4.08)

−1.26 (−0.87)

0.84 (0.80)

0.42

−3.77 (−4.11)

−1.26 (−0.87)

0.82 (0.81)

0.44

4.30 (4.40)

−0.92 (−0.83)

0.72 (0.67)

0.20

3.85 (3.12)

−0.89 (−0.83)

0.84 (1.06)

0.05

4.32 (4.40)

−0.92 (−0.83)

0.71 (0.66)

0.21

4.08 (4.21)

−0.87 (−0.83)

0.85 (0.83)

0.02

Mn-d

(0.54) (0.61) (0.46) (0.67) (0.46) (0.67) (0.70) (0.47) (0.65) (0.52) (0.70) (0.47) (0.69) (0.48)

1.60 4.41 1.14 4.68 1.14 4.69 4.91 0.81 4.74 1.10 4.91 0.79 4.87 0.98

(1.61) (4.46) (0.96) (4.83) (0.95) (4.85) (4.92) (0.75) (4.53) (1.54) (4.92) (0.75) (4.91) (0.91)

0.38 (pz) 0.08 (Pz)

0.30

1.53

a The negative sign means the orbital loses electrons, while the positive sign means the orbital gains electrons for charge transfer Δq. The charge transfer is in the unit of electron. The negative sign indicated that spin-down states dominated for magnetic moment. The magnetic moment μ is given by μB. The up arrow suggested spin-up state, and the down arrow suggested spin-down state.

Figure 4. Atomic orbital energy levels of the Mn atoms and carbon atoms from the QUAMBO analysis: (a) an isolated Mn atom; (b) Mn atoms in free-standing Mn7 cluster; (c) pz orbitals of two different carbon atoms in the graphene, where one is right underneath the Mn7 and another is far away from the Mn7; (d) Mn atoms in Mn7 on graphene. The atomic orbital energy levels are defined as the diagonal matrix elements under the QUAMBO basis.

enhancement of magnetic moment in the Mn7/graphene system. In order to gain more insights into the origins of the enhanced magnetic moment and the microscopic bonding nature and interaction between Mn7 and graphene, we further performed quantitative analysis to study the electron transfer and bonding characteristics among the different orbitals of Mn atoms and between Mn and graphene, in comparison with those in a free-standing Mn7 cluster. We adopt the quasi-atomic minimal basis orbitals (QUAMBO)21−23 and Mulliken charge

in the graphene layer. Indeed as one can see for Figure 3c, the carbon atoms beneath the Mn cluster exhibit a noticeable magnetic moment. It is interesting to note that the magnetic moment induced by Mn7 cluster on graphene exhibits oscillatory behavior. There are spin-up states next to the Mn atoms and spin-down charge densities in the next shell, as one can see from the 2D contour plot. The integration of spinpolarized charge density on all carbon atoms is positive; therefore, the net magnetic moment contributes to the 19125



Article

first layer Mn atoms and the pz orbitals of the carbon atoms close to the cluster. These strong interactions lead to additional ∼0.4 electron transfer from the s orbital of the three first layer Mn atoms. These electrons are mostly transferred to the graphene. The electron transfer changes in the spin-up and spin-down electron occupations on each atom in the cluster according to Hund’s rules, resulting in reduction of magnetic moment on each atom from its atomic value of 5.0 μB. As one can see from Table 1, the main difference in the electron transfer in Mn7/graphene system as compared to that in the free-standing Mn7 cluster is the enhanced electron transfer in Mn-2, Mn-3, and Mn-5, which is consistent with larger changes in the magnetic moments in these atoms upon adsorption as discussed above. Since Mn-2 and Mn-3 are closely in contact with graphene, it is expected that the interaction with graphene can modify their electronic structures and lead to the larger change in their magnetic moment from their values in the freestanding cluster. It is interesting to note that the distance between Mn-5 and graphene is the largest, yet the influence of graphene on the electronic structure of Mn-5 is the strongest. This result indicates the interaction between graphene and Mn atoms in the cluster can be longer ranged, mediated by other Mn atoms in the cluster. We have also studied the spin-polarized density-of-states (DOS) from the QUAMBO analysis. Figure 5 shows the

analysis method to estimate the amount of electron transfer and to study the bonding properties. The QUAMBOs are constructed by a series of unitary transformations among the occupied bands and the complementary virtual bands obtained from the VASP calculations to maximize the similarity between QUAMBOs and the atomic orbitals. Hence, it transforms the electron Hamiltonian from a large plane-wave basis representation in the VASP calculations to a minimal-basis tight-binding representation in the truncated Hilbert space containing the occupied subspace without resorting to any fitting procedure. When this set of localized QUAMBOs is used as basis for electronic structure calculations, it reproduces exactly the occupied band structures and wave functions as those from the self-consistent plane-wave basis (i.e., VASP) calculations. Compared to other types of local orbitals used in quantum chemistry bonding analysis, the QUAMBOs should be more accurate and robust for chemical bonding and charge transfer analysis. More details about the QUAMBO method can be found in refs 21−23. The electron transfer among different atoms and different orbitals of the same atom from our QUAMBOs analysis is summarized in Table 1 for Mn7 on graphene in comparison with those in a free-standing Mn7 cluster (the number shown in the parentheses). The orbital energy levels of the Mn atoms in the forms of isolated atoms, free-standing Mn7 clusters, and Mn7 on graphene obtained from the QUAMBO analysis are also shown in Figure 4. The contribution to the enhancement of the magnetic moment mainly comes from three Mn atoms, i.e., Mn-2, Mn-3, and Mn-5. As one can see from Table 1, while Mn-2 and Mn-3 reduce the spin-down magnetic moment by about 0.66 μB, the spin-up magnetic moment of Mn-5 is increased by ∼0.63 μB. The other four Mn atoms reduce net spin-up magnetic moment by about 0.3 μB. Therefore, the net magnetic moment contribution from Mn7 clusters is 1.0 μB. Because graphene gains about 0.3 μB net spin-up magnetic moment due to Mn7 adsorption, the total magnetic moment of the Mn7/graphene system is enhanced by about 1.3 μB in comparison with that of the free-standing Mn7 cluster. The origin of the magnetic moment enhancement is electron redistribution upon Mn7 adsorption on graphene as shown in Figure 4 and Table 1. In Figue 4, the diagonal matrix elements under the QUAMBO basis are plotted which define the QUAMBO energy levels for different atomic orbitals at different situations (i.e., isolated atom, free-standing Mn7, and Mn7 on graphene). An isolated Mn atom has five 3d electrons and two 4s electrons. Each of the d electrons occupies one of the five d atomic orbitals and with the same spin polarization which yields the magnetic moment of 5.0 μB for an isolated Mn atom. The pair of 4s electrons have opposite spin and do not contribute to the magnetic moment. It is interesting to note that the energy levels of the s electrons in an isolated Mn atom are about 3 eV higher than that of the d orbitals as shown in Figure 4 a. Therefore, when the Mn7 cluster is formed, there is a substantial amount of s electrons (more than 0.8 electrons per atom) transfer to the d orbitals, as one can see from Table 1. The electron transfer is necessary to lower the total energy of the system. As one can see from Figure 4 b, the energy level of the s orbital in the cluster is much lower than that in the isolated atoms. Further electron transfer occurs upon adsorption of Mn7 on graphene because of the interaction of the Mn atoms with the carbon atoms in the graphene. As one can see from Figure 4c and Figure 4d, noticeable interactions are among the s orbitals and the dxz, dyz, and dz2 orbitals of the

Figure 5. Difference (i.e., D↑(ε) − D↓(ε)) between spin-up and spindown partial density of states (DOS) of Mn atoms and graphene from QUAMBOs analysis.

difference between spin-up and spin-down DOS (i.e., D↑(ε) − D↓(ε)) in s, p, d states in the graphene and the Mn7 clusters, respectively, in the energy window from 6 eV below the Fermi level to 3 eV above the Fermi level (Ef = 0 eV). From Figure 5 we can see that the electronic structures of graphene have been affected by the Mn7 adsorption. In isolated graphene, the difference between spin-up and spin-down DOS should be zero. However, in the Mn7/graphene system, oscillation in the spin-up and spin-down DOS difference can be clearly seen from Figure 5 which leads to the net magnetic moment of about 0.3 μB in the graphene layer. The local d valence states of the Mn atoms are below the Fermi level and interact with the pz orbital of the carbon atoms in graphene. From the DOS analysis, we can see that while the contribution to the magnetic moment in the graphene mainly comes from the pz orbitals, the dominate contribution to the magnetic moment in Mn7 clusters are the d states, as one can see from Figure 5. From Figure 5, we can also see that for Mn-1, Mn-2, and Mn-3 atoms (labeled in Figure 3a) in the first layer from graphene, the occupation of the spin19126



Article

to form a two-layer structure on graphene. Mn7 cluster on graphene exhibits a ferrimagnetic coupling with the opposite magnetization between the two layers. The magnetic moment has been enhanced from 5.0 to 6.3 μB for Mn7 cluster on graphene. The origin of the enhancement of the magnetic moment can be attributed to the electron redistribution due to the interaction with graphene.

down states is larger than that of spin-up states, leading to a large negative local magnetic moment. The magnetic moment obtained by integrating DOS for each of these Mn atoms gives −2.9 to −3.8 μB and agrees well with the results from the QUAMBO analysis listed in Table 1. On the other hand, for the other four Mn atoms in the second layer away from the graphene, the spin-up DOS is larger than the spin-down DOS (both of s and d sates) below the Fermi level, resulting in a large positive magnetic moment. The magnetic moment by integrating method is about 4.1 μB per atom which is also consistent with the QUAMBO analysis results shown in Table 1. From Figure 5 we can also see that the difference in the occupied spin polarized DOS is more pronounced in the energy window −4.5 to −1.5 eV. Therefore, the magnetic moment on the Mn atoms may not be easily detected by spin-polarized scanning tunneling microscopy (STM),24,25 which is usually operated at relatively lower bias voltage (e.g., 1−2 V). For example, as shown in Figure 6 where the spin-polarized

■

AUTHOR INFORMATION

Corresponding Authors

*C.-Z.W.: phone, 515-294-6934; e-mail, [email protected]. *H.-Q.L.: phone, 86-01-8268-7022; e-mail, [email protected]. cn. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Work at Ames Laboratory was supported by the U.S. Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering, including a grant of computer time at the National Energy Research Scientific Computing Centre (NERSC) in Berkeley, CA, under Contract DE-AC02-07CH11358. X.L. also acknowledges the support by the National Natural Science Foundation of China under Grant 11204013 and the China Postdoctoral Science Foundation under Grant 2013T60056.

■

REFERENCES

(1) Li, Y. L.; Tang, S. L.; Xie, R.; Wang, Y.; Yang, M.; Gao, J. L.; Xia, W. B.; Du, Y. W. Fabrication and Magnetic Properties of FreeStanding Ni Nanotube Arrays with Controllable Wall Thickness. Appl. Phys. Lett. 2012, 100, 052402(1)−052402(3). (2) Vo-Van, C.; Schumacher, S.; Coraux, J.; Sessi, V.; Fruchart, O.; Brookes, N. B.; Ohresser, P.; Michely, T. Magnetism of Cobalt Nanoclusters on Graphene on Iridium. Appl. Phys. Lett. 2011, 99, 142504(1)−142504(3). (3) Lim, D.-H.; Negreira, A. S.; Wilcox, J. DFT Studies on the Interaction of Defective Graphene-Supported Fe and Al Nanoparticles. J. Phys. Chem. C 2011, 115, 8961−8970. (4) Logsdail, A. J.; Akola, J. Interaction of Au16 Nanocluster with Defects in Supporting Graphite: A Density-Functional Study. J. Phys. Chem. C 2011, 115, 15240−15250. (5) Fampiou, I.; Ramasubramaniam, A. Binding of Pt Nanoclusters to Point Defects in Graphene: Adsorption, Morphology, and Electronic Structure. J. Phys. Chem. C 2012, 116, 6543−6555. (6) Kabir, M.; Mookerjee, A. Structure, Electronic Properties, and Magnetic Transition in Manganese Clusters. Phys. Rev. B 2006, 73, 224439(1)−224439(11). (7) Bobadova-Parvanova, P.; Jackson, K. A.; Srinivas, S.; Horoi, M. Emergence of Antiferromagnetic Ordering in Mn Clusters. Phys. Rev. A 2003, 67, 061202(1)−061202(4)(R). (8) López-Urías, F.; Diaz-Ortiz, A. Magnetism in Mn Clusters: Interplay between Spin Ordering and Structure. Phys. Rev. B 2003, 68, 132405(1)−132405(4). (9) Rao, B. K.; Jena, P. Giant Magnetic Moments of Nitrogen-Doped Mn Clutters and Their Relevance to Ferromagnetism in Mn-Doped GaN. Phys. Rev. Lett. 2002, 89, 185504(1)−185504(4). (10) Nayak, S. K.; Nooijen, M.; Jena, P. Isomerism and Novel Magnetic Order in Mn13 Cluster. J. Phys. Chem. A 1999, 103, 9853− 9856. (11) Evans, R. F. L.; Chantrell, R. W.; Nowak, U.; Lyberatos, A.; Richter, H.-J. Thermally Induced Error: Density Limit for Magnetic Data Storage. Appl. Phys. Lett. 2012, 100, 102402(1)−102402(3). (12) Tannous, C.; Ghaddar, A.; Gieraltowski, J. Nanowire Arrays, Surface Anisotropy, Magnetoelastic Effects and Spintronics. Appl. Phys. Lett. 2012, 100, 182401(1)−182401(4).

Figure 6. Spin-polarized electron density contours (the contour value is 0.04 electron/Å3) and simulated STM images for the energy window of −1.5 eV from the Fermi level. The STM images are simulated at a constant height of 1.5 Å from the top of the highest Mn atom.

electron contours and simulated STM images for the energy window −1.5 eV from the Fermi level are plotted, we can see that the three Mn atoms in the bottom layer (close to graphene) have more spin-up electrons while the other four Mn atoms on the top layer display more occupied spin-down states. These results are clearly opposite to the overall magnetic moments distribution in the Mn7 cluster where the bottom layer has net spin-down and top layer has net spin-up moments as discussed above. Therefore, if we use STM to measure the shallow spin-polarized states, we will get the wrong conclusion on the magnetic states of the atoms. On the other hand, the spin-polarized DOS at deeper energies from the Fermi level would be better detected by spin-polarized photoemission experiments.

■

CONCLUSION In summary, using first-principles calculations, we have systematically studied Mn7 cluster on graphene. The most stable isomers of Mn7 on graphene are the structures with triangular face of the pentagonal bipyramid motif on graphene 19127



Article

(13) Tudosa, I.; Lubarda, M. V.; Chan, K. T.; Escobar, M. A.; Lomakin, V.; Fullerton, E. E. Thermal Stability of Patterned Co/Pd Nanodot Arrays. Appl. Phys. Lett. 2012, 100, 102401(1)−102401(4). (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (15) Kresse, G.; Furthmüller, J. Efficiency of ab-Initio Total Energy Calculatios for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (16) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metlas. Phys. Rev. B 1993, 47, 558−561. (17) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for ab Inito Total-Enery Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (18) Makov, G.; Payne, M. C. Periodic Boundary Conditions in ab Initio Calculations. Phys. Rev. B 1995, 51, 4014−4022. (19) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979. (20) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Methods. Phys. Rev. B 1999, 59, 1758− 1775. (21) Chan, T. L.; Yao, Y. X.; Wang, C. Z.; Lu, W. C.; Li, J.; Qian, X. F.; Yip, S.; Ho, K. M. Highly Localized Quasiatomic Minimal Basis Orbitals for Mo from ab Initio Calculations. Phys. Rev. B 2007, 76, 205119(1)−205119(10). (22) Qian, X. F.; Li, J.; Qi, L.; Wang, C. Z.; Chan, T. L.; Yao, Y. X.; Ho, K. M.; Yip, S. Quasiatomic Orbitals for ab Initio Tight-Binding Analysis. Phys. Rev. B 2008, 78, 245112(1)−245112(22). (23) Yao, Y. X.; Wang, C. Z.; Ho, K. M. Chemical Bonding Analysis for Solid-State Systems Using Intrinsic Oriented Quasiatomic Minimal-Basis-Set Orbitals. Phys. Rev. B 2010, 81, 235119(1)− 235119(6). (24) Eelbo, T.; Waśniowska, M.; Thakur, P.; Gyamfi, M.; Sachs, B.; Wehling, T. O.; Forti, S.; Starke, U.; Tieg, C.; Lichtenstein, A. I.; Wiesendanger, R. Controllable Magnetic Doping of the Surface States of a Topological Insulator. Phys. Rev. Lett. 2013, 110, 126804(1)− 126804(5). (25) Kawahara, S. L.; Lagoute, J.; Repain, V.; Chacon, C.; Girard, Y.; Rousset, S.; Smogunov, A.; Barreteau, C. Large Magnetoresistance through a Single Molecule due to a Spin-Split Hybridized Orbital. Nano Lett. 2012, 12, 4558−4563.

19128


Magnetic Moment Enhancement for Mn7 Cluster on Graphene - The

Recommend Documents